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Metallic part fabrication wiht selective inhibition sintering (SIS) based on microscopic mechanical inhibition

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Metallic part fabrication wiht selective inhibition sintering (SIS) based on microscopic mechanical inhibition

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METALLIC PART FABRICATION WITH SELECTIVE
INHIBITION SINTERING (SIS) BASED ON MICROSCOPIC
MECHANICAL INHIBITION

by

Mahdi Yoozbashizadeh

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(Industrial and Systems Engineering)

December 2012

i

Acknowledgments
I would like to thank my advisor, Professor Behrokh Khoshnevis, for giving me the
opportunity to work on the Selective Inhibition Sintering project. His insight, directions
and guidance were very crucial to the success of this project
I would also like to thank Professor Yong Chen who became involved in the later
stages of this project and offered his insight and support.
I would also like to acknowledge my father, Professor Hossein Yoozbashizadeh
who helped me at various stages of this project.

ii

Abstract
The Selective Inhibition Sintering (SIS) process is an additive manufacturing (AM)
technology which builds parts on a layer-by-layer basis. The principle idea of the SIS
process is based on the prevention of selected segments of each powder layer from
sintering. The purpose of this research is to investigate the fundamentals of the Selective
Inhibition Sintering (SIS) process for the fabrication of metallic parts. A SIS-Metal process
has been developed based on the microscopic mechanical inhibition principle. In this
process the inhibitor, which is a salt solution or a carbohydrate solution (sucrose), is
printed in the selected areas of each metal powder layer; the salt re-crystallizes when water
evaporates under moderate heat; salt crystals decompose to second phase metal oxide
during the sintering cycle; the decomposed solid particles cover the surface of affected
metal powder particles and exert a retarding force on the surface movement and prevent
the sintering. This thesis presents the results of the conducted research on the inhibition
mechanism and control of the SIS process. Experimental results are also presented to
demonstrate the capability of the process in fabricating metallic parts with various
geometries. The SIS-Metal process has numerous advantages including low cost, minimal
shrinkage and deformation effects and independence from polymeric binders which cause
shrinkage and adverse effect on sintering furnace. The factors affecting the SIS-Metal
process based on microscopic mechanical inhibition are investigated. By the aid of
response surface methodology the effective factors are evaluated to improve the part
strength, surface quality and dimensional accuracy of the parts made with the SIS-Metal
process.

iii

Table of Contents
Acknowledgments ii
Abstract iii
List of Tables vii
List of Figures ix
Chapter One: Introduction 1
1.1. Introduction to AM 1
1.2. Introduction to SIS 2
Chapter Two: Fundamentals of Selective Inhibition of Sintering 5
2.1. Selective Inhibition Sintering (SIS) 5
2.2. Research Focus 6
2.3. Research Objectives 6
2.4. Research Contributions 7
Chapter Three: Background of AM of Metallic Parts and the SIS
Methodology 8
3.1. Review of Existing AM Methods 8
3.2. The SIS Method 11
3.2.1. SIS for Polymer 12
3.2.2. SIS for Metallic Parts Based on Macroscopic Inhibition 13
3.2.3. SIS for Metallic Parts Based on Microscopic Inhibition 14
3.3. Current Metallic Part Fabrication Processes 16
3.4. Advantages of the SIS-Metal 17
3.5. Section Summary 20

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Chapter Four: Research Methodology 21
4.1. Research Plan and Procedure 22
4.2. Major Stages of the Procedure 22
4.3. Research Methodology 23
4.3.1. Analytical Approach 24
4.3.2. Experimental Approach 25
4.3.3. Developmental Approach 26
Chapter Five: Preliminary Experiment 28
5.1. Preliminary Experiment for Loose Powder Sintering and Retardation
from Sintering 28
5.2. SIS Machine Fabrication 29
5.3. Material Selection and Part Fabrication 36
Chapter Six: Loose Powder Sintering 44
6.1.Sintering Mechanism 44
6.1.1. Solid Phase Sintering 47
6.1.2. Stages in Sintering 49
6.1.3. Loose Powder Sintering for Bronze 50
6.1.3.1. Design of Experiment Settings for Loose Powder Sintering 51
6.1.3.2. Micro-Tensile Test for Loose Powder Sintering 76
6.1.3.2.1. Design of Experiment for Tensile Test 82
Chapter Seven: Sintering Inhibition 84
7.1. Introduction and Prior Studies 84
7.2. The Inhibition Mechanism by Dispersion of Second Phase Metal Oxides 87

v

7.3. SIS Process with Dispersed Carbon Particles as Inhibitor 96
7.3.1. Design of Experiment for the Inhibition Mechanism 102
7.3.2. Micro-Tensile Test for the Printed Sections 113
Chapter Eight: Effect of Droplet on Powder bed 117
8.1. Droplet Properties 117
8.2. Droplet Penetration on Powder Bed 119
Chapter Nine: Conclusion and Future Work 128
9.1. Future Work 129
Bibliography 132
Appendix A: The DOE Results 136
Appendix B: XRD Settings 170

vii

List of Tables
3.1. Summary of disadvantage and advantage of AM systems for metal 11
5.1 Properties of the inhibitor 38
5.2 Properties of alloyed bronze 51
6.1 Coded values for design parameters T1, t1, T2 and t2 52
6.2 Full Factorial design table 53
6.3 Estimated Effects and coefficients for shrinkage 56
6.4 Estimated Effects and Coefficients for Hardness 57
6.5 Mechanical property and sintering rate for pure bronze sintered at different
Temperature and duration 60
6.6 ANOVA table for linear regression for shrinkage 64
6.7 ANOVA table for linear regression for hardness 66
6.8 ANOVA table for linear regression for porosity 67
6.9 ANOVA table for linear regression for X/D 68
6.10 ANOVA table for exponential model for Shrinkage 72
6.11 ANOVA table for exponential model for Hardness 73
6.12 ANOVA table for exponential model for Hardness Vs. Shrinkage 74
6.13 ANOVA table for the regression model for yield strength 82
7.1 Mechanical properties of the printed sections with Sucrose after sintering 103
7.2 ANOVA table for linear regression model for shrinkage for printed sections 106
7.3 ANOVA table for the exponential fitted model for the printed sections for
shrinkage 107
7.4 ANOVA table for the exponential fitted model for the printed sections for

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hardness 109
7.5 ANOVA table for the linear regression model for the printed sections for
Hardness 110

ix

List of Figures
2.1. A Copper part fabricated based on macroscopic mechanical inhibition 5
3.1. SLS process 8
3.2. FDM process 9
3.3. 3DP process 9
3.4. LPF.LENS process 10
3.5. CAM-LEM process 11
3.6. Sample parts made with polymer through the microscopic inhibition 13
3.7. Sample copper part made with ceramic inhibitor through the macroscopic
Inhibition process 14
3.8. A classification of the metallic part fabrication processes 19
4.1. Major stages in the SIS process 24
4.2. Research methodology 27
5.1. Alumina-Silica ceramic blocks used for preliminary sintering tests 28
5.2. Loose powder sintering path for bronze 29
5.3. The CAD model of the SIS machine 30
5.4. Stages in the SIS metallic fabrication based on Microscopic inhibition 31
5.5. Temperature measurement during the heating of every layer 32
5.6. The SIS metal machine 33
5.7. Heater in the SIS machine which is used for drying the inhibitor 33
5.8. The printer head for printing the inhibitor 34
5.9. Inhibitor container and the air pressured container 34
5.10. Controller boards which are used for controlling the stepper motors

x

for the X,Y and Z axis 34
5.11. Build tank in the SIS machine 35
5.12. The SIS software interface for automatic control of the machine by
the input path file 35
5.13. The SIS software interface for manual control of the SIS machine 35
5.14. The sintering furnace initially used in the SIS process 39
5.15. Sintering cycle for bronze 39
5.16. Sample 2.5 D parts made by the SIS process 40
5.17. 3D model designed and sliced to be built by the SIS machine 41
5.18. Tool path planning for different slices in an specific 3D model 41
5.19. A fabricated 3-D part (left) and the inhibited sections (right) 41
5.20. A 3D model designed and sliced to be built by the SIS machine 42
5.21. A fabricated 3-D part (left) and the inhibited sections (right) 42
5.22. 3D parts made by the SIS process 42
6.1. Theoretical model of two spherical particles with a diameter of D
Sintered with a neck diameter of X 45
6.2. Two classes of mass transport mechanism for sintering 48
6.3. A sample bronze on a ceramic plate being sintered in a furnace at a
Temperature of 775 C 51
6.4. Block sample used in the SIS loose powder sintering process improvement 52
6.5. Sintering cycle for loose powder sintering for Bronze 5890 52
6.6. The setup for the hardness test used in the experiments 54
6.7. Normal plot of the factors affecting shrinkage in the full factorial design 54

xi

6.8. Pareto chart of the factors affecting shrinkage in the full factorial design 55
6.9. Main effect plot for shrinkage 55
6.10. Contour plot for the effect of time2 and temperature2 on shrinkage 57
6.11. Normal plot of the factors affecting hardness in the full factorial design 58
6.12. Pareto chart of the factors affecting hardness in the full factorial design 58
6.13. Contour plot for the effect of time2 and temperature2 on hardness 59
6.14. Main effect plot for hardness 59
6.15. X/D ratio for different sintering parameters 61
6.16. Regression model for shrinkage for pure bronze 63
6.17. Residual plot for linear regression model for shrinkage 64
6.18. The effect of Temp2 and time2 on hardness 65
6.19. Surface hardness for pure bronze 65
6.20. Contour plot for hardness Vs. temperature and time 66
6.21. Contour plot of porosity Vs. temperature and time 67
6.22. Contour plot of X/D ratio Vs. temperature and time 69
6.23. Increase of sintering rate with time in pure bronze 69
6.24. Pore closure and grain boundary formation in bronze 810 C-1Hr 70
6.25. Line plot effect of sintering time and temperature on mechanical
property and sintering rate 71
6.26. Exponential fitted model for shrinkage 72
6.27. Exponential fitted model for hardness and porosity 73
6.28. Relation between surface hardness and shrinkage 75
6.29. Dimensions for the micro-tensile test used in the stress-strain diagram 76

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6.30. Tensile test system 77
6.31. Tensile test result from a sample sintered at 770 C-0Hr 78
6.32. Tensile test result from a sample sintered at 770 C-1Hr 79
6.33. Tensile test result from a sample sintered at 770 C-2Hr 80
6.34. The effect of sintering time on the stress-strain diagram 81
6.35. The effect of sintering time on the stress-strain diagram 81
6.36. Regression model for yield strength Vs. Shrinkage 82
6.37. Effect of time and temperature on the yield strength 83
7.1. Geometry of a particle pinned to an advancing surface 85
7.2. Expansion of decomposed Aluminum Sulfate 88
7.3. The SEM micrograph of different samples: (Left): a metal powder particle
Before sintering; (right): a metal powder particle that is coated with ceramic 90
7.4. Distribution of different elements in the printed sections with aluminum
sulfate after sintering 91
7.5. The SEM micrograph of a sintered sample with printed aluminum sulfate
And the related EDS analysis result 92
7.6. SEM micrograph of printed sections with aluminum sulfate before
and after sintering 93
7.7. Retardation from sintering by ZrO
2
93
7.8. The SEM micrograph of a sintered sample with printed
Zirconium-Sulfate and the related EDS analysis result 94
7.9. The SEM micrograph of a sintered sample with printed
Zirconium-Sulfate and the related EDS analysis result 94

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7.10. Retardation from sintering by MgO 95
7.11. The SEM micrograph of a sintered sample with printed
Magnesium-Sulfate and the related EDS analysis result 95
7.12. SEM micrograph of printed and non-printed sections with sucrose 96
7.13. Distribution of different elements in the printed sections with aluminum
sulfate after sintering 97
7.14. EDS analysis of the printed sections with sucrose 97
7.15. EDS point analysis on small carbon particles pinned to the Surface of
bronze 98
7.16. X-Ray diffractometer used in the SIS analysis 99
7.17. XRD diagram of printed sections with aluminum sulfate after sintering 99
7.18. XRD diagram of pure bronze after sintering (Non-printed sections) 100
7.19. XRD diagram of printed sections with sucrose after sintering 100
7.20. Surface hardness comparison between different inhibitors 102
7.21. Printed sample used in the mechanical property test 102
7.22. Neck growth for printed sections in different temperature and
time settings during the sintering process 104
7.23. Contour plot of shrinkage for the printed sections Vs. Temperature and time 106
7.24. Fitted exponential curve for shrinkage in printed sections 107
7.25. Plot of Shrinkage between the printed and non-printed sections 108
7.26. Plot of Shrinkage difference between the printed and non-printed sections 109
7.27. Exponential fit for hardness in the printed sections 110
7.28. Contour plot of hardness on printed sections Vs. Temperature and time 111

xiv

7.29. Plot of hardness for printed and non-printed sections 111
7.30. Plot of hardness difference between the printed and non-printed sections 112
7.31. Micro-Tensile test for printed sections sintered at 810 C for 2 hours 113
7.32. Micro-Tensile test for printed sections sintered at 810 C for 1 hour 114
7.33. Micro-Tensile test for printed sections sintered at 810 C for 0 hour 114
7.34. Micro-Tensile test for printed sections sintered at 770 C for 2 hours 115
7.35. Micro-Tensile test for printed sections sintered at 770 C for 0 hour 115
7.36. Sample parts built by the SIS machine using the inhibitor as a binder
Sintered at 810 C for a duration of 2 Hour in a vacuum sintering environment 116
8.1. Droplet size per pulse duration for the Solenoid valve 118
8.2. Velocity of the droplet after the nozzle head 118
8.3. The cutting effect of printed lines in the powder bed 121
8.4. The printing of the inhibitor with different settings of the nozzle 122
8.5. Line formation during the SIS process 123
8.6. Line formation during the SIS process 123
8.7 SEM micrograph of a sample droplet formation and its related measurements 124
8.8 A porous part that was made by the SIS process 125
8.9 Pore measurement of the porous part 125
8.10. Separation between the printed and non-printed sections of metal powder 126
8.11. A sample made by the SIS process with the optimized printer settings 127
9.1. Initial and final stage sintering for titanium 129
9.2. Printed Aluminum Sulfate and Sucrose on titanium powder bed before
Sintering 129

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9.3. Decomposed aluminum sulfate and sucrose on titanium powder after
Sintering 130
9.4. Two sample Titanium parts that was used for testing 130
9.5. Loose powder sintered 440C stainless Steel and diffused alloy Steel 130
9.6. Initial and intermediate stage sintering for 440C 131

1

Chapter One: Introduction
1.1. Introduction to AM
There are three types of fabrication methods: 1-fabrication by subtraction like in
milling machine, 2-fabrication by forming like in forging and 3- fabrication by adding
material like in casting and the more recent digital additive manufacturing approach.
Additive Manufacturing (AM) or Solid Free Form Fabrication (SFF) is based on building
physical parts from CAD data. The methods in all AM processes are the same in that they
add and bond materials layer by layer to form a 3D part.
All AM processes follow four major steps in fabrication:
1. A three dimensional model of the physical part is modeled in a 3D CAD
environment software such as Solid Works, Mechanical Desktop etc. and the model
is saved as a 3D CAD output file.
2. The CAD output file is sliced in one direction.
3. The physical model is fabricated layer by layer.
4. Different treatments and operations may be performed on the final part to improve
the surface quality and mechanical property.
There are advantages and disadvantages of AM compared to traditional manufacturing
processes such as milling and forming. The disadvantages are poor surface finish, poor
material mechanical property, low precision and low fabrication speed. The advantages are
low setup time, not needing mold, minimum or no material waste and the ability to build
complex geometries. In certain conditions these advantages render the AM processes more
favorable than traditional manufacturing processes. Several AM techniques such as Stereo
Lithography (SLA), Laser Powder Forming (LPF), Selective Laser Sintering (SLS), Fused

2

Deposition Modeling (FDM) and Three Dimensional Printing (3DP) are available in the
field. Each of these technologies has its own strengths and weaknesses which will be
discussed in more details in Chapter Three. The limitation of current techniques such as
limited range of applicable materials, poor material property, high cost of material, high
cost of machine and low dimensional accuracy motivates the development of better AM
methods.
1.2. Introduction to SIS
The S e lec ti ve I nhibi ti on S int e ring (S I S ) pr oc e ss i s a n a ddit ive manuf a c tur ing (A M)
tec hnolog y whi c h buil ds pa rts on a la y e r -by- la y e r ba sis . The pr inciple i de a of the S I S pr oc e ss is pr e ve nti on of se lec ted se g ments of e a c h powde r la y e r fr om sint e ring . Th e re for e , the S I S proc e ss m a y b e c onsi de re d a s an opposi te a pproa c h to t he S e lec ti ve L a se r S int e rin g (S L S ) pr oc e ss in whic h se lec ted a r e a s of powde r a re sint e re d b y a fine lase r be a m. The re se a rc h wor k fo r S I S f or pol y mer powd e r [ Khoshne vis et al , 2003; Asia ba npour et al ., 2004; Asia ba npou r et al ., 2006] de mons tra ted that the S I S - P ol y mer pr o c e ss c a n fa br ic a te hig h qu a li t y p a rts a t a hig h spe e d usin g re lativ e l y lo w c ost m a c hines . Due to the hi g h tempe ra tur e a nd ox y ge n - fr e e e nvi ronme nt re quire d in sint e rin g of meta ll ic powde rs (e . g . 800- 1300C ) the pre viou sl y de v e loped S I S - P ol y m e r pr o c e ss i n whic h e a c h la y e r is si nter e d on the fa br ica ti on ma c h ine is not a ppli c a ble to the S I S- Meta l pr oc e ss. He nc e , the S I S -
Meta l pr oc e ss re quir e s a de dic a ted e f for t for i de nti f y in g n e w inhi bit ion a nd sint e rin g mec ha nism s b y c onsi de r ing the sint e rin g pr ope rties of meta l powde r a n d ne w sint e rin g
re g im e n , pr e f e ra bl y using c onve nti ona l sint e ri ng fur n a c e . E x pe rimen tal re sult s ha ve de mons tra ted that the S I S - Meta l c onc e pt is fe a sibl e a nd that c omm e rc ial qua li t y m e talli c pa rts c a n b e f a b ric a ted us ing thi s pr oc e ss.

3

The inhi bit ion mec ha nism used in the S I S pr oc e s s pla y s a major role in s uc c e ssfull y de ve lopi ng the p roc e ss [ Khoshne vis et al , 200 3] . The re a r e fou r po ssi ble inhi bit io n mec ha nism s in S I S w hich will be de sc ribe d in more de tail s in C ha pter T wo: (1 ) macroscopic mechanical inhibition ; (2) microscopic mechanical inhibition ; (3) chemical
inhibition ; a nd (4) thermal inhibition . Due to th e hig h sint e rin g tempe ra ture of meta ll ic
powde rs , a ppl y in g ther m a l inhi bit ion to the S I S - Meta l pr oc e ss is dif fic ult . C onseq ue ntl y ,
the re mainin g thr e e in hibi ti on mec ha nism s ha ve be e n tried for m e ta l powde rs. Th e inhi bit ion methods investi g a ted a r e : (1) the use of a c e ra mi c ba rr ie r a s a macroscopic
mechanical inhibitor, (2) a ppli c a ti on of sulfur ic a c id a nd h y dr o ge n pe rox ide a s chemical
inhibitors , a nd (3) a ppli c a ti on of S uc rose a nd a lu mi num sulfa te a s microscopic mechanical
inhibitors whic h is t he f oc us of this r e se a rc h .
The e x pe rimen tation of th e macroscopic mechanical inhibition a pproa c h ha s be e n
li mi ted to a fe w ba sic trials [ B . Khoshne vis a nd M. Moj de h 2006] . How e ve r , the e x pe rimen ts support the fe a sibi li t y a nd me rit of the a pproa c h, whic h c a n be fu rthe r de ve loped if a n a c c ur a te a nd ve rsa ti le c e r a mi c pri nti ng method be c om e s a va il a ble.
S e ve ra l suc c e ssful e x pe r im e nts ha ve a lso be e n p e rf or med using c he mi c a l inhi bit ion. This method of inhi b it io n is li mi ted be c a use the re late d c he mi c a l re a c ti ons a re of ten slow
a nd man y d e sira ble met a ls a nd a ll o y s (e . g . sup e r a ll o y powd e rs) a re r e sis tant to c he mi c a l
re a c ti on. F u rthe rmor e , man y c he mi c a ls that a r e used to e tch or ox idi z e met a ls a lso c or rod e the meta ll ic c omponents of the pr int ing me c ha nis ms a n d other mac hine c o mponents. Also c he mi c a ls c ould be i rr it a ti ng a nd/or h a rmf ul to li ving or ga nism s a nd he nc e pr e se nt s a fe t y a nd e nvironmen tal c on c e rns.

4

Based on the above observations and further reasons it has been decided that the
most promising inhibition method for SIS-Metal process is microscopic mechanical
inhibition. Through this research a microscopic mechanical inhibition theory has been
established which encompasses the selection method of inhibitors and the inhibition
behavior in the presence of metal powders prior and during the sintering process.
Furthermore, the loose powder sintering process and the effect of sintering parameters on
the mechanical property of the parts are investigated.

5

Chapter Two: Fundamentals of Selective Inhibition of Sintering
2.1: Selective Inhibition Sintering (SIS)
The main idea of the SIS process is the prevention of selected segments of each powder
layer from sintering. In the SIS process the particles are joined through the sintering
process. The sections that need to be prevented from sintering may be inhibited by the
following methods:
1. Macroscopic mechanical inhibition: The inhibitor physically divides regions of as a
barrier wall and separates the powder particles to such an extent that they are no
longer in sufficient proximity to bond to each other during sintering.

F ig u re 2 .1. A c opp e r pa rt f a br ic a ted ba se d on th e mac rosc opic m e c ha nic a l inhi bit ion
( S ourc e : M. Moj de h 2005)

2. Microscopic mechanical inhibition: In this method droplets of the inhibitor
penetrate the metal powder (due to capillary force) layer without disturbing the
surface and spread through the voids between the powder particles. During the
sintering process the decomposed inhibitor particles coats the surface of the particle
and prevents bonding during sintering.

6

3. Chemical inhibition: Droplets of the inhibitor penetrate the powder layer without
disturbing the surface and spread through the voids between the powder particles.
The inhibitor reacts with the powder particles at their surface and produces a
chemical compound that is resistant to sintering.
4. Thermal inhibition: In this method the droplets of the inhibitor lay on top of the
powder. The inhibitor prevents heat from reaching the powder bed and thus
prevents bonding the printed section.
2.2: Research Focus
In this research the focus is on building metallic parts using microscopic mechanical
inhibition.
The advantages of SIS compared to other approaches such as Selective Laser
Sintering (SLS), 3D Printing (3DP), Fused Deposition Modeling (FDM), Direct Metal
Laser Sintering (DMLS), Laser Engineered Net Shaping (LENS) and Electron Beam
Melting (EBM) are not using binder, the sintering approach and the simplicity of the
process which results in less expensive machines. These features will be explained more in
details in Chapter Three.
2.3 Research Objectives
The objectives of this research are to identify the process characteristics and
elements including appropriate metal powder choice and effective inhibitor choice by
devising a systematic methodology. The underlying principle for loose powder sintering
and the inhibition mechanism is studied. Next, the basic parameters of the process are
identified. These parameters affect the effectiveness of inhibition, ease of separation of
inhibited regions after sintering, p re c isi on (p a rt’ s dim e nsion a nd surf a c e quality) and

7

mechanical properties (hardness, yield strength, etc.). A systematic methodology is then
needed to identify the preferred values of the process parameters in order to obtain the best
possible results.
2.4 Research Contributions:
This research has made the following contributions:
1. An experimental and a theoretical methodology for selecting the metal powder and
the corresponding inhibitor have been developed.
2. The underlying process of microscopic sintering inhibition is investigated.
3. The loose powder sintering process factors optimization procedure for the SIS
process is established.
4. By using response surface methodology (RSM) the impacts of the effective control
parameters have been investigated and the control factors have been optimized and
formulized to measure the effect of changes on the mechanical properties of the
final parts.
5. The effect of inhibitor droplets on powder bed is studied to improve the printing
quality.
6. The effect of loose powder sintering and inhibition on mechanical property of the
parts has been examined and several empirical models have been developed.

8

Chapter Three: Background of AM of Metallic Parts and the
SIS Methodology
In this section a review of the existing methods for building metallic parts is presented
and the methods are compared. The SIS process is then described in more detail.
3.1 Review of Existing AM Methods
As mentioned in chapter one there are several AM methods for metals that are
commercialized and being used. The most well-known ones are:
SLS (Selective Laser Sintering): In this technology thermoplastic powder is used to
build the model. One layer of thermoplastic powder is spread on top of the previous layer
and a laser beam is used for sintering. DMLS (Direct Metal Laser Sintering) has the same
concept of SLS except that instead of the thermoplastic powder Metal powder is used. The
powder used in DMLS is a mixture of two different kinds of metal powder. One metal has
a low melting point which is used to sinter and bond by the laser beam and the other metal
with a high melting point. The process is shown in figure 3.1.

Figure 3.1. SLS process
FDM (Fused Deposition Modeling): The FDM process builds metallic parts via a
mixture of binder and metal powder that is made into a filament [Greul et al. 1995]. The
filament is fed through a heated extrusion nozzle and deposited to form the layers. After

9

layer fabrication, the green part consists of binder (polymer and waxes) and metal powder.
The binder is removed in an oven and the porous metal is sintered to final density (95-
98%).

Figure 3.2. FDM process for plastic
3DP (Three Dimensional Printing): 3D printing starts by depositing a layer of powder
object material at the top of the previous layer. After the powder is spread a multi-channel
nozzle deposits a liquid adhesive onto the layer of the powder which becomes bonded in
the areas where the adhesive is deposited, to form a layer of the object. After printing all
the layers, the platform comes up and the loose powder is vacuumed away. The green part
is then transferred to a sintering furnace where the adhesive burns away and the green part
is sintered in the furnace.

Figure 3.4. 3DP process
EBM (Electron beam melting): In this process one layer of metal powder is spread on
top of the previous layer. An accelerated electron beam hits certain parts that need to be

10

bonded. The kinetic energy of the electron beam raises the temperature of the powder
resulting in sintering in that section.
LPF (Laser Powder shaping) or Laser Engineered Net Shaping (LENS): In this
technology laser is used to melt metal powder supplied coaxially to the focus of the laser
beam through a nozzle.

Figure 3.4. LPF/LENS process
CAM-LEM: every cross section is cut out of a metal sheet. The actual model is defined
by laminating and assembling the metal sheets on top of each other. The laminated "green"
object is then fired and removed to give the final unified 3D physical model. The steps for
the CAM-LEM process are shown in Figure 3.5.

Figure 3.5. CAM-LEM process
The advantages and disadvantages of all of the aforementioned processes are listed in
table 1.1:

11

Table1.1. Summary of disadvantage and advantages of AM systems for metal (Source: M.
Mojdeh 2004)
process
Mechanical
property
Dimension
accuracy
Complex
geometry
Range of
material
Cost of
fabrication
Special
fabrication needs
SLS/DMLS poor good Complex
Limited to
special alloys
high
Binder removal
and special
handling
3D printing poor poor Complex
Limited to
special alloys
and non
reactive metals
Moderate
Binder removal
and careful
handling
FDM Very poor
Low due
to the high
shrinkage
Moderate
(Not for
high
resolution )
Very limited high
Support material
removal, Binder
removal
EBM poor poor Complex Limited
High due
to the high
technology
none
LPF/LENS
Good

Very low Low high low none
DMLS poor Poor Complex
Limited to
special alloys
high
Hard to control
the uniform
density,
CAM-LEM poor poor Simple
Limited to
special alloys
High due
to demand
Robot assembly
etc.

There are several disadvantages in each of these processes which have been listed.
These disadvantages motivate the development of other AM techniques.
3.2 The SIS Method
Selective Inhibition of Sintering (SIS) is a new AM method invented and patented
by Dr. Behrokh Khoshnevis. In this method which is a layer by layer manufacturing
pr oc e ss t he powd e r pa rticle s ar e joi ne d a nd si nter e d in t he pa rt’ s bod y a nd inhi bit e d fr om
sint e ring in t he pa rt’ s boundary.

12

3.2.1 SIS for Polymer
The first implementation of the SIS idea was for polymeric materials (B. Asiabanpour
2004). In this process thermoplastic polymer powder was used. Inhibition was done by a
chemical salt (Potassium Iodide) .The SIS for polymer is a four stage fabrication process.
The stages are as follows:
1. A thin layer of powder polymer is spread uniformly on top of the previous layer
2. The sections and the boundaries of the model cross section that will be inhibited
from sintering are printed by the inhibitor.
3. A heat preventive frame is put on the outer side of the building envelope to prevent
the outside parts from sintering
4. The entire layer is heated by a heater to sinter and join the particles in the unprinted
sections.
Stages 1-4 are repeated for each of the layers until all the layers in the physical model
are completely built. After all the layers are built, the prototype is dipped in water were the
salt dissolves in water and the final part is separated from the printed sections.
High precision, fast fabrication, high accuracy and low price are the advantages of this
process. Due to the nature of polymer compared to metallic parts, the final parts by the
SIS-polymer have a poor material property such as low strength.
Figure 3.6. Sample parts made with polymer through the microscopic inhibition process
(Source: B. Asiabanpour 2004)

13

3.2.2 SIS for Metallic Parts Based on Macroscopic Inhibition and Compaction:
This method was invented after the SIS for polymer (B. Khoshnevis and M. Mojdeh
2005). Since sintering metal parts requires high temperature sintering is done in a neutral
environment (Oxygen free) to prevent any oxidization in high temperature. This SIS
process for metallic parts has the following stages:
1. An extrusion nozzle delivers a paste inhibitor material through a fine orifice to
create the layer boundary in form of a physical wall with height equal to the layer
height.
2. A layer of metal powder is spread on top of the layer which contains the deposited
inhibition material.
3. The boundary of the layer is printed by an adhesive to enable moving the whole
model to the furnace.
4. As an option, the new layer is compacted by a press mechanism.
Stages 1-4 are repeated until all the layers are built and the whole model is delivered to
the furnace for sintering.
The method has the following disadvantages:
1- Since this is a macroscopic inhibition there is less precision in geometry because of
the significantly wider separation gap at the layer boundary.
2- After completion of sintering removal of the inhibitor material from the final part
could be cumbersome for complicated geometries.
Furthermore, with respect to the compaction process (which is optional) the following
pitfalls exist:

14

1- Because of layer by layer compaction, lower layers could get more compacted and
this distorts the final part geometry
3- Due to the creation of very smooth top surface after each compaction inter-layer
adhesion could be weak for certain metals because of poor sintering of powders on
the inter layer surfaces.

3.2.3. SIS for Metallic Parts Based on Microscopic Inhibition:
The SIS-Metal process based on the microscopic mechanical inhibition is described as
follows:
(1) Printing sintering inhibitor: A deposition nozzle with a fine orifice, or an inkjet
print head, is used to deliver sintering inhibitor solution to the selected areas (i.e.,
layer profile) of the powder layer. The layer is dried before continuing with the
subsequent layer. Given the small amount of water in the printed solution, the
drying time is relatively small. A small infrared lamp or a heating filament may be
used for drying.
Figure 3.7. Simple copper part made with ceramic inhibitor through the
macroscopic inhibition process (Source: M. Mojdeh 2004)

15

(2) Laying thin powder layer: Metal powder is spread as a thin layer over the build
tank.
(3) Creation of a boundary to contain part: The inhibitor liquid is deposited on the
powder bed at the periphery of the part profile. Dried inhibitor creates a mechanical
interlock and consolidates the boundary. The profile of this deposition may be a
simple shape such as square or circle. When all layers are completed, these
depositions create a solid container around the 3D part. Using this container the
completed green part can be removed from the machine and transferred to the
sintering furnace. It is a fortunate phenomenon that the inhibitor can as well be
used to consolidate the desired boundary.
(4) Heating and compression: A heater is used to evaporate water/alcohol in the
inhibitor first; an optional motorized press equipped with a pressure sensor
compacts the newly spread metal powder layer to create a powder bed with the
specified density. In this research the compaction option is not used.
(5) Bulk sintering in an oven: After all layers have been completed, the metal powder
block is extracted from the build tank and placed in a conventional sintering oven.
After sintering and cooling, the sintered block is removed from the oven. Due to
the effect of the inhibitor on sintering, the part can be extracted from un-sintered
sections.
(6) Post recessing: Sand blasting or bead blasting is used to remove the printed
sections from the part.

16

3.3 Current Metallic Part Fabrication Processes
Manufacturing complex parts with conventional casting method is expensive,
inaccurate, and may require advanced machinery and incurs significant material waste.
Powder metallurgy is a process for forming metal parts by heating compacted metal
powders to just below their melting points (German 1998). This process can fabricate
semi-dense and fully dense products using several different technologies, including
pressing and sintering, injection molding, and hot isostatic pressing, and forging. The
capability to produce near-net shape components with tight dimensional tolerances at
modest temperatures provides powder metallurgy a distinct advantage over metal forming
techniques such as forging and casting. However, tooling construction for the process is
costly and time consuming especially for small quantities or parts with complex geometry.
The usage of molds also limits the complexity of part geometries that can be fabricated by
the powder metallurgy processes.
Layered fabrication techniques offer some important advantages over the
conventional powder metallurgy process. For small order quantities, layered techniques are
faster and less expensive because they do not require machining a mold from block
material. Layered techniques are also capable of manufacturing parts with more complex
features because the powder is laid and shaped in a sequence of thin layers. There is no
need to force the mixture into fine structures within the mold during a bulk filling
operation.
As discussed earlier current major layered fabrication methods for building metallic
parts include SLS, 3D printing, FDM, DMLS, LENS, and EBM. These processes may be
divided into two classes: with use of binders and without use of binders.

17

1. With the use of binders: this class includes SLS, 3D printing, and FDM.
2. Without the use of binders: this class includes DMLS, LENS, and EBM.
Layered metal fabrication methods may also be classified into two other classes: bulk
metal sintering and layer metal sintering.
1. Bulk metal sintering: this class includes SLS, 3D printing, and FDM. In bulk
sintering, no metal powder sintering is performed in the building machine. The green
part is transferred to a sintering oven after its geometry is formed by a mold or some
binders. The main advantages of the bulk sintering are (1) the machine is
significantly simplified since no heating element or environmental control would be
needed; (2) it also results in minimal part deformations due to the sintering of the
entire part at once.
2. Layer metal sintering: this class includes DMLS, LENS, EBM. In layer sintering,
powders are sintered into predefined geometry layer by layer. Generally a laser or an
electric beam is required to provide sufficient power in the process. Due to the high
temperature involved in the process, a controlled atmosphere chamber is required to
avoid oxidation of powder during sintering. The parts generated by layer sintering
are generally anisotropic with weaker mechanical strength in the Z direction than in
X and Y directions.
3.4 Advantages of SIS-Metal
Metallic parts fabrication based on metal casting and powder metallurgy (P/M)
[Kalpakjian and Schmid, 2006] requires tooling construction. However, the construction of
such tooling can be expensive and time consuming, especially for small quantities of parts

18

or parts with complex geometry. In comparison, additive manufacturing (AM) processes
can be much faster and less expensive for such small lot or complex part fabrication.
All the AM processes for building metallic parts can be classified based on the usage
of binders and the sintering approach as shown in Figure 3.8.
(i) Usage of binders: Some AM processes such as SLS, 3DP, and FDM utilize certain
binders in the fabrication of green parts. For example, the SLS process uses
polymer-coated metal powder [Wohlert, et al. 1996; Pease 1998]; the 3DP process
deposits droplets of liquid acrylic copolymer binder onto a bed of metal powder
[Sachs, et al., 2000; Pease 1998]; and the FDM process uses filaments that are
made by a mixture of binder and metal powder [Greul et al. 1995]. The binders in
the fabricated green parts can then be removed in a thermal debinding step. In
comparison, AM processes such as DMLS, LENS, and EBM can directly sinter
metal powders layer-by-layer using high-power energy sources. For example, the
DMLS process can directly sinter metal powder without using polymer coating
[Simchi, et al. 2001; Kotila, et al. 2001; Behrendt and Shellabear, 1995]. The
LENS process directly produces metal parts from metal powder injected by a
powder delivery nozzle [Atwood, et al. 1998]. The EBM process can also directly
melt metal powder in a controlled atmosphere chamber using an electron beam.
(ii) Sintering approach: Based on how metal powders are sintered into finished
metallic parts, AM processes can also be classified into bulk sintering and layer
sintering. In the AM processes based on bulk sintering of metal powders (e.g. SLS,
3DP, and FDM), green parts are fabricated first and are then transferred to a
sintering oven. In comparison, in the AM processes based on layer sintering of

19

metal powders (e.g. DMLS, LENS, and EBM), powders are sintered into the
predefined geometry layer by layer. As discussed before, bulk sintering can have
advantages such as lower hardware cost, reduced deformation and higher building
speed.

F ig u re 3.8 . A c lassific a ti on of the me talli c pa rt f a br ica ti on pr oc e sses
Based on such a classification the SIS-Metal process is uniquely positioned among
all the metallic part fabrication processes because it is a layered fabrication process which
is based on the bulk sintering approach without using any binder. As shown in Figure 3.8,
the SIS-Metal process is classified in the same category as the traditional powder
metallurgy process. However, as no tools are required, the SIS-Metal process may be
regarded as a moldless powder metallurgy process.
The SIS-Metal process has the following advantages.
 The hardware of the SIS-Metal process can be inexpensive. A green part can be
fabricated using a print head to deposit the inhibitor solution to powder layers; the
green parts can then be sintered in a conventional sintering oven, which is widely
available in a typical powder metallurgy manufacturing facility.
Usage of
binders
Sintering
approach
Without the
use of binders
With the use of
binders
Bulk
sintering
Layer
sintering
SIS-Metal
SLS
3D-printing
FDM
DMLS
LENS
EBM
Powder
metallurgy
Require tooling
Additive process

20

 The SIS-Metal process is potentially fast. The inhibitor can be deposited using a multi-
jet print head, which has proven performance and impressive speed in other
applications such as two-dimensional (2D) printing. The printing time can be further
reduced using a vector (instead of a raster) printer, because in most cases the inhibitor
needs to be deposited as a thin line only along the boundary of each layer profile.
 The SIS-Metal process can have less shrinkage and deformation since no de-binding is
involved.
 Unlike LENS or DMLS, no complex supports are required in the SIS-Metal process
since overhang features are supported by powder volumes underneath.
 Since there is no need for binder burn out, much less void space exists between the
metal particles prior to sintering. Therefore the SIS process will produce parts that
experience less shrinkage during sintering.
In summary the SIS-Metal process has the advantages of both layered fabrication and
powder metallurgy processes. These characteristics make SIS well aligned with current
intense interest productivity, energy conservation and reduction of material waste.
3.5 Section Summary
The above sections have provided a comprehensive survey of previous AM systems
for building metallic parts and an explanation of the SIS concept for metallic parts.
The focus of this research is on the microscopic inhibition option. By this method with the
right material and equipment several desirable features may be achieved including: high
resolution, complex geometry, wide range of metal powders, low cost for fabrication, high
speed of fabrication and no need for binders which these features make this process unique
in comparison with current processes.

21

Chapter Four: Research methodology
The basic elements in the SIS-Metal which are the metal powder and the inhibitor
need to be characterized. Metal powder is characterized by metal type, grain size, grain
shape and material property such as hardness, yield strength and density. The inhibitor is
characterized by molecular mass weight (which is related to the penetration of inhibitor in
the metal powder), decomposition temperature, melting temperature, expansion of salt
crystal during sintering, solubility, surface tension of the inhibitor solution and the
decomposed particles of the inhibitor at high temperatures.
After specifying the basic elements of the process the next stage is to find the
reason behind the sintering inhibition phenomenon. Different hypotheses have been
proposed which will be discussed in Chapter Seven.
The next stage of the process is to define and control all important parameters in
the process. These parameters affect the precision (part dimension and surface quality) and
mechanical properties (hardness, yield strength, ductility and ultimate tensile strength). For
measuring the effect of these parameters which are responsible for surface quality and
mechanical properties of the final part a systematic methodology is needed to identify the
preferred values of the process parameters which yield the best possible results.
The parameters that affect the part precision (part dimension and surface properties)
and mechanical properties (strength and hardness) are: inhibitor type, metal type, printing
process characteristics, sintering path ( sintering time and progression of sintering
temperature), heating rate and layer thickness. The effects of these parameters have been
studied using response surface methodology.
This research will involve the following activities:

22

1. Development of an experimental and a theoretical methodology for selecting the
metal powder and the inhibitor in order to identify the appropriate material choices.
This is explained more in the next section.
2. Fabrication of a SIS machine in order to check the feasibility of the SIS method
using the selected metal powder and the inhibitor.
3. Investigation of the effect of control parameters using response surface
methodology (RSM). These control factors then need to be optimized and
formulized (i.e. a formula which can predict part properties (shrinkage, hardness,
etc.) based on the values of the effective input parameters).
4.1 Research Plan and Procedure
The fabrication quality is achieved through improving the following five major
parameters:
1- Complete inhibition by the inhibitor and perfect separation at inhibited regions by
the aid of sand blasting or ultrasonic vibration
2- Maximum possible sintered part density
3- Part strength
4- Part accuracy (minimum distortion in geometry and repeatability in the samples)
4.2 Major Stages of the Procedure
There are six major stages in the procedure as shown in Figure 4.1 which is
highlighted in Blue. Every stage is carried out and defined through experimental research,
analytical research and developmental research.
Stage 1 defines the appropriate metal powder and the proper inhibitor for the SIS
process. There are many parameters involved in choosing the right material the most

23

important of which are listed in Figure 4.1. Both analytical and experimental research
activities are carried out for defining the suitable metal powder material and the proper
inhibitor.
Stage 2 is the process of printing the inhibitor on the metal powder. Both analytical
and experimental research are carried out to specify the best printing (i.e., inhibitor
deposition) configuration.
Stage 3 is specifying the sintering process that yields a complete inhibition from
sintering for sections treated with the inhibitor while allowing maximum sintering for the
unprinted sections. This stage is carried out both by analytical and experimental research.
This stage is experimented after stage 1 and 2.
Stage 4 is the stage of automating the SIS process
Stage 5 is an experimental stage in which 3D samples are fabricated.
Stage 6 involves analyzing and defining the properties of the 3D physical model to
satisfy the five major research goals.
The relationships between the stages are shown by arrows in Figure 4.1.
4.3 Research Methodology:
Three different research methodologies are employed for characterizing the SIS-
metal process. These are Analytical methodology, Experimental methodology and
Developmental methodology. Each methodology type encompasses different aspects of the
process which are shown in Figure 4.2. The relation between these research methods and
their content are shown in Figure 4.2 as well.

24

Figure 4.1. Major stages in the SIS procedure
4.3.1 Analytical Approach
This approach is very closely related to the experimental approach. In the analytical
approach the focus is on the following major categories:
Material selection
Inhibitor selection
Grain size Type of metal Grain shape Mix or fully
alloyed
Type of
Inhibition
Characteristics
of the inhibitor
Printing the inhibitor
on metal powder
Type of printing Printing rate Droplet size Set up time
Sintering method
Sintering
environment
Sintering
temperature diagram
Sintering stages (two
stages vs. one stage)
Machine fabrication and
development of control
software
Building experimental 3D parts
Running different mechanical and qualitative test on
the final model and analyzing the results

25

1- Microscopic inhibition concept: In this section the inhibition phenomenon is
studied by the aid of SEM images of the samples and the theoretical concepts in the
field of material science.
2- Sintering concept: In this section the fundamentals of loose powder sintering is
studied. By the aid of response surface methodology, the factors affecting the
sintering process will be identified. Several empirical models will be developed to
model the effect of the identified factors on sintering rate and mechanical properties
of the part.
3- Printing concept: In this section the droplet behavior and behavior of droplet
impacts on metal powder particles and parameters which are involved in the
printing method is studied.
4- Identifying and quantifying the factors affecting the process.
5- Analyzing the fabricated parts.
4.3.2 Experimental Approach
The experimental activities in this research are closely related and hence affect one
other. The following categories of experiments have been considered:
1- Material selection and Inhibitor selection: Material selection is the main challenge
of this project and once the metal powder and inhibitor are identified the rest of the
process depend on these selections. Metal powder selection is based on the
commercially available metal powders and the inhibitor is selected by testing a
variety of inorganic chemical salts.

26

2- Printing method verification: Printing is based on the available commercial
technologies and the challenge is delivery of the inhibitor with a desirable
resolution and quantity.
3- Sintering process characterization: There are many factors involved in the sintering
process which are all related to the type of metal powder used. The main challenge
is to run different experiments and optimize them through analytical methods to
find the right temperature/time diagram for the sintering process. The sintering
procedure impacts the ease of separating the inhibited sections of the final part
from its uninhibited sections. The procedure also impacts the final density and
hence the strength of the sintered part.
4- Preliminary feasibility testing: In this section preliminary carbon crucibles are
made and some 2.5D samples are built to check the feasibility of the process and to
confirm the suitability of the selections made in the first three categories listed
above.
5- Complete process testing: In this stage after building 3D green (unsintered) parts
by the SIS machine the green parts are sintered to obtain the final 3D parts.
The last part is evaluating the fabricated 3D parts using standard mechanical property
tests and empirical models (Using response surface methodology to find the effective
parameters and formulize the responses which are shrinkage and hardness).
4.3.3 Developmental Approach
The SIS software is improved with respect to two aspects. One aspect is to run the
SIS machine by an input file which is a result of an existing slicing program. The software
generates a tool path for every cross section of the 3D model and will control and guide the

27

machine through the SIS process. The SIS machine is improved specially in the heating (to
evaporate water in the inhibitor solution and yield crystal particles) and printing stages
which are critical in creating good green parts.

Analytical
research
Experimental
research
Developmental
research
Sintering Concept
Printing concept
Microscopic
Inhibition concept
Identifying the
factors affecting
the process
Identifying and
quantifying the
effect of selected
factor
Material selection
Inhibitor selection
Printing method
Sintering method
Preliminary 2.5 D
sample parts
SIS machine
design and
development
Building 3D parts
by the SIS method
Developing the
software for the
SIS machine
SIS machine
modification and
improvement
Developing new
methods for
separating un-
sintered sections
from the sintered
sections
Analyzing the fabricated 3D model properties
Figure4.2. Research methodology

28

Chapter Five: Preliminary Experiment
In order to test the feasibility of the SIS process several experiments have been
carried out to make sure the process is feasible before going any further. Before the SIS
machine was development a set of experiments were carried out to test the feasibility of the
process.
5.1 Preliminary Experiments for Loose Powder Sintering and Retardation from
Sintering
A ceramic block made out of Silica-Alumina (AlO)
2
SiO
3
was used to experiment
with the sintering process. Alumina Silica has a very high melting point of 2010° F, has a
porosity of 2% and is highly stable and non-reactive to metals. For these reasons Alumina-
Silica is a good choice for the sintering experiments that are carried out in this research. In
order to mill the ceramic as a mold for the experiments, titanium nitride coated high speed
milling bit was used for this purpose. The material removal rate for the ceramic block is .5
in
3
/min. The ceramic block used for the loose powder sintering and inhibition from
sintering experiments are shown in Figure 5.1.

Figure 5.1. Alumina-Silica ceramic blocks which are used for the preliminary sintering test
A typical sintering path is shown in Figure 5.2. Sintering is carried out in an Argon
gas environment. Further studies were carried out for vacuum, hydrogen and hydrogen –

29

nitrogen environments as well. For bronze with a powder bed density of 0.005 gr/mm
3
, the
sintering path that has been shown in Figure 5.2 yields a porosity of 25% which was a
good preliminary success.

Figure 5.2. Loose powder Sintering path for bronze
In order to test the sintering inhibition different inorganic salts were used. In order
to test the inhibition phenomenon, droplets of the chemical salt solution were deposited on
the powder bed and after sintering the surface fracture toughness was measured. Several
salts such as aluminum sulfate showed success in this stage.
5.2 SIS Machine Fabrication
A prototype machine was designed and developed for the SIS Metal process. The
machine has 3 axes. One axis is for controlling the up down movement of the platform (Z-
axis). The platform moves in the tank that contains the metal powder. The platform moves
down one layer thickness to accommodate the new layer of powder. The two other axes are
for controlling the movement of a dispensing valve which deposits the inhibitor on every
layer of bronze powder.
Sintering diagram
0
100
200
300
400
500
600
700
800
900
0 50 100 150 200 250
Time ( Min.)
Temperature
( Centigrade)

30

Figure 5.3. The CAD model of the SIS machine

Build Tank
Feeder Tank
X-Axis
Linear guide
Heater
Y-Axis
Linear guide

31

Powder delivery

Printing the
inhibitor and the
boundary

Heating every
layer

Figure 5.4. Stages in the SIS metallic part fabrication based on microscopic inhibition

A Graphical User interface is developed in VB.NET to communicate with the
electronics .The software input is a series of points that are imported through a slicing
program.
A single nozzle (Lee Company INKA 2457210 H) with an orifice size of .005 Inch
(0.12 mm) is used to print the inhibitor on every layer. Micro-Dispense valves were
originally designed for the drop-on-demand inkjet market. This single-orifice nozzle is
actually an electro-magnetic solenoid valve which can operate at high frequency (up to
1000 Hertz). These valves provide high-speed control for very small volumes of liquids.

32

Note that this droplet size is far larger than typical droplet sizes generated by commercial
inkjet printers. The nozzle settings are listed below:
 Frequency: 200-1000 Hz
 Spike voltage: 13 V
 Hold voltage: 10 V
 Max back pressure 5-10 psig
A heater is used to heat up every layer after printing in order to dry the inhibitor in
the printed sections. The heating of every layer is caused mainly by infrared radiation. The
heater was fabricated using Nichrome 80/20 (80% nickel, 20% chromium) wire connected
to the output of a rheostat. Every layer is heated up to approximately 110° C which is
shown in Figure 5.5.

Figure 5.5. Temperature measurement during the heating of every layer
After the 3D model is sliced by a slicing software and the boundary of every cross
section is interpolated and represented by points, the software sends a command for every
path in each layer to the controller boards and the controller board activates the stepper
motors and the printer head to print the corresponding layer profile.

33

Figure 5.6. The SIS-Metal machine

Figure 5.8. The heater in the SIS machine which is used for drying the inhibitor

34

Figure 5.8. The printer head for printing the inhibitor

Figure 5.9. Inhibitor container and the air pressurized container

Figure 5.10. Controller boards which are used for controlling the stepper motors for X,Y
and Z axis
Micro switch
.5 Micron filter
Solenoid valve
Build tank
platform (Z-axis)
Pressurized Air
tank
Inhibitor
container

35

Figure 5.11. Build tank in the SIS machine

Figure 5.12. The SIS software for automatic control of the machine by the input path file

Figure 5.13. The software interface for manual control of the SIS machine

36

5.3 Material Selection and Part Fabrication
Inhibitor selection: In order to find the best inhibitor the underlying of inhibition
mechanism has been studied which will be discussed further in Chapter Seven. We have
chosen salts as the proven best inhibitor. There are several important factors to be
considered when choosing an appropriate salt candidate, which include: (1) melting
temperature, (2) correlation between the initial salt crystal size and salt crystal growth rate,
(3) molecular mass weight for getting a high penetration, (4) high solubility for nucleating
more crystals from a droplet, (5) Chemical properties of the decomposed salt particles and
(6) decomposition temperature. In our preliminary results the best inhibitor candidate for
this purpose is found to be aluminum sulfate with the properties shown in table 5.1. In our
experiment the decomposition temperature is less than the sintering temperature of the
choice of metal powder.
T a ble 5.1. P rope rties of t he inhi bit or
Properties of the inhibitor (Aluminum Sulfate)
Molecular formula Al
2
(SO
4
)
3

Molar mass 342.15 g/mol (anhydrous)
Melting point 770 °C (decomp, anhydrous)
Solubility in water 31.2 g/100 mL (0 °C)
36.4 g/100 mL (20 °C)
89.0 g/100 mL (100 °C)
Solubility in alcohol and acids slightly soluble in alcohol and dilute
mineral acids

Metal powder selection: We focused our efforts on bronze powder because of its
popularity and its relative ease of sintering. In selecting the choice powder the following
have been done:

37

1. Mixed, partially and fully alloyed bronze powders have been investigated. Sintered
parts with fully alloyed bronze powders show the best mechanical properties, the
least shrinkage and best inhibition in the printed sections.
2. Metal powders with different mesh sizes have also been examined. The finer the
grain size, the better the sintering process will be; however, if the grain size is too
small, it would be difficult to spread the powder in a uniform layer. The best grain
size that was chosen is 325 mesh or 44 micron.
3. The shape of metal powder is an important factor. The density of green parts is
directly related to the packing density of the powder bed. The packing density of
spherical powder is better than other shapes. Therefore, spherical fully alloyed
bronze powder with a grain size of 325 mesh was chosen for this research. The
bronze powder used in our experiments( Bronze 5890) has the following chemical
composition
Copper: 89.79%
Tin: 10%
Lead: 0.025%
Zinc: 0.04%
Iron: 0.058%
Phosphorous: 0.085%
The powder particle size has the following distribution:
325 Mesh (44 Micron) 98.7 %
200/325 Mesh (44/75 Micron) 1.3 %

The bronze powder has the following properties:

38

Table 5.2. Properties of pre-alloyed bronze
Bronze 5890

Metric
Melting Point - Liquidus 999 C
Melting Point - Solidus 843 C
Theoretical Density 8.77 gm/cm
3
@ 20 C
Specific Gravity 8.78
Electrical Resistivity 15.68 microhm-cm @ 20 C
Electrical Conductivity 0.064 MegaSiemens/cm @ 20 C
Thermal Conductivity 50.2 W/m ·
o
K at 20 C
Coefficient of Thermal Expansion 18.4 ·10
-6
per
o
C (20-300 C)
Specific Heat Capacity 377.1 J/kg ·
o
K at 293 K
Modulas of Elasticity in Tension 110000 MPa
Crystal type Fcc
Surface energy j/m
2
1.7
Yield Strength(MPa) 83
GBD activation energy (kj/mol) 105
VD activation energy (kj/mol) 207
Solid-vapor surface energy(j/m
2
) 1.7
SD activation energy(kj/mol) 205

Green part fabrication procedure: The 3-dimensional CAD model of a part is sliced in a set
of layers. The thickness of each layer is between 0.25-1mm in different experiments based
on different settings of the machine and the inhibitor. After the SIS machine builds every
layer the whole green part is transferred to a tube sintering furnace shown in Figure 5.15.
The furnace has a neutral argon gas environment to prevent any reactions during sintering.
One of the challenges that were encountered repeatedly during the sintering process was
the failure of the ceramic tube during the heating cycle. The following provisions were
made in order to reduce the chance of failure of the ceramic tube:
 Slow heat ramp less than or equal to 25 C/min. was used
 Very low flow of argon gas was used

39

 Refractory plugs were used for the both ends of the ceramic tube to avoid
heat shock
 Support were used for both ends of the ceramic tube

Figure 5.14 Sintering furnace
Sintering sequence: After completing all layers, the fabricated green part is transferred
to a sintering furnace. The preliminary sintering sequence which yields minimum
shrinkage with an acceptable mechanical property was determined to be: sinter the part at
600
o
C for 15 minutes, increase temperature to 810
o
C for 10 minutes, and then slowly cool
down the part. The sintering temperature curve is shown in Figure 5.16.

Figure 5.15. Sintering cycle for bronze
0
100
200
300
400
500
600
700
800
900
0 50 100 150 200 250
Temperature(Celsius)
Time ( Min.)
Sintering cycle for Bronze
Series1
810 ◦C for 10 min.
25 ◦C/min.

40

Sand blasting was used to remove the inhibited sections from the sintered sections.
In this method pressurized sand hits the part and removes the un-sintered sections from the
model.
Af ter r unnin g sev e r a l sa mpl e s the f e a sibi li t y of th e S I S pr o c e ss for m e tal b a se d on
mi c rosc opic me c h a nica l i nhibi ti on c onc e pt wa s pr ove n . As shown in F ig u r e 5.16, the
se c ti ons tre a ted with t he pr int e d salt ar e b rittl e a nd c a n e a sil y be b roke n, w hil e the othe r
re g ions wi thout salt a re s int e re d pro pe rl y with g oo d st re ng th.

F ig u re 5.16. S a mpl e 2.5 D pa rts made b y the S I S pr oc e ss . L e ft pic ture sho ws the gre e n p a rt
be for e sint e ring a nd ri g ht pictur e shows the pa rt a f ter sint e ring

The ne x t st e p wa s to bui ld 3 - D mode ls . Af ter d e si g nin g the 3 - D mode l suc h a s the
one shown in F i g ur e 5.17 , the mode l i s sl ice d using a sli c in g softw a re . F or e ve r y sli c e th e bounda r y point s ar e s e nd to t he S I S softwa r e whic h sen ds the moti on c omm a nds t o the S I S mac hine. The S I S ma c hine tool path f oll ows the po int s for e ve r y sli c e a nd pr int s the
inhi bit or on the pr int e d sec ti ons de fine d b y the so ftwa re . The tool pa th s for e ve r y sli c e a nd
the pr int e d sec ti on s for e ve r y sli c e a re shown in F ig ur e 5.1 8 .An e x a mpl e s of f ull y sint e r e d
br onz e pa rts a r e shown i n F ig u re 5.19. I n thi s ex pe rimen t we w e re a ble to a ppl y the S I S c onc e pt fo r buildi ng 3 - D obje c ts . As it c a n be se e n these samples ha ve a r ou g h sur fa c e due to t he c oa rse p rinte r he a d .
Inhibited sections
with printed
inhibitors
(powders can be
separated easily)

Non-printed
sections

41

F ig u re 5.17 . 3D mod e l desig ne d a nd sl ice d to be buil t b y th e S I S ma c hine

F ig u re 5.18. T ool p a th pl a nning f o r dif f e re nt sl ic e s in a s pe c ific 3 - D mode l de sc ribe d in
F ig u re 5.18 wh e r e t he blue lines de fin e the bounda r y li ne s fo r pr int ing

F ig u re 5.19 . A f a br ica t e d 3- D pa rt ( le ft) a nd the in hibi ted se c ti ons (r ig ht)
I n F i g ur e s 5.20 a nd 5.21 t he pa rt on the le ft is t he 3D mode l af ter sint e ring a nd the
pa rt on the r i g ht i s made of the pr int e d sec ti ons t h a t ar e inhi bit e d fr om si nt e ring a nd it ge ts
se pa ra t e d fr om t he sint e r e d sec ti on .
Slice # 1-3 Slice # 4-6 Slice # 7
Slice # 8-10 Slice # 11 Slice # 12-14

42

F ig u re 5.20 . A 3D mode l de sig ne d a nd sl ice d to b e buil t b y the S I S m a c hin e

F ig u re 5.21 . . A fa br ic a te d 3- D pa rt ( le ft) a nd the i nhibi ted se c ti ons (r ig ht)

F ig u re 5.22. S e v e ra l 3- D br onz e pa rts made b y the S I S method
S e ve ra l br onz e pa rts we r e f a br i c a ted b y the S I S pr oc e ss base d on mi c rosc o pic
mec ha nic a l i nhibi ti on wh ich is shown in F ig u re s 5 .19, 5.21 a nd 5.22 . The i nhibi tor tha t
wa s used in the pr e li mi na r y e x pe rimen ts wa s alum inum sul fa te. As it will be de sc rib e d in
C ha pter S e ve n other in hi bit or s ha ve a lso be e n t e sted a nd c ompa re d. F a br i c a ti on of the sa mpl e pa rts g a ve th e a ss ur a nc e o f the f e a sibi li t y o f the S I S pr o c e ss fo r me t a l lic pa rts
ba se d on m icr oscop ic m e c ha nica l inhi bit ion. The ne x t st e p wa s to st ud y th e unde rl y in g re a sons behind the ph e no mena of loose pow d e r si nter ing a nd inhi bit ion fr om sint e ring .
Af ter the inhibi ti on mec h a nism a nd the sint e ring mec ha nism wa s identifie d, the sint e ring

43

ra te a nd the m e c ha ni c a l p rope rt y of the p rinte d a nd non - pr int e d sec ti ons we r e te sted a nd
se ve ra l e mpi ric a l m ode ls we re d e ve loped b a se d o n re sponse sur f a c e metho dology .
Note that the pr int noz z le used in our te st s ha s a lo w r e solut ion with re late d iss ue s
in C ha pter E ig ht. Ac c or ding l y , the la y e r li ne s on the pa rts a r e re l a ti ve l y c o a rse . Usin g a n
inkj e t print e r he a d with fi ne re solut ion shoul d lea d to dra sti c a ll y b e tt e r pa rt qua li t y .

44

Chapter Six: Loose Powder Sintering
B e fo re investi g a ti n g the i nhibi ti on mec ha nism the sint e ring me c ha nism shoul d be investi g a ted . Ac c or din g l y , thi s cha pte r f irst pr e se nts t he a va il a ble sint e rin g knowle d ge a nd
then the sint e ring m e c ha nism in br onz e a nd the e f fe c t of sint e rin g on the m e c ha nic a l
pr ope rties of b ronz e will be studi e d.
6.1 Sintering Mechanism
In sintering, particles sinter by atomic level events that reduce surface energy.
Surface energy is related to the surface area, so bigger particles have a lower surface area
therefore, they have less energy per unit, which results in a lower sintering rate. Smaller
particles have a higher surface energy per unit volume which accelerates sintering.
Every particle has an effective stress. A spherical shaped particle with a diameter of
D and a surface energy of ϒ has an effective stress shown in equation below.

In other words the stress associated with a curved surface is shown by the equation above.
During sintering the stress shown in the equation causes flow of the mass in a direction
that minimizes the surface curvature (In a flat surface D = ∞ the re fo re σ=0).
In order for the atoms to move from their current site to a new site, the atoms must
attain energy. The Arrhenius equation shown below shows the ratio of number of activated
atoms (N) to the number of total atoms (N
0
).

45

Where R is the gas constant (8.314 J.Mol
-1
.K
-1
), T is the absolute temperature, Q is
the activation energy. As it can be seen the temperature plays a big role in the sintering
cycle which will be discussed more in detail.
The gre e n de nsit y o f the powde r is de noted b y ρ a nd the the or e ti c a l d e nsit y is
de noted b y ρ
T
.

The compact density V
s
is equa l t o ρ/ρ
T
.

The fractional porosity V
p
is
fractional pores between the contact points, where V
P
= 1-V
s.

The sintering extent can be measured in many different ways. Assuming two
spherical particles with a diameter of D being sintered as shown in Figure 6.1, one measure
of sintering is the neck size ratio X/D. Another measure of sintering is the linear shrinkage
rate which is normally measured by a dilatometer. The shrinkage rate is the change in the
compact dimension ∆L divided by the original dimension L
0
. So the shrinkage will be
∆L/L
0
.
In the earlier stage of single-phase solid state sintering the relation between the
neck size and the shrinkage is shown below [H.E Exner 1979]:

Figure 6.1. Two spherical particles with a diameter of D sintered with a neck diameter of X
D
X
P

46

The relation between the initial green fractional density V
G
, V
s
and shrinkage is
shown below.

Another measure of sintering is densification ψ which is shown below:

The thermal and electrical conductivity of metallic structures are reduced by the
presence of pores. During sintering the conductivity increases as the number of pores
decrease. The equation below shows the relation between the conductivity of porous
sintered material (k) and the conductivity of the fully densified material (k
0
):

The χ value is a function of the pores. Based on the analysis of several materials with
different pore seizes, the best fitted value is approximately 11.
The mechanical property of a sintered part is proportional to the number of pores in
the material. The relation between the Elastic Modulus of the sintered material (E) and the
Full density Elastic modulus (E
0
) is shown below [R. Haynes 1981]:

Where the exponent Z falls in the range of [0.3-4].

47

6.1.1 Solid-State Sintering
Since our parts are made out of fully alloyed bronze, the rest of the focus of this
section is on Solid-State sintering. Because pressure-less sintering is practiced in our
process, a high porosity is achieved during sintering. Such parts have applications in
dampers, capacitors, bearings, filters, battery electrodes, sound absorbers, permeators,
foam, mechanical spacers and any other application that requires low densification.
The sintering temperature to induce bonding between the particles depends on
compaction rate, material property and particle size. A homologous temperature is the
sintering temperature divided by the melting point. Most materials exhibit a
homologous temperature between .5 and 0.8. In our preliminary results the
homologous temperature is 0.96. Since loose powder sintering is practiced there are
less contact points between the particles, therefore a higher homologous temperature is
needed for sintering. Neck growth between two particles is one of the best measures for
solid state sintering which is directly related to the sintering rate.
During sintering the flow of atoms are in the direction of reducing the stress that is
associated with convex and concave surfaces. Assuming a point with two radii curvatures
R
1
and R
2
,

ha s a str e ss σ whic h is g iven b y L a plac e e qua ti on shown be low:

The stress in the neck region is derived from the equation below with the
assumption that the radius P at the neck shown in Figure 6.1 is equal to

.

48

The stress in a point away from the neck on the surface of the particle is given by
the equation below which was shown earlier at the beginning of this chapter:

As it can be seen from the last two equations there is a stress gradient between the
neck region and the surface of the particle.
There are several mechanisms that represent the flow of atoms due to stress
gradients. There two main groups of mechanisms for the mass flow during sintering are
surface transport and bulk transport mechanism.
Surface transport mechanism consists of surface diffusion, volume diffusion and
evaporate condensation.

Figure 6.2. Two classes of mass transport mechanism for sintering (Source: German 1984)
Surface diffusion dominates the low-temperature sintering of many metals,
including bronze and stainless steel .It involves the motions of atoms from the defects of a
crystal structure such as ledges, kinks and vacancies. There is a lower thermal activation
needed for surface diffusion compared to other transport mechanisms. Surface diffusion is
the initial contributor to sintering [Kuczynski 1949]. The mass flows from surface sources

49

to surface sinks and the process slows down when the surface defects are consumed or
disappeared due to bonding during sintering. Surface diffusion does not cause shrinkage.
Volume diffusion consists of the motion of vacancies inside the crystal structure.
There are three possibilities during volume diffusion which are listed below:
1-Flow of vacancy from the neck surface to t he pa rticle ’s inter ior and finally
e mer g in g to t he pa rticle ’ s surf a c e (no densification happens)
2-Vacancy flow from the neck surface to the interparticle grain boundary
3-Vacancies in the particle not at the surface can be destroyed by dislocations
(Densification happens since vacancy is not at the surface)
The vacancy at any point and temperature can be calculated from the equation
below:

(

)
Where C is the vacancy concentration under a curved surface with radii of
curvature R
1
& R
2,
K is t h e B olt z man’ s con stant ( 1.380650 × 10
-23
m
2
kg s
-2
) ,Ω is the
atomic volume, T is the absolute temperature and C
0
is the equilibrium vacancy
concentration. Due to a gradient of vacancy in the neck region, the flux of atoms per unit
a re a c a n b e c a l c ulate d usi ng the F ick’ s fir st l a w:

Where Dv is the diffusivity and J is the flux in terms of numbers of atoms per unit area.
6.1.2 Stages in Sintering
Initial stage of sintering: In this stage the neck bonding grows at the initial contacts
and the necks grow independently at this stage. The necks are small in this stage. The X/D

50

ratio at this stage is approximately 0 .3.The sintering rate in the initial stage of sintering
can be calculated from the equation below:

Where X is the neck diameter, D is the particle diameter, t is the isothermal sintering time,
and B is a constant that varies with different sintering mechanisms.
Intermediate stage of sintering: In this stage the neck growth will become less important
and the interconnected pores become important. In this stage the pores remain connected to
the grain boundaries. In this stage the porosity can be calculated from the equation below:

Where d
p
is the cylindrical pore diameter and G is the grain size
Final stage of sintering: At this stage the cylindrical pores become spherical, break away
from the grain boundary and become isolated. In this stage the pores become bigger but the
number of pores decrease which results in a total densification and shrinkage. Normally
pores start to close at 15% porosity and they are all closed at 5% porosity. It can be shown
[Coble 1961] that the porosity can be calculated from the equation below:

√

Where l is the grain edge length d
p
is the pore diameter.
6.1.3 Loose Powder Sintering for Bronze:
The first stage of this research is focused on loose powder sintering for bronze. The
sintering study was carried out under isothermal conditions in a batch furnace shown in
Figure 6.3. The furnace works both under vacuum and inert gas environment. The furnace
has the following properties:

51

Temperature Range 800 – 1200°C (1472 – 2192°F)
Ramp Rate 200° (360°F)/minute max.
Time Range 59:59 minutes max.
Vacuum Programmable Levels
0 - 100% and 101% (off, programmed
level and continuous)
Electrical*
100/120VAC, 50/60Hz, 13/14.5A,
1740W max.
Overall Dimensions 33 x 33 x 41c m (13” x 1 3” x 16” )

Figure 6.3. A sample bronze on a ceramic plate being sintering in the furnace at a
tempe ra tur e 0f 775 C
There are several parameters that affect part quality in the SIS process. Sintering
process is one of the main stages in the SIS process that affects the part quality the most. In
this section the effect of sintering parameters on part quality during the loose powder
sintering is studied.
6.1.3.1 Design of Experiment Settings for Loose Powder Sintering
A sample bronze block with dimensions shown in Figure 6.4 was used in experiments.
The main sintering parameters that affect the sintering process are the temperature during
the first stage of sintering (T1), duration of the first stage of sintering(t1), the temperature
during the second stage of sintering(T2) and the duration of the se c ond st a g e o f sinter in g (t2) . The tempe ra ture ra mp wa s kep t at a c onst a n t ra te of 25 C /m in ute.

52

Figure 6.4. Block sample used in the SIS loose powder sintering process improvement

Figure. 6.5. Sintering cycle for loose powder sintering for Bronze 5890
Table 6.1 Coded values for design parameters T1, t1, T2 and t2
-1 0 1
Te mp1(◦ c ) 500 550 600
time1(hr) 0 .25 .5
Te mp2(◦ c ) 770 790 810
time2(hr) 1 .5 2

t1 t2
T1
T2
Time (hr)
Temperature ( ◦c)
25 ◦c /min.
25 ◦c /min.
Volume = 4794 mm
3

53

The sintering was carried out in a vacuum environment of .1 Torr. A full factorial
design with 4 design parameters Temp1, Temp2, time1 and time2 with responses being
hardness ( HRB) and linear shrinkage percentage was implemented in Minitab. The
hardness was measured by an analog hardness tester shown in Figure 6.6. The responses
for different settings in the full factorial design are shown in table 6.2.
Table.6.2. Full factorial design table
Temp1 time1 Temp2 time2 Shrinkage%
Hardness
(HRB)
500 0.5 810 1 6.6% 98
600 0.5 810 2 7.9% 100
500 0.5 810 2 7.9% 100
500 0.0 810 2 8.2% 99
600 0.5 770 2 5.1% 91
600 0.0 810 1 6.6% 95
600 0.0 770 2 5.8% 91
500 0.5 770 1 4.1% 89
500 0.5 770 2 5.4% 91
500 0.0 770 1 4.9% 89
600 0.0 810 2 8.2% 99
600 0.5 810 1 7.6% 94
500 0.0 770 2 5.8% 91
600 0.0 770 1 4.9% 89
500 0.0 810 1 6.6% 95
600 0.5 770 1 4.1% 90

The test procedure for the hardness test employs a ball indenter with a dimater of
1.588 milimeters to press into the speciman, an initial test pressure P
0
equal to 10
kilogram-force and a main test pressure P
1
equal to 100 kilogram-force will be appliad on
the indenter in sequence, and the total froce 110 kilogram force will be kept for a few
seconds,then the P
1
will be removed, only P
0
will be left. The e value which is the
difference between the indent depth under the total load and the initial load is recorded.

54

Every 0.002 mm of this increment represents the a unit of analog hardness. The hardness
values is calculated by the following equation:
HRB= 130-e/.002

Figure 6.6. The setup for the hardness test used in the experiments
The normal plot, Pareto chart and the main effects plot for the full factorial design
with shrinkage as the response has been shown in Fugures 6.7 through 6.9:

Figure 6.7. Normal Plot of the factors affecting Shrinkage in the full factorial design

55

AB
A
CD
ABCD
ACD
BD
AD
AC
ABC
ABD
BCD
B
BC
D
C
2.5 2.0 1.5 1.0 0.5 0.0
Term
Effect
0.627
A Temp1
B time1
C Temp2
D time2
Factor Name
Pareto Chart of the Effects
(response is Shrinkage, Alpha = 0.05)
Lenth's PSE = 0.24375

Figure 6.8. Pareto Chart of the factors affecting Shrinkage in the full factorial design
600 500
7
6
5
0.5 0.0
810 770
7
6
5
2 1
Temp1
Mean
time1
Temp2 time2
Main Effects Plot for Shrinkage
Data Means

Figure 6.9. Main effect plot for shrinkage

56

Table 6.3. Estimated Effects and Coefficients for Shrinkage (coded units)
Term Effect Coef
Constant 6.2313
Temp1 0.0875 0.0437
time1 -0.2875 -0.1437
Temp2 2.4375 1.2187
time2 1.1125 0.5562
Temp1*time1 0.0875 0.0437
Temp1*Temp2 0.1625 0.0813
Temp1*time2 -0.1625 -0.0812
time1*Temp2 0.3875 0.1938
time1*time2 -0.1375 -0.0687
Temp2*time2 0.0875 0.0437
Temp1*time1*Temp2 0.1625 0.0813
Temp1*time1*time2 -0.1625 -0.0813
Temp1*Temp2*time2 -0.0875 -0.0438
time1*Temp2*time2 -0.2625 -0.1312
Temp1*time1*Temp2*time2 -0.0875 -0.0438
It can be seen that the Temp2 and time2 are the most significant factors in affecting
the shrinkage with a confidence level of 95%. The effect of the significant factors on
shrinkage is shown in Figure 6.10.

57

Temp2
time2
810 800 790 780 770
2.0
1.8
1.6
1.4
1.2
1.0
Temp1 600
time1 0.5
Hold Values
>
–
–
–
–
–
–
–
–
–
–
<
6.96 7.28
7.28 7.60
7.60
4.40
4.40 4.72
4.72 5.04
5.04 5.36
5.36 5.68
5.68 6.00
6.00 6.32
6.32 6.64
6.64 6.96
Shrinkage
Contour Plot of Shrinkage vs time2, Temp2

Figure 6.10. The effect time2 and Temp2 on the shrinkage
Estimating the hardness of the parts was the next step in the DOE experiments.
Even though shrinkage is one measure of sintering but it does not necessarily define the
material property of the parts. This is due to the fact that in the initial stage of sintering
neck growth between particles happens due to surface diffusion but there is little to no
shrinkage. Shrinkage primarily happens in the intermediate and final stages of sintering.
Table 6.4. Estimated Effects and Coefficients for Hardness (coded units)
Term Effect Coef
Constant 93.8125
Temp1 -0.3750 -0.1875
time1 0.6250 0.3125
Temp2 7.3750 3.6875
time2 2.8750 1.4375
Temp1*time1 -0.3750 -0.1875
Temp1*Temp2 -0.6250 -0.3125
Temp1*time2 0.3750 0.1875
time1*Temp2 0.3750 0.1875
time1*time2 -0.1250 -0.0625
Temp2*time2 1.1250 0.5625
Temp1*time1*Temp2 -0.6250 -0.3125

58

Temp1*time1*time2 0.3750 0.1875
Temp1*Temp2*time2 0.6250 0.3125
time1*Temp2*time2 0.1250 0.0625
Temp1*time1*Temp2*time2 0.6250 0.3125

8 6 4 2 0
99
95
90
80
70
60
50
40
30
20
10
5
1
Effect
Percent
A Temp1
B time1
C Temp2
D time2
Factor Name
Not Significant
Significant
Effect Type
D
C
Normal Plot of the Effects
(response is Hardness (HRC), Alpha = 0.05)
Lenth's PSE = 0.5625

Figure 6.11. Normal plot effects for hardness
BCD
BD
ABD
BC
A
AB
AD
ACD
ABCD
ABC
B
AC
CD
D
C
8 7 6 5 4 3 2 1 0
Term
Effect
1.446
A Temp1
B time1
C Temp2
D time2
Factor Name
Pareto Chart of the Effects
(response is Hardness (HRC), Alpha = 0.05)
Lenth's PSE = 0.5625

Figure 6.12. Pareto chart of the factors affecting the hardness

59

As it can be seen from the normal plot the most significant factors are Temp2 and
time2. It is also observed that the time2*temp2 has a high effect and close to being
significant.

Figure 6.13.The effect of Temp2 and time2 on hardness

Figure 6.14. Main effect plot for hardness
Temp2
time2
810 800 790 780 770
2.0
1.8
1.6
1.4
1.2
1.0
Temp1 600
time1 0.5
Hold Values
>
–
–
–
–
–
–
–
–
–
–
<
98 99
99 100
100
90
90 91
91 92
92 93
93 94
94 95
95 96
96 97
97 98
(HRC)
Hardness
Contour Plot of Hardness (HRC) vs time2, Temp2
600 500
98
96
94
92
90
0.5 0.0
810 770
98
96
94
92
90
2 1
Temp1
Mean
time1
Temp2 time2
Main Effects Plot for Hardness (HRC)
Data Means

60

It can be concluded from these results that temp2 and time2 are the most effective
factors in setting the mechanical property and sintering rate.
Since it was concluded that time2 and temp2 are the most significant factors, in the
subsequent step more points were derived for t2 and T2 to observe the mechanical property
and the the sintering rate. Hardness, shrinkage, yield strength, X/D ratio and porosity were
measured as shown in table 6.5.
Table 6.5. Mechanical property and sintering rate for pure bronze sintered a
different Temperature and duration

Temperature-
time
Shrinkage
Surface
Hardness
(HRB)
Porosity X/D ratio
Yield
strength
(Mpa)
770-0hr 1.2% 76 33% 11/29.7=.37 50
770-1hr 4.1% 82 19% 16.1/38.4=.41 65
770-2hr 5.9% 84 12.7% 11.7/24.6=.47 80
810-0hr 1.8% 80 30% 15.4/31.3=.49 64
810-1hr 6.1% 88 12.8% 14/27.3=.51 103
810-2hr 7.9% 93 10% 17.4/29.2=.59 110

The porosity was measured by the Wet and Dry Weight method. In this method the
volume of the sample block (V
b
) and weight of the block (W
2
) are measured. After boiling
the sample in hot water for 10 minutes the weight of the sample is measured again (W
2
).
The volume of the pore is calculated by the equation below:

Where ρ
w
is the density of absorbed water. The porosity is calculated by the following
formula:

61

Temperature-Time SEM micrograph for neck growth
770-0 hour

770-1hour

770-2 hour

Figure 6.15. X/D ratio for different sintering parameters

62

810-0 hour

810-1 hour

810-2 hour

Figure 16.15. Continued

63

The X/D ratio for different settings is shown in figure 6.15. The X/D ratio in every
setting was obtained by finding two particles with a diameter between 25µm to 30µm.

Figure 6.16. Regression model for shrinkage for pure bronze = -0.146583 + 0.000208333
Temperature - 0.11125 Time + 0.000175* Temperature*Time
The regression model for shrinkage as a function of time, temperature and
time*temperature is shown in Figure 6.16. It is observed that at lower temperatures time is
more significant in the shrinkage rate. At higher temperatures both temperature and time
become significant in the shrinkage rate. In the next step the effect of the significant factors
on shrinkage is studied. Linear regression model is used to find the significance of time
and temperature on shrinkage rate. Followed by the linear regression model a better fitted
model for shrinkage rate is obtained.
Linear regression analysis for shrinkage:
Shrinkage = - 0.285 + 0.0270 Time + 0.000383 Temperature

64

Table 6.6. ANOVA table for linear regression for Shrinkage
Predictor Coef SE Coef T P
Constant -0.2848 0.1227 -2.32 0.103
Time 0.027000 0.003801 7.10 0.006
Temperature 0.0003833 0.0001552 2.47 0.090
S = 0.00760117 R-Sq = 95.0%
R-Sq(adj) = 91.6%

Analysis of Variance
Source DF SS MS F P
Regression 2 0.0032687 0.0016343 28.29 0.011
Residual Error 3 0.0001733 0.0000578
Total 5 0.0034420

As it can be seen from table 6.6, time is the most significant factor in the linear regression
analysis.
0.01 0.00 -0.01
99
90
50
10
1
Residual
Percent
0.08 0.06 0.04 0.02 0.00
0.010
0.005
0.000
-0.005
-0.010
Fitted Value
Residual
0.010 0.005 0.000 -0.005 -0.010
2.0
1.5
1.0
0.5
0.0
Residual
Frequency
6 5 4 3 2 1
0.010
0.005
0.000
-0.005
-0.010
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Shrinkage

Figure 6.17. Residual plots for linear regression model for Shrinkage

65

Time
Temperature
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
0.063 0.069
0.069 0.075
0.075
0.015
0.015 0.021
0.021 0.027
0.027 0.033
0.033 0.039
0.039 0.045
0.045 0.051
0.051 0.057
0.057 0.063
Shrinkage
Contour Plot of Shrinkage vs Temperature, Time

Figure 6.18 .The effect of Temp2 and time2 on shrinkage
The regression model for hardness as a function of time, temperature and
time*temperature is shown in Figure 6.19.

Figure. 6.19. Surface hardness for pure bronze = 2.875 + 0.0958333 Temperature – 44.125
Time + 0.0625. Temperature*Time

It is observed that both time and temperature are significant in the hardness. Similar
to shrinkage analysis, in the next step the effect of the significant factors on hardness is

66

studied. Linear regression model is used to find the significance of time and temperature
on hardness. Followed by the linear regression model a better fitted model for hardness is
studied.
Linear regression for surface hardness:
Surface hardness = - 46.5 + 5.25 Time + 0.158 Temperature
Table 6.7. ANOVA table for linear regression model for hardness
Predictor Coef SE Coef T P
Constant -46.50 30.07 -1.55 0.220
Time 5.2500 0.9317 5.63 0.011
Temperature 0.15833 0.03804 4.16 0.025
S = 1.86339 R-Sq = 94.2%
R-Sq(adj) = 90.4%

Analysis of Variance
Source DF SS MS F P
Regression 2 170.417 85.208 24.54 0.014
Residual Error 3 10.417 3.472
Total 5 180.833

Time
Temperature
2.0 1.5 1.0 0.5 0.0
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
89.0 90.5
90.5 92.0
92.0
77.0
77.0 78.5
78.5 80.0
80.0 81.5
81.5 83.0
83.0 84.5
84.5 86.0
86.0 87.5
87.5 89.0
hardness
Surface
Contour Plot of Surface hardness vs Temperature, Time

Figure 6.20. Contour plot of hardness vs. temperature and time

67

As it can be seen from Table 6.7 and Figure 6.20 time and temperature are both
significant in the hardness response. This is concluded because the p value is less than .05,
where .05 is the alpha value.
Linear Regression model for Porosity:
Porosity = 1.08 – 0.000992 Temperature – 0.101 Time
Table 6.8. ANOVA table for the linear regression model for porosity
Predictor Coef SE Coef T P
Constant 1.0800 0.6213 1.74 0.181
Temperature -0.0009917 0.0007858 - 1.26 0.296
Time -0.10075 0.01925 -5.23 0.014
S = 0.0384986 R-Sq = 90.6% R-Sq(adj) = 84.4%

Source DF SS MS F P
Regression 2 0.042962 0.021481 14.49 0.029
Residual Error 3 0.004446 0.001482
Total 5 0.047409

Time
Temperature
2.0 1.5 1.0 0.5 0.0
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
0.284 0.307
0.307 0.330
0.330
0.100
0.100 0.123
0.123 0.146
0.146 0.169
0.169 0.192
0.192 0.215
0.215 0.238
0.238 0.261
0.261 0.284
Porosity
Contour Plot of Porosity vs Temperature, Time

Figure 6.21. Contour plot of porosity Vs. temperature and time

68

As it can be seen from Table 6.8 and Figure 6.21 the time value has the most
significant effect on porosity. This is concluded because the only p value less than 5% is
for the time. The same result was also observed for shrinkage.
Regression model for X/D:
X/D ratio = - 1.82 + 0.0500 Time + 0.00283 Temperature
Table 6.9. ANOVA table for the linear regression model for X/D
Predictor Coef SE Coef T P
Constant -1.8150 0.2406 -7.54 0.005
Time 0.050000 0.007454 6.71 0.007
Temperature 0.0028333 0.0003043 9.31 0.003
S = 0.0149071 R-Sq = 97.8% R-Sq(adj) = 96.3%

Analysis of Variance
Source DF SS MS F P
Regression 2 0.029267 0.014633 65.85 0.003
Residual Error 3 0.000667 0.000222
Total 5 0.029933

As it can be seen from Table 6.9 and Figure 6.22 both time and temperature are
significant in the X/D ratio. This is concluded because the p value for both time and
temperature is less than 5%. The same result was also observed for hardness.

69

Time
Temperature
2.0 1.5 1.0 0.5 0.0
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
0.54 0.56
0.56 0.58
0.58
0.38
0.38 0.40
0.40 0.42
0.42 0.44
0.44 0.46
0.46 0.48
0.48 0.50
0.50 0.52
0.52 0.54
X/D ratio
Contour Plot of X/D ratio vs Temperature, Time

Figure 6.22. Contour plot of X/D ratio vs. temperature and time

810 C -0Hr 810 C -1Hr 810 C -2Hr
Figure 6.23. Increase of sintering rate with time in pure bronze
It is apparent from Figure 6.23 that with the increase of time the sintering rate
increases and bulk diffusion becomes more dominant than surface diffusion. Since
sintering happens under a vacuum environment pore closure and densification is greater
than sintering in an inert gas environment.

70

Figure 6.24. Pore closure and grain boundary formation in bronze at 810-1hour

Pore closure which
is an indication of
final stage of
sintering.This pore
closure happens
more often under
vaccuum sintering
environment
Pore isolation with an
average pore size of 5 μm.
Pore isolation happens
during final stage of
sintering and transforms
from cylindrical shape to
spherical shape

71

Line plot
2 1 0
2 1 0
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
Time
Mean of Shrinkage
770
810
Temperature
Line Plot of Mean( Shrinkage )

2 1 0
2 1 0
95
90
85
80
75
95
90
85
80
75
Time
Mean of Surface hardness
770
810
Temperature
Line Plot of Mean( Surface hardness )

2 1 0
2 1 0
35.00%
30.00%
25.00%
20.00%
15.00%
10.00%
35.00%
30.00%
25.00%
20.00%
15.00%
10.00%
Time
Mean of Porosity
770
810
Temperature
Line Plot of Mean( Porosity )

2 1 0
2 1 0
0.60
0.55
0.50
0.45
0.40
0.60
0.55
0.50
0.45
0.40
Time
Mean of X/D ratio
770
810
Temperature
Line Plot of Mean( X/D ratio )

Figure 6.25 Line plot effect of sintering time and temperature on mechanical property
As it can be seen in Figure 6.25 since shrinkage decreases exponentially when
sintering time increases, the next step is to find the best fitted value based on an
exponential function. As it was shown earlier time is the most significant factor impacting
shrinkage. So the shrinkage model must be a function of time. The function that was
chosen for this purpose is an asymptotic regression (concave) function shown in following
equation:
Shrinkage = Theta1 - Theta2 * Exp (- Theta3 * Time )
Where theta1, theta2 and theta3 are constant values which would be defined by
regression analysis. In order to have a concave function the following conditions must
hold: Theta2>0 & Theta3>0
Gauss-Newton method is used for fitting the model in the equation.

72

Shrinkage = 0.087 - 0.072 * Exp (-0.693147 * Time)
Table 6.10. ANOVA table for the exponential model for shrinkage
Parameter Estimate SE Estimate
Theta1 0.087000 0.047948
Theta2 0.072000 0.047216
Theta3 0.693147 0.867509

Final SSE 0.000418
DFE 3
MSE 0.0001393
S 0.0118040

2.0 1.5 1.0 0.5 0.0
12.50%
10.00%
7.50%
5.00%
2.50%
0.00%
-2.50%
-5.00%
Time
Shrinkage
Regression
95% CI
95% PI
Fitted Line Plot
Shrinkage = 0.087 - 0.072 * exp(-0.693147 * Time)

Figure 6.26. Exponential fitted model for Shrinkage
Variation of surface hardness with time can be derived in the same way. The
equation is shown in Figure 6.27.
Since porosity exponentially decreases as a convex function as time increases, the
next step is to find the best fitted value based on an exponential function. The function that
was determined for this purpose is an asymptotic regression (convex) function shown in
equation below:

73

Porosity = Theta1 - Theta2 * Exp (- Theta3 * Time )
Where theta1, theta2 and theta3 are constant values which would be defined by regression
analysis. In order to have a convex function then following conditions must hold:
Theta2 < 0 & Theta3 > 0
The Gauss-Newton method is used to fit the following model.
Porosity = 0.0947647 + 0.220235 * exp(-1.23214 * Time)
2.0 1.5 1.0 0.5 0.0
110
100
90
80
70
60
Time
Surface hardness
Regression
95% CI
95% PI
Fitted Line Plot
Surface hardness = 92 - 14 * exp(-0.693147 * Time)
2.0 1.5 1.0 0.5 0.0
40.00%
30.00%
20.00%
10.00%
0.00%
Time
Porosity
Regression
95% CI
95% PI
Fitted Line Plot
Porosity = 0.0947647 + 0.220235 * exp(-1.23214 * Time)

Figure 6.27. Exponential fitted model for hardness and porosity

74

Table 6.11. ANOVA table for the exponential model for porosity
Parameter Estimate SE Estimate
Theta1 0.09476 0.049410
Theta2 -0.22024 0.052371
Theta3 1.23214 0.778845

Iterations 5
Final SSE 0.0027365
DFE 3
MSE 0.0009122
S 0.0302021

Linear relation between shrinkage and surface hardness:
The regression equation is
Shrinkage = - 0.3027 + 0.004147 Surface hardness
S = 0.00910221 R-Sq = 90.4% R-Sq(adj) = 88.0
Table 6.12. ANOVA table for the exponential model for shrinkage Vs. hardness
Analysis of Variance
Source DF SS MS F P
Regression 1 0.0031106 0.0031106 37.54 0.004
Error 4 0.0003314 0.0000829
Total 5 0.0034420

As it can be seen from Figure 6.28 and Table 6.12 there is a consistent linear
relation between surface hardness and shrinkage. This linear relation has less error at
higher hardness and higher shrinkage rate. This confirms that at lower temperature and
lower sintering time the surface diffusion is more dominant and at higher temperature and
higher sintering time the bulk transport mechanism becomes more dominant in sintering
mechanism.

75

95 90 85 80 75
9.00%
8.00%
7.00%
6.00%
5.00%
4.00%
3.00%
2.00%
1.00%
Surface hardness
Shrinkage
S 0.0091022
R-Sq 90.4%
R-Sq(adj) 88.0%
Fitted Line Plot
Shrinkage = - 0.3027 + 0.004147 Surface hardness
Figure 6.28. Relation between surface hardness and shrinkage
Hardness test is a one criterion for determining the mechanical property of the part.
Since parts are sintered in a pressureless sintering process, their core can have a lower
hardness and a weaker mechanical property than their surface regions due to the lower
thermal conductivity of porous bronze. Therefore, hardness test might not always be a
good measure for the mechanical property of the parts but it provides a good measure of
surface quality. However surface hardness is a good measure for the surface quality.
Surface hardness is an important measure when it comes to the separation between the
printed and non-printed sections which will be discussed more in details in Chapter seven.
6.1.3.2 Micro-Tensile test for loose powder sintering
A non-standard micro-tensile test was carried out to measure the yield strength,
ult im a te te nsil e stre ng th a nd the Y oun g ’s modulus of the sintered parts at different
temperature settings. For the Micro-tensile testing the parts were made with a dimension
shown in Figure 6.29

76

Figure 6.29. Dimensions for the Micro-Tensile test used in the Stress-Strain diagram
The experimental setup consists of the sample, a force sensor, two-dimension
adjustable stages, a microscope, a displacement sensor and a piezoelectric motor. The
schematic of the tensile test system is shown in Figure 6.30. In addition, an external
microscope equipped with a high-resolution CCD is used to obtain images during the
testing process.
All the sa mpl e s we re sint e re d in a v a c uum envir on ment. The sint e rin g r a mp f or the
sa mpl e s wa s set to 25 C /m in. The mot or spee d du ring the te st w a s set to .1 mm ./sec ond,
he nc e the str a in ra te wa s 0.033 1/s e c ond. As it wa s noted this is a non - standa rd te st.
St a nda rd te nsil e tests re q uire a la r g e r s a mpl e siz e . Due to t he siz e li mi t of th e S I S mac hine ’ s bui ld cha mber a nd the siz e li mi t of the fur na c e , the non - standa rd Mi c ro - T e nsil e test wa s the onl y possi ble opti on I thi s ca se to t e st the me c ha nic a l prope rt y of t he samples.
I t w a s obser v e d e x pe rimen tall y that the te st r e sult s ar e de p e nde nt on t he th ickne ss of the
sa mpl e s. The r e for e it wa s assur e d that a ll samples ha ve a unifo rm thi c kne s s. The r e sult s for Mi c ro- T e nsil e tests at dif fe re nt t e mp e ra tur e a nd ti me se tt in g s ar e pr e se nted in F ig u re s 6.31
throug h 6.35.
Thickness: 1.1 mm

77

F ig u re 6.30. T e nsil e test s y stem

78

Figure 6.31. Tensile test from a sample sintered at sintered at 770 C for 0 hour
0
10
20
30
40
50
60
-0.01 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07
Stress(Mpa)
Strain
Micro-Tensile test for bronze sintered at
770°C for 0-hour
Yield Strength= 50 Mpa
UTS=50 Mpa
y = 1791.8x
R² = 0.96
-10
0
10
20
30
40
50
60
-0.01 0 0.01 0.02 0.03 0.04
Stress(mpa)
Strain
Elastic range for bronze
sintered at 770°C for 0-
hour

79

Figure 6.32. Tensile test from a sample sintere d a t si nter e d a t 770 C f or 1 hour
0
10
20
30
40
50
60
70
80
90
-0.02 0 0.02 0.04 0.06 0.08 0.1
Stress(Mpa)
Strain
Micro-Tensile test for bronze sintered at
770°C for 1 hour
UTS=76 Mpa

80

Figure 6.33. Tensile test from a sample sintere d a t si nter e d a t 770 C f or 2 h our
-20
0
20
40
60
80
100
120
140
160
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(Mpa)

Strain
Micro-Tensile test for bronze sintered at
770°C for 2 hour
Series1
y = 2749.5x
R² = 0.9822
-10
0
10
20
30
40
50
60
70
80
90
100
0 0.01 0.02 0.03 0.04
Stress(Mpa)
Strain
Elastic range for bronze
sintered at 770°C for 2
hour
UTS=136 Mpa

81

Figure 6.34. The effect of sintering time on the stress-strain diagram

Figure 6.35 The effect of sintering time on the stress strain diagram

6.1.3.2.1 Design of Experiment for Tensile Test
-20
0
20
40
60
80
100
120
140
160
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(Mpa)
Strain

Micro-Tensile test for bronze sintered at
770°C for different time periods
Series
3
Series
4
Series
5
1-Hr
2-Hr
-20
0
20
40
60
80
100
120
140
160
180
-0.05 0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(Mpa)
Strain
Micro-Tensile test from bronze sintered at
810°C at different time periods
Series2
Series3
Series1
0-Hr
1-Hr
2-Hr

82

The next step is to observe the relation between yield strength and shrinkage. A
linear regression model was proposed for yield strength vs. shrinkage.
Regression Analysis: Yield Strength versus Shrinkage
Yield Strength = 41.14 + 833.8 Shrinkage
S = 10.0782 R-Sq = 85.5% R-Sq(adj) = 81.9%
Table6.13. ANOVA table for the regression model for yield strength
Analysis of Variance
Source DF SS MS F P
Regression 1 2393.06 2393.06 23.56 0.008
Error 4 406.28 101.57
Total 5 2799.33

8.00% 7.00% 6.00% 5.00% 4.00% 3.00% 2.00% 1.00%
110
100
90
80
70
60
50
Shrinkage
Yield Strength
S 10.0782
R-Sq 85.5%
R-Sq(adj) 81.9%
Fitted Line Plot
Yield Strength = 41.14 + 833.8 Shrinkage

F ig u re 6.36 . Re gr e ssi o n model f or y i e ld st re n g th Vs. s hr inka g e

83

Temperature
Time
810 800 790 780 770
810 800 790 780 770
2.0
1.5
1.0
0.5
0.0
2.0
1.5
1.0
0.5
0.0
>
–
–
–
–
–
–
–
–
–
–
<
98 104
104 110
110
50
50 56
56 62
62 68
68 74
74 80
80 86
86 92
92 98
Strength
Yield
Contour Plot of Yield Strength vs Time, Temperature

F ig u re 6.37. E f fe c t of ti me a nd tempe r a ture on th e Y ield S tre n g th
S e ve ra l t e nsil e tests we re c a rr i e d out for loose po wde r sinter in g . As ha s be e n shown ther e is a g e n e ra l p a tt e rn of im pr ove ment in t he y i e ld st re n g th whe n the sin ter ing ti me
incr e a s e s. I t ca n b e see n i n F ig u re 6.36 that the re i s a line a r r e lation betwe e n shrinka ge a nd
y i e ld st re n g th. Th e c h a n ge of sint e rin g tempe r a tur e in t he r a n g e o f 770 - 810 doe s not show
a sig nific a nt cha n ge in y i e ld st re n g th a s the c ontou r plot indi c a tes. S ince pa r ts have a hi g h
porosit y a nd a re full of gr a in boundar y d e fe c ts , the re sult s fr om t he tensil e tests ar e not
pr e c ise but pr ovide a g oo d e sti mate of the mate ri a l prope rt y . W it h the inc re a se of tim e the
y i e ld st re n g th i s im pr ove d , howe ve r , a li ne a r re la ti onshi p with a hig h si g ni fic a nc e ( P =
0.008 with a lpha= 5%) e x ist s be twe e n the y ield st r e ng th a nd shrinka g e . The re for e a li mi t shoul d be obse rve d fo r sinter ing du ra ti on in orde r to avoid to e x c e ssi ve shrinka ge . The other prop e rt y that is a f f e c ted b y sint e rin g ti me is t he qua li t y of inhi bit io n in t he printed
se g ments. Th e ne x t c ha pter the stud y f oc us e s on the inhibi ti on phe nomena .

84

Chapter Seven: Sintering Inhibition
7.1. Introduction and Prior Studies
F or meta ls t he a c ti va ti on e ne r g y (mini mum e ne r g y r e quire d to s tar t sint e rin g ) for volum e dif fusion is g r e a t e r tha n the a c ti va ti on e ne r g y f or g r a in boundar y o r surf a c e dif fusion. The r e for e , a t l owe r te mpe ra ture v a lues surf a c e dif fusion is more domi na nt t ha n volum e dif fusion. I t h a s be e n shown tha t di sper si on of sec ond pha s e meta l o x ide or a n y stable iner t par ti c le in the meta l powde r slows dow n the sint e ring pro c e ss. D isper se d
pa rticle s which a re pinne d to the sur fa c e c a n b e i mm obil e or mobi le . I f su c h pa rticle s a re im mobi le the meta l surf a c e is pi nne d down a nd in or de r f o r the meta l surf a c e to m ove , it
shoul d e x e rt a f or c e on th e pa rticle . This for c e de p e nds on t he r e sis tanc e of the pa rticle to
be we t ted b y th e sur fa c e . F or mobi le pa rticl e s the pa rticle s move w it h a spe e d lowe r tha n
whe n the sur f a c e is p a rtic le f re e .
I t w a s shown b y Kuc z y n ski & L e va nd e l (1969) th a t shrinka g e of the po re s during sint e ring will be r e tar d e d b y a for c e whic h is a re s ult of the r e sis tanc e o f the ox ide pa rticle to we tt ing b y the me tal s ur fa c e . J ohnson (1976) prop osed that surf a c e di f fu sion - c ontroll e d
sint e ring a nd su rf a c e mo ve ment c a n b e r e ta rde d b y disper s e d pa rticl e s pi nne d a t t he surf a c e . A model pr opose d b y J ohn son i s shown in t he F i g ur e 7.1, whic h sh ows the
g e om e tr y of a p a rticle b e ing pinned in t he surf a c e of a subst ra te.
I n the mod e l shown in F i g ur e 7.1, the sur f a c e e ne r g ies of th e subst ra te a nd t he pa rticle a re ϒ
1
a nd ϒ
2
, re spec ti ve l y . Th e int e rf a c ia l ene r g y be tw e e n the in e r t par ti c le a nd
the substra te is ϒ
3 . The f or c e e x e rte d b y th e surf a c e on the pa rticle is s hown in t he e qua ti on be low:
𝐹 . . .

.sin 𝛼

85

Dur ing th e sint e ring p roc e ss hi g h c u rva tur e r e g ion s ar e f il led in b y a flow o f a tom s
to re duc e the c ur v a ture . This flow of a tom s ca n b e looked a t as a su rf a c e moveme nt
movi ng norma l t o it se lf.

F ig u re 7.1. G e ometr y of pa rticle pinned to a n a dv a nc in g surf a c e
W he n a surf a c e is adva n c ing durin g sint e rin g , the dr a g on the sur f a c e b y the
pa rticle s pi nne d to t he su rf a c e wor ks a g a inst the c a pil lar y p re ssur e drivin g the sur fa c e . This
dr a g c a n b e pr e se nted a s a pre ssur e on the sur f a c e shown in the e qua ti on be low:

𝐹
In thi s equ a ti on , K i s the c ur va tur e of the sur fa c e a nd N is the numbe r of pa rticle s per unit a re a .
M.F Ashb y ( 198 0) studi e d the inhibi ti ng e f f e c t of fine disper si on iner t st a bl e pa rticle s on sint e rin g of meta ls. I t w a s shown that we ll we tt e d pa rticl e s ca u se the f re e -
surf a c e of the met a l t o be c ome le ss ef fe c ti ve a s a s ourc e of m a tt e r f or sint e r ing proc e ss. Inert particle
α

ϒ
1
ϒ
2
ϒ
3
Ɓ
2
a

Ɵ
1
Ɵ
2

86

The r e a son pr opose d b y Ashb y is t ha t as the su rf a c e r e c e d e s the pa rticl e s be c ome more e x posed a nd a ne w hi g h e ne r g y su rf a c e is cr e a ted. The other r e a son g iven i s that t he pa rticle s pi n to t he g ra in bounda r y de f e c ts whic h i s a sour c e o f a tom s to d e tac h dur in g the
sint e ring pro c e ss.
B re tt a nd S ie g le (1966 ) s tudi e d the e f f e c t of Al
2
O
3
on c oppe r . The y pr e pa r e d 150
μ m coppe r w ire s c ontaining 1% v olum e o f 0.02 μ m Al
2
O
3.
The c oppe r w ire s we re sint e r e d
a t 1050 C f or 600 hr . The de nsifica ti on wa s st ron gl y inhi bit e d a nd the por e s we re sti ll obser ve d in t he meta l. I n pure c oppe r a ft e r 400 h ours pa rt re a c h the fina l t he or e ti c a l
de nsit y . The e x pe rimen t wa s also c a rr ied f or pur e c oppe r c ont a ini ng 6 % vo lum e Z r O
2
a nd
e ve n a g r e a te r inhibi ti on wa s obser v e d .
T ikkane n a nd Yla s a a ri ( 1 969) studi e d the de nsific a ti on of disper sion s tre n gthene d
powde rs. The y p re ssed a nd si nter e d - 325 mesh N i and Co powde rs c ont a ini ng M g O a nd
C a O p owde r p a rticle s. T he two ox ides w e re not e qua ll y e f f e c ti ve . M g O w a s a be tt e r
inhi bit or of sint e ring C o a nd Cao w a s a b e tt e r inhi bit or of sint e ring Ni.
L e n e l (1969 & 1970 ) stu died the e f fe c t of Al
2
O
3 a nd S iO
2
pa rticle s in s int e ring br onz e . I t w a s obser v e d t ha t i n a sint e ring t e mper a ture be twe e n 800 C a nd 1025 C the
disper se d pa rticl e s of Al
2
O
3
re du c e the ra te of sh rinka ge a nd n e c k g ro wth. The S iO
2
pa rticle s re du c e n e c k g ro wth si g nific a ntl y in t he si nter ing p roc e ss.
House man ( 1971) studi e d the e f f e c t of T iO
2
, Al2 O3 a nd Z rO
2
on 7 μ m I ro n powde r . The a mount of the inhi bit or wa s betw e e n .5 – 2 wt% . All t hr e e re du c e d the de nsifica ti on
during sint e rin g . Z r O
2
showe d a be tt e r re t a rda ti on than T iO
2
a nd Al
2
O
3 .

87

7.2. The Inhibition Mechanism in the SIS Process by Dispersion of Second Phase
Metal Oxides
I n the S I S pro c e ss the ob jec ti ve is t o slow down or stop the sint e ring pro c e ss i n the
pr int e d sec ti ons. Our r e se a rc h on br onz e powd e r si nter ing c onfir med the p re vious wor ks
done on the r e ta rda ti on fr om si nter ing f or c oppe r . It wa s obser ve d th a t t he disper sion o f se c ond pha se in e rt pa rticl e s of me tal ox ides in t he br onz e meta l powde r s lo w s down the sint e ring pro c e ss. Th e f ir st i nh ibi tor tha t wa s cho se n to buil d the br onz e pa rts ba se d on the
pr e vious studi e s and e x pe rimen t wa s a lum inum sul fa te .
V a rious tests ha ve b e e n pe rf or med in thi s re se a rc h in or d e r to und e rsta nd the inhi bit ion mec ha nism in the pr e s e nc e of p rinte d sa lt in meta l powde r . S c a nnin g e le c tron
mi c rosc ope (SEM) , En e r g y disper siv e X - ra y a nd X - ra y dif fr a c ti on we r e u se d to e x a mi ne the inter a c ti ons be tw e e n meta l powde r pa rticle s a nd sa lt c r y stals i n the S I S - Meta l proc e ss.
T o e x plain the inhi bit io n phe nomenon a s show n in ou r e x pe rimen tal r e sult s, two inhi bit ion m e c ha nism s a re pr e se nt e d a s follows
(1) S e pa ra ti on of meta l powde rs du e to th e e x pa nsion of s a lt c r y stals int o de c ompos e d pa rticle s
During the SIS-Metal process salt solution is first printed in the selected areas of
metal powder. In the presence of moderate heat the water content of the salt solution
evaporates; hence salt crystals form between the metal powder particles in the printed area.
When the green part is moved to the sintering furnace, in the early stages of sintering, the
inorganic crystal salt, which has high melting temperature, rapidly expands in size when
heated. The expanded crystal salt then starts to decompose at around 500°C [Tagawa, 1984;

88

Apte, et al., 1988; Pelovski, et al., 1992]. The decomposition of aluminum sulfate during
the sintering process is shown as follows:
2 2 3
3 3 2 3 4 2
2 2
3 ) (
O SO SO
SO O Al SO Al
 
 

The decomposed salt particles create a gap in the affected metal powder region at the
boundary due to their volumetric growth in the transformation process. Therefore, the
affected metal powder particles in the printed sections can be prevented from proper
sintering at the sintering temperature of metal powder. To observe the extent of expansion
of aluminum sulfate (our choice of salt) an experiment was performed in isolation from
metal powder. In this experiment with aluminum sulfate it was noticed that salt crystals
decompose and grow rapidly during the heating process. As shown in Figure 7.2 the
volumetric size of the salt sample is almost quadrupled based on the measured dimensions.
F ig u re 7.2. Ex pa nsion of de c ompos e d a lum inum sul fa te ( sa lt ) into a lum inum ox ide
(c e r a mi c ) a s a r e sult of h e a t in g
I t is be li e ve d th a t the ra pid c r y stal e x pa nsion c a uses int e rn a l stre sses in the de c ompos e d s a lt c r y stals . The str e sses e v e ntuall y fr a c ture the c r y stals a n d a t hi g he r he a t fine c e r a mi c pa rticle s st a rt for mi n g . T he fine c e ra mi c pa rticle s c ould th e n a tt a c h to the
meta l powde r p a rticle s in the ne i g hborin g a re a s. O bvious l y , the qu a nti t y o f these c r y stals is
a n im porta nt f a c tor for the e f f e c ti ve ne ss of si nter ing inhi bit ion. De po sit ing a hig h e r

89

a mount of sa lt solut ion mea ns putt ing more c e ra mi c pa rticle s be tw e e n meta l powde r pa rticl e s; he nc e r e sult ing in be tt e r se p a ra ti on . Ho we ve r , too mu c h inhi bit or de posi ti on c a n ne ga ti ve l y im pa c t the r e solut ion of the fa br ica ti on pr oc e ss, be c a use th e sa lt solut ion would
unc ontroll a bl y p e ne tr a te be y ond th e de sire d s e pa r a ti on re g ion.
After sintering a discoloration of the metal surface is observed. This discoloration is
due to metal oxidation. Since sintering happens in an inert environment the oxygen must
come from the decomposition of aluminum sulfate as shown in later in this chapter. This is
also verified by the fact that in SIS part surfaces are always adjacent to thin layers of
aluminum oxide. Both aluminum oxide and the very shallow metal oxide can easily be
removed by sand blasting, after which the surface becomes quite shiny. This proves that
only the part boundary sections near which aluminum sulfate has been printed are oxidized;
the part core which is not affected by decomposition of aluminum sulfate never gets
oxidized.
(2) C e ra mi c c oa ti n g of meta l par ti c le
The second which and the main reason behind the retardation from sintering is the
aluminum Oxide particles pinning to the surface of metal particles. As noted before,
aluminum sulfate starts decomposing at 500
o
C and fully decomposes at around 800
o
C.
Aluminum sulfate decomposes to Al
2
O
3
without the formation of an intermediate material.
The decomposed aluminum oxide is amorphous however in some studies the ϒ-Al
2
O
3
was
obtained. No solid-solid transitions are known and the solid decomposes without melting.
As the temperature rises this salt coating decomposes into aluminum oxide which gives a
near-perfect ceramic coating (Figure 7.4) to the affected metal particles. Since the sintering
temperature of aluminum oxide is much higher than that of bronze powders, the metal

90

bronze particles that are covered with ceramic particles have a slower sintering process
than pure bronze.

F ig u re 7.3. Th e S EM pictur e s of dif fe r e nt sampl e s: ( l e ft) : a me tal powd e r p a rticle be for e
sint e ring ; (r ig ht): a meta l powd e r p a r ti c le tha t is coa ted w it h c e ra mi c

Thermogravimetric test shows that after the sintering process the weight loss of the
decomposed aluminum sulfate is nearly 80% of its original weight. Energy dispersive x-
ray spectroscopy (EDS) analysis has been performed to determine the existence of
aluminum oxide on surfaces of metal powders. It can be shown that the approximate
percentage of aluminum oxide in the metal powder is 4.5 wt% .
As it c a n be s e e n in t he S EM im a g e s whe n sa l t sol uti on (i.e ., a lum inum sul fa te) is
pr int e d on the br onz e me tal powde r the salt c r y sta l g row th c re a tes a mi c ros c opic se pa ra ti on
be twe e n met a l powde r p a rticle s. I t i s h y pothesiz e d that dur ing sint e rin g th e a lum inum sulfa te inhibi tor de c omp oses into alumi num o x id e a nd sulfur diox ide (SO
2
) w he r e the
sulfur diox ide ( SO
2
) e va pora tes a nd a lum inum oxide c oa ts t he a dja c e nt m e tal powde r
pa rticle s. S ince a lum inu m sul fa te ha s a much hi gher melti ng point than th e meta l used it pr e ve nts t he meta l p a rticl e s fr om bondi n g togethe r .

91

F ig u re 7.4 . Dist ributi on o f dif fe re nt ele m e nts i n the pr int e d sec ti ons wit h a l umi num
sulfa te a fte r sinter ing

As the dispersion of aluminum oxide in bronze powder particles succeed in slowing
down the sintering process, the next step was to try different types of inhibitors that
decompose to other ceramics. The next two candidates were dispersion of ZrO
2
and MgO
in the metal powder bed. In order to disperse ZrO
2
particles in the powder bed, zirconium
sulfate (Zr(SO
4
)
3
) solution was used to print into the powder bed. The decomposition of
zirconium sulfate results in the formation of ZrO
2
. There is no intermediate formation
during the decomposition. The decomposition temperature is around 820K. The inhibition
for of bronze by ZrO was also successful during the sintering process. The related SEM
micrograph shows the inhibition of the printed segments from sintering (See Figure 7.7).
CuL SnL
AlK OK

92

F ig u re 7.5. Th e S EM im a g e o f a sint e r e d sample w it h printed a lum inum s ulf a te a nd the
re late d ED S a n a l y sis r e s ult

93

B e fo re sint e rin g Af ter sint e rin g
U ninhi bit e d se c ti on s

Un

Inhibit e d sec ti ons

Figure 7.6. SEM micrograph (a): a sample that is unsintered and without salt; (b): a
sample that is sintered and without salt; (c): salt crystals are embedded in a
sample that is unsintered and with salt; (d): metal powder particles are
covered by ceramic particles

Figure 7.7. Retardation from sintering by ZrO
2
Bonding
Salt Crystal Aluminum Oxide

94

Figure 7.8. The SEM image using zirconium sulfate as an inhibitor of a sintered bronze
sample and the related EDS point analysis result in the inhibited section on
covered bronze particles

Figure 7.9. The SEM image using zirconium sulfate as an inhibitor of a sintered bronze
sample and the related EDS point analysis result in the inhibited section on
non-covered bronze particles

95

In the EDS point analysis it is clearly shown that the particles covering the bronze
powder particles are ZrO
2
which prevents the particles from bonding. The other inhibitor
that was chosen for this process was magnesium sulfate (MgS0
4
)
.
During the sintering
process magnesium sulfate begins to decompose to MgO directly without an oxysulfate
intermediate. The initial decomposition temperature was observed to be close to 1170 K.

Figure 7.10. Retardation from sintering by MgO

Figure 7.11. The SEM image using magnesium sulfate as an inhibitor of a sintered bronze
sample and the related EDS analysis

96

7.3. SIS Process with Dispersed Carbon Particles as Inhibitor
In this experiment sucrose (water-soluble crystalline carbohydrates with a formula
of C
n
H
2n
O
n
) was used as the inhibitor. The inhibitor used in this experiment is sugar
(C
12
H
22
O
11
). The inhibitor solution is achieved by dissolving 100 grams of C
12
H
22
O
11

anhydrous in 100 ML of water at room temperature and 100 ML of isopropyl alcohol is
added to the mixture to reduce the surface tension of the liquid for ease of printing.
During sintering Sugar starts to decompose at 185
o
C and fully decomposes at
around 820
o
C which is the maximum sintering temperature used in the experiments. The
decomposition reaction for sugar is shown below:

The carbon left behind gives a carbon coating to the affected metal particles. Carbon
particles are spread uniformly on the metal powder and slows down the surface diffusion
and grain boundary diffusion during the solid phase sintering process.
Non-printed sections Printed sections

Figure.7.12. SEM micrograph of printed and non-printed sections with sugar

2 2 2 11 22 12
12 zCO yC O H xO O H C    

97

F ig u re 7.13. Dist ributi on of dif fe re nt ele m e nt s in t he printed se c ti ons with s uc rose a fte r
sint e ring

Figure 7.14. EDS analysis of the printed sections by sucrose
CuL SnL
CK OK

98

Figure 7.15. EDS point analysis on small carbon particles pinned to the surface of bronze
In the printed sections with sugar during the sintering process the sugar
decomposes to carbon particles during the sintering cycle which As it can be seen from
Figures 7.13 through 7.15. The carbon particles pin to the surface of the bronze and retard
the sintering process. In order to make sure no intermediate compound have been made
during the sintering process a set of XRD analysis was done on the printed and non-printed
sections. C a rbon pa rticle s a re a morphous a nd c a n ’t be de te c ted b y th e X-Ray difractometer
but metal-carbon compounds can be detected. In order to make sure no metallic
compounds have been formed in the printed segments, it is sufficient to compare the X-
Ray diagrams for the printed and non-printed segments. Since the sintering happens in a
vacuum environment there are no other outside elements involved in the metallic
compound. The specimen thickness was 1 mm and the following setting was used for the
X-Ray diffractometer:
Start angle: 14 degree; End angle: 75 degree; Sampling step: 0.05 degree;
Scanning speed: 1 degree/minute; Repeat: 2 cycles

99

Figure 7.16. X-Ray diffractometer used in the SIS analysis

Figure 7.17. XRD of printed sections with aluminum sulfate after sintering

100

Figure 7.18. XRD diagram of pure bronze after sintering (Non-printed section)

Figure 7.19. XRD of printed sections with sucrose after sintering (printed sections)

101

After comparing the XRD results for sugar as an inhibitor in bronze (Figures 7.18
and 7.19), it was noted that the peaks in both printed and non-printed sections remain the
same. It can be concluded that there is no intermediate metallic compounds in the printed
sections and what is left is dispersed carbon particles being pinned to the surface of bronze.
In the XRD results for aluminum sulfate as an inhibitor on bronze, there is a high chance
that the compound Aluminum Copper Tin (Al
0.05
Cu
0.9
Sn
0.05
) is formed during sintering in
the printed sections.
Between all the inhibitors used so far dispersed carbon particles, which are the
product of decomposed sucrose, performs the best inhibition in the printed sections. In
order to compare the inhibition effect between different inhibitors, surface hardness test
was used as a criteria to compare different inhibitors with one another. This criterion is
very useful because the printed sections must be removed by sand blasting and the lower
the surface hardness the easier the printed segments can be removed.
The best inhibitors that showed success in the experiments were Aluminum Sulfate
(Al2(SO4)
3
), magnesium sulfate (MgS0
4
), zirconium sulfate (Zr(SO
4
)
3
) and sucrose. To
run the comparison test between different inhibitors, droplets with a volume of 34 mm
3
of
each solution were deposited on one layer of bronze powder. All the solutions where
diluted to half the saturation point. Between all these inhibitors sucrose (dispersed carbon)
particles showed the best results.
S olubi li t y of the inhi bit or s pl a y s a si g nific a nt role in t he inhi bit ion m e c ha nism .
Ac c or din g to equ a ti on ( 𝐹 ) w he re N a re the numbe r of pa rticle s pe r sur f a c e a re a , th e more p a rticle s p e r sur f a c e a re a the mor e dr a g pre ssu re will be on t he br onz e surf a c e to adva n c e durin g the sint e rin g me c ha nis m.

102

Figure 7.20. Surface hardness comparison between different inhibitors
It is observed that dispersed carbon particles (which are the result of decomposed
sucrose) on bronze shows the best retardation from sintering. The next step is to study the
effect of sintering on the inhibited sections for different sintering settings and compare the
characteristics with non-printed regions of sintered parts. Surface hardness, shrinkage,
yield Strength and the X/D ratio are the factors that have been measured at different
settings.
7.3.1 Design of Experiment for the Inhibition Mechanism
The printed sample used in our settings is shown in Figure 7.21. The sample total
length is 34.5 mm and the thickness is 1.1 mm.

Figure 7.21. Printed sample used in the mechanical property test

Aluminum
Sulfate (
Al2O3)
Aluminum
Nitrate (
Al2O3)
Zirconium
Sulfate(
ZrO2)
Magnesiu
m
Sulfate(M
gO)
Sucrose(
C )
Inhibitor 72 72 71 77 70
Pure Bronze 80 80 80 80 80
72 72
71
77
70
80 80 80 80 80
60
62
64
66
68
70
72
74
76
78
80
Hardness (HRB)
Hardness test of different inhibitors on
bronze
Inhibitor
Pure Bronze

103

Table 7.1. Mechanical properties of the printed segments with sucrose after sintering

Temperature-
time
Shrinkage
Surface
Hardness(HRB)
X/D ratio
Yield strength
(Mpa)
Non-
Inhibit
Inhibit
Non-
Inhibit
Inhibit
Non-
Inhibit
Inhibit
Non-
inhibit
Inhibit
770-0hr 1.2% 1.1% 76 73
11/29.7
=.37
< 0.2 50 33
770-1hr 4.1% 2% 82 80
16.1/38.
4 =.41
11/45=
0.24
65 35
770-2hr 5.9% 3.7% 84 82
11.7/24.
6=.47
11/32=
0.37
80 36
810-0hr 1.8% 1.3% 80 75
15.4/31.
3=.49
< 0.3 64 40
810-1hr 6.1% 3.7% 88 82
14/27.3
=.51
13/33=
0.39
103 84
810-2hr 7.9% 4.9% 93 84
17.4/29
= 0.59
11/26=
0.42
110 88

In table 7.1 the sintering rate (Shrinkage and X/D ratio) and the mechanical
property (Surface hardness and Yield Strength) is shown for non- printed sections which is
highlighted in yellow. In the next sections several empirical models will be developed to
model the behavior of sintering rate and mechanical properties as a function of sintering
time and sintering temperature. These models become important when it is compared to
the empirical models developed in the previous chapter for non-printed sections.

104

Tempera
ture-
Time
SEM micrograph for neck growth
770-0Hr

770-1Hr

770-2Hr

Figure 7.22. Neck growth for printed sections in different temperature and time settings
during the sintering process

105

810-1Hr

810-2Hr

Figure 7.22. Continued
In order to identify the significant factors during sintering in the shrinkage of the
printed sections a linear regression model has been defined below:
The regression equation is
Shrinkage of printed section = - 0.192 + 0.000258 Temperature + 0.0155 Time
The chosen confidence level for this regression model is 95%.

106

Time
Temperature
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
0.0396 0.0428
0.0428 0.0460
0.0460
0.0140
0.0140 0.0172
0.0172 0.0204
0.0204 0.0236
0.0236 0.0268
0.0268 0.0300
0.0300 0.0332
0.0332 0.0364
0.0364 0.0396
Printed-Shrinkage
Contour Plot of Printed-Shrinkage vs Temperature, Time

Figure 7.23. Contour plot of shrinkage for the printed sections Vs. Temp. and Time
Table 7.2. ANOVA table for linear regression model for shrinkage for the printed sections
Predictor Coef SE Coef T P
Constant -0.19175 0.07197 2.66 0.076
Temperature 0.00025833 0.00009103 2.84 0.066
Time 0.015500 0.002230 6.95 0.006
S = 0.00445970 R-Sq = 94.9% R-Sq(adj) = 91.6%

Analysis of Variance
Source DF SS MS F P
Regression 2 0.00112117 0.00056058 28.19 0.011
Residual Error 3 0.00005967 0.00001989
Total 5 0.00118083

As it is shown in Table 7.2 and Figure 7.22 the p-value for time is less than 5%
indicating that time is significant and the p-value for temperature is greater than 5 %
indicating that temperature is insignificant in this analysis. It should be noted that
temperature is insignificant for the range of 770-810.
Since shrinkage exponentially decreases when time increases the next step is to
find the best fitted value based on an exponential function. The function that was chosen

107

for this purpose is an asymptotic regression (concave) function shown in the equation
below:
Shrinkage = Theta1 - Theta2 * Exp ( - Theta3 * Time )
Where theta1, theta2 and theta3 are constant values which will be defined by regression
analysis. In order to have a concave function the following conditions must hold:
Theta2 > 0 & Theta3 > 0
In order to fit the model, Gauss-Newton algorithm is used to find the best fit.
Shrinkage of printed section = 0.148125 - 0.136125 * Exp (-0.129212 * Time)
Table 7.3. ANOVA table for the exponential fitted model for shrinkage of printed sections
Iterations 17
Final SSE 0.0002185
DFE 3
MSE 0.0000728
S 0.0085342

2.0 1.5 1.0 0.5 0.0
5.00%
4.00%
3.00%
2.00%
1.00%
Time
Printed-Shrinkage
Fitted Line Plot
Printed-Shrinkage = 0.148125 - 0.136125 * exp(-0.129212 * Time)

Figure 7.24. Fitted non-linear curve for shrinkage of the printed segments

108

The exponential fit for shrinkage in the printed sections gives a very low mean square of
error which is equal to 0.00007. Therefore the empirical model shown in Figure 7.24 is a
reasonable choice to represent the shrinkage in the printed sections. It should be noted that this
model is dependent on time because as it was pointed out earlier time is the most significant factor
in shrinkage
One important factor to consider in the SIS-metal is the difference of shrinkage between
the printed and non-printed sections, as shown in figures 7.25 and 7.26. It is observed that the
shrinkage difference increases with the increase of sintering time and temperature. This difference
of shrinkage improves the separation process which is a favorable condition for SIS.

Figure 7.25. Shrinkage between the printed and non-printed sections

109

Figure 7.26. Shrinkage difference between the printed and non-printed sections
Table 7.4 ANOVA table for the linear regression fit for hardness of printed sections
Predictor Coef SE Coef T P
Constant 35.33 26.90 1.31 0.280
Temperature 0.05000 0.03402 1.47 0.238
Time 4.5000 0.8333 5.40 0.012
R-S = 1.66667 R-Sq = 91.3% R-Sq(adj) = 85.4%

Analysis of Variance
Source DF SS MS F P
Regression 2 87.000 43.500 15.66 0.026
Residual
Error
3 8.333 2.778
Total 5 95.333

110

Time
Temperature
2.0 1.5 1.0 0.5 0.0
810
800
790
780
770
>
–
–
–
–
–
–
–
–
–
–
<
81.5 82.5
82.5 83.5
83.5
73.5
73.5 74.5
74.5 75.5
75.5 76.5
76.5 77.5
77.5 78.5
78.5 79.5
79.5 80.5
80.5 81.5
Printed-Hardness
Contour Plot of Printed-Hardness vs Temperature, Time

Figure 7.27. Contour plot of hardness on printed sections vs. Temperature and time
Since hardness decreases exponentially as time increases, the next step is to find
the best fitted value based on an exponential function. The function that was chosen for
this purpose is an asymptotic regression (concave) function which is shown in the
following equation:
Hardness=Theta1 - Theta2 * Exp ( - Theta3 * Time )
For the equation above, Gauss-Newton algorithm is used to find the best fit.
Hardness of printed sections = 83.8 - 9.8 * Exp (-1.25276 * Time)
Table 7.5 ANOVA table for the exponential fit for the hardness on the printed sections
Iterations 7
Final SSE 6
DFE 3
MSE 2
S 1.41421

111

2.0 1.5 1.0 0.5 0.0
84
82
80
78
76
74
72
Time
Printed-Hardness
Fitted Line Plot
Printed-Hardness = 83.8 - 9.8 * exp(-1.25276 * Time)

Figure 7.28. Exponential fit for hardness in the printed sections

Figure 7.29. Hardness for printed and non-printed segment

112

Figure 7.30. Hardness difference between the printed and non-printed sections
The exponential fit for hardness of printed sections gives an acceptable mean square of
error of 2. Therefore the empirical model shown in Figure 7.28 is a reasonable choice to represent
the hardness of the printed sections. It should be noted that this model is dependent on time
because as mentioned earlier time is the most significant factor in hardness.
Another important factor to consider besides shrinkage is the difference of hardness
between printed and non-printed sections, which is shown in Figures 7.29 and 7.30.
It was observed that at higher temperatures and longer sintering durations the
difference of hardness between the printed and non-printed sections increases which is
shown in Figure 7.29. This is a very useful phenomenon in the SIS process. Because
difference of hardness helps the separation process. If the difference is very low it is hard
to adjust the sand blasting machine to only remove the printed sections and not remove the
non-printed sections. The higher the difference of hardness, the easier it is to adjust the
sand blaster and remove the printed sections and leave the non-printed sections unaffected.

113

Theoretically, it is obvious that the hardness rate of increase decreases as the
sintering temperature increases. This is because of the fact that during sintering there is a
reduction in the surface area. When the surface area is reduced the number of dispersed
carbon particle per surface area increased and according to the formula ( 𝐹 )
the drag force is increased and consequently the sintering rate drops. This confirms our
empirical results that the difference between the printed and non-printed sections increases
with sintering time.
7.3.2 Micro-Tensile Test for the Printed Sections
A micro-tensile test similar to the micro-tensile test for non-printed sections was
carried out for the printed sections under the same conditions. The results of the Stress-
Strain diagram are shown in Figures 7.31 through 7.35.

Figure7.31. Micro-Tensile test for printed sect ions sint e re d a t 810 C f or 2 h our s
0
20
40
60
80
100
120
140
160
180
0 0.05 0.1 0.15 0.2 0.25
Stress(Mpa)
Strain
Stress-Strain diagram for printed and
non-printed segments sintered at 810 °C
for 2 hours
Serie
s2
Serie
s1
Printed
Non-printed

114

Figure 7.32. Micro-Tensile test for printed sect ions s int e re d a t 810 C f or 1 hour

Figure 7.33. Micro-Tensile test for printed sect ions s int e re d a t 810 C f or 0 hour
0
20
40
60
80
100
120
140
160
0 0.05 0.1 0.15 0.2 0.25 0.3
Stress(Mpa)
Strain
Stress-Strain diagram for printed and non-
printed segments sintered at 810 °C for 1
hour
Serie
s1
Serie
s3
printed
Non-printed
0
20
40
60
80
100
120
0 0.02 0.04 0.06 0.08 0.1
Stress(Mpa)
Strain
Stress-Strain diagram for printed and non-
printed segments sintered at 810 °C for 0
hour
Series
1
Series
3
Printed
Non-printed

115

Figure 7.34. Micro-Tensile test for printed sect ions s int e re d a t 770 C f or 2 hours

Figure 7.35. Micro-Tensile test for printed sect ions s int e re d a t 770 C f or 0 hour

0
10
20
30
40
50
60
70
80
90
0 0.02 0.04 0.06 0.08 0.1
Stress(Mpa)
Strain
Stress-Strain diagram for printed and
non-printed segments sintered at 770 °C
for 2 hours
Series1
Series3
Printed
Non-printed
0
10
20
30
40
50
60
0 0.02 0.04 0.06 0.08 0.1
Stress(Mpa)
Strain
Stress-Strain diagram for printed and non-
printed segments sintered at 770 °C for 0
hour
Seri
es1
Seri
es3
Printed
Non-printed

116

As it can be seen from the tensile test results, there is a significant decrease in the
printed sections and this difference will increase with sintering time. However, the results
are not very accurate due to the fact that there are lots of pores, grain boundary defects and
micro cracks in the printed sections. Under tensile test these defects cause the failure of the
printed samples under the tensile test faster than non-printed samples.
It can be concluded that with an increase of time the hardness and shrinkage which
are an indication of sintering rate increase. It was shown that hardness can be fitted in an
exponential function (hardness of printed sections = 83.8 - 9.8 * Exp (-1.25276 * Time)).
Therefore the inhibitor can also be used as a binder in higher temperatures to build parts
with the same process as 3D printing. The sample parts shown in Figure 7.36 are sintered
at 810 C f or 2 hour s using the sucrose inhibitor as a binder.

Figure 7.36. Sample parts built by the SIS machine using the inhibitor as a binder

117

Chapter Eight: Effect of Droplet on Powder Bed
In this chapter the interaction between the inhibitor and the metal powder bed in the
printing stage is studied. The inhibitor is printed on the powder bed in form of droplets
leaving a single nozzle solenoid valve.
8.1 Droplet Properties
For printing the inhibitor, a Micro-Dispense valve was used as a single nozzle
printer. This nozzle is actually an electro-magnetic solenoid valve but can operate at high
frequency (between 200 Hertz to 1000 Hertz). These valves provide high-speed control for
very small volumes of liquids (less than 100 nanometer droplets). The droplet sizes
generated by inkjet printers are in nano-liter range (0-300 Nano-liters).
It was observed that higher frequency and voltage are needed for inhibitor solutions
with higher surface tension, otherwise either there is no droplet generation, or liquid
accumulates at the outlet of the nozzle as a growing droplet .Since the inhibitor that was
used has a higher viscosity than water, the diagram given by The Lee Company was not
reliable and a set of experiments was conducted to determine the droplet size per pulse.
The minimum feature size in the SIS process is limited by the dimension of the line
formation and the dimensions of a single droplet. The dimensional accuracy is defined by
the variation of the line dimension and the single droplet. The droplet size for every droplet
is shown in Figure 8.1. Even though lower pulse duration results in a smaller droplet size,
it should be noted that based on experimental observations the most reliable range is 9-8
psi with pulse duration of 5 milliseconds.

118

Figure 8.1 Droplet size per pulse duration for the Solenoid valve
It was observed that the pulse duration does not change the speed of the droplet
coming out of the nozzle but the pressure has a significant effect on the speed of the
droplet coming out of the nozzle.

Figure 8.2 Velocity of the droplet after the nozzle head
Since the distance between the nozzle and the powder bed is 3 mm, the velocity
impact of the powder bed can be assumed to be the same as the velocity of the droplet
4.8
15.4
26
8.1
29
50
0
10
20
30
40
50
60
0 2 4 6
Per Pulse
Dispense
Volume
(Nanoliters)
Solenoid valve pulse duration (Miliseconds)
Pressure ( 5 psi)
Pressure ( 9 Psi)
2.03
2.51
3
0
0.5
1
1.5
2
2.5
3
3.5
4 5 6 7 8 9 10
Velocity
(m./sec.)
Pressure (psi)
Velocity of the droplet ( m/sec.)
Velocity of the
droplet ( m/sec.)

119

leaving the nozzle. However, if the distance is considerably large considering the drag
force on the particle, the velocity can be calculated from the following equation which
a work was done by Duchamp, T.:

.

(

.

)
.

In our setting the following properties for the droplet holds:
ρ= 1470 gr / L it e r (The density of the inhibitor)
m=Droplet mass=0.000047 gr
V
0
=3 m/sec.
G=9.8 m/sec.
2
K=drag coefficient
8.1 Droplet Penetration on Powder Bed
After the droplet hits the powder bed due to the velocity of the droplet and the low
compaction of the loose powder, there is a cutting effect that makes the powder go
down and penetrate into the powder bed. Fan (1995) developed a model for the impact
penetration of a droplet penetrating the loose powder bed which is a very good fit for
the SIS process. The model is shown below:

𝐹
Where:
m(z): The mass of the droplet and powder together
Z: Depth of cutting
t: Time
F(Z): Resisting force of the droplet

120

ρ
b
: The density of the powder bed
A
p
: Depending on the geometry of the droplet-powder mixture
Agglomeration phenomena in the SIS process is the binding between metal powder
particles (bronze powder) by the inhibitor (which also acts as a binder to keep the powder
particles together) to form a large porous structure.
When the droplet hits the powder bed, it is absorbed by the powder bed due to capillary
forces. Schaafsma (2000) proposed a model for the saturation (S), and growth time (t)
shown below:

∫

ε: P or osit y
R
d
: Droplet radius
R
a
: Agglomerate radius
K: Absolut permeability
K
rl
: Relative permeability depending the liquid saturation of a porous structure
∆P: Capillary pressure gradient
η : L iqui d d y na mi c viscos it y
In order to observe the effect of the printed inhibitors on the metal powder bed several
experiments were conducted as follows:
The first step was to observe the cutting effect on the metal powder bed. Cutting effect
is the penetration depth of the primitive pellet structure formed by a droplet with particles
from the bed. In Figure 8.3 the cutting effect of the droplets on the powder bed has been

121

measured and studied. As shown in Figure 8.3 the printed droplets push down the powder
approximately 0.22 mm. The cutting distance depends on: a) the velocity of the droplet
when is hitting the powder bed, b) the volume of the droplet and c) the bed density of the
powder bed. The next issue to be studied is the formation of lines during printing. A set of
experiments was carried out to find the optimum setting for printing the inhibitor. The
variables that were studied are the frequency of the nozzle which defines the volume of the
droplets, the printing speed of the nozzle and the pressure of the solenoid valve which
defines the speed of the droplets. The results are shown in Figure 8.4.

Figure 8.3 The cutting effect of printed lines on the powder bed
In Figure 8.4 the distance between the droplets were measure and it was observed
that the best settings for printing was with frequency 1000, pressure 10 psi and speed.
200Several observations can be made from this experiment. It can be seen that the droplet
size decreases as the frequency increases. As for printing continuous lines the lower the
speed the better the result will be, but the thickness of the line will become an issue if
nozzle movement is too low.
Cutting effect
One layer

122

Figure 8.4 Printing one layer of inhibitor with different nozzle settings
The best reliable setting that was chosen was for printing the inhibitor is the
following setting:
Droplet size: 50 Nano-liters
Nozzle speed: 20 mm/sec
Pulse duration: 5 Miliseconds
Speed of the droplet leaving the nozzle: 3 m/sec.
With the setting shown above the line formation achieved during the SIS process is
shown in Figure 8.5. The line formation in the printed layers is a good measure for surface
smoothness of the final part. One observation that was made is that if the lines overlap for
a value of 50% the surface smoothness increases. In other words if the line thickness is .7
mm and the distance between the lines are .35mm which is shown in figure 8.6 a more
precise surface smoothness can be achieved.
Pressure
(psi)
Low frequency 200 High frequency 1000

10

9

8

7

Nozzle
speed
mm/sec
50 40 30 20 50 40 30 20

123

Figure 8.5. Line formation during the SIS process (The line thickness is .7 mm)

Figure 8.6. Line formation during the SIS process (The line thickness is .7 mm and the
distance between the lines are .35 mm)

Another important aspect of the process is the boundary between the printed and non-
printed sections. In order to study this phenomenon, SEM micrographs were taken from
printed sections. As it can be seen in Figure 8.7 due to the difference between shrinkage
rates of the printed and non-printed sections a gap of approximately 30µm has been
observed. This phenomenon helps in the separation process during the removal of the
printed sections from the fabricated parts. Note that similar observations were made during
line formation between printed and non-printed sections as shown in Figure 8.10.

124

Figure 8.7 SEM micrograph of a sample droplet formation and its related measurements
If printed lines are not continuous, then each isolated droplet creates a void in the
final part yielding a highly porous part as shown in Figure 8.8. This highly porous parts
with a porosity of 50% can be used in applications such as dampers, capacitors, bearings,
filters, Battery Electrodes, sound absorbers, permeators, foam, mechanical spacers and any
other application that requires a low densification. Uniformly porous part can be achieved
by the SIS process. The dimension of the pores has been shown in the Figure 8.9. The
pores where achieved by spreading uniform discontinuous droplets of the inhibitor along
the powder bed.

125

Figure 8.8. A porous part that was made by SIS

Figure 8.9. The pores have a uniform pore size between 500-600 micron
Inhibitor deposition plays the most important role in the geometrical accuracy of
parts fabricated by the SIS process. As it can be seen in Figure 8.11, with the improved
settings, fine features and smooth surface can be fabricated by SIS. However the limitation
of the solenoid valve in dispensing finer droplets of inhibitor solution prevented the
fabrication of parts with higher resolution.

126

Figure 8.10. Separation between the printed line sections and the metal powder

Printed line
Bronze
powder
Gap due to a
difference in
shrinkage rate
Printed line

127

Figure 8.11. Samples made by the SIS process with the optimized printer setting
As it can be seen from Figure 8.11 the fabricated parts have been improved by
implementing the optimum settings that was discussed earlier. The following settings were
used in the fabrication of the parts shown in Figure 8.11.
Inhibitor droplet size: 50 Nano-liters
Nozzle speed: 20 mm/sec
Pulse duration: 5 Miliseconds
Speed of the droplet leaving the nozzle: 3 m/sec.
Sintering temperature: 780 C
Sintering duration: 10 minutes

128

Chapter Nine: Conclusion and Future Work
Our preliminary results have established that the SIS concept based on microscopic
mechanical inhibition for metallic powders is feasible. In summary the SIS-Metal process
based on the microscopic mechanical inhibition for bronze was studied in this research.
The factors affecting the process were identified and the effect of each factor on the
process was studied. Several empirical models for the effect of temperature and time on
loose powder sintering were developed and analyzed. Several inhibitors were tested and
the inhibition mechanism was studied. Several empirical models were developed as well to
model the effect of the inhibitor on the sintering parameters.
9.1 Future Work
There are several improvements that can be made for the SIS-Metal process which
is explained in the following:
1. Currently a single nozzle solenoid valve is used for printing the inhibitor.
Accordingly the lines on the parts (surface quality) are relatively coarse. By
implementing other commercial processes such as 3DP, improving the nozzle
resolution can lead to drastically better surface quality.
2. The choice of inhibitor is based on retardation from sintering by dispersion of
second phase metal oxides which is a result of decomposed salt particles. Not all
types of second phase metal oxides were tested. There is a high chance that a better
choice of inhibitor can be found by testing more chemicals.
3. Currently the separation between the printed and non-printed sections is carried out
by a fixed speed sand blaster. However several other mechanisms for separation
can be studied such as bead blasting, chemical reaction and heat shock.

129

4. Fabrication of titanium parts is another future work for this research. This research
was focused on bronze but a few preliminary studies were carried out on titanium
as well. For titanium parts the powder that was selected is pure (99.9%) titanium
with a -100/325 mesh size. Both sucrose and aluminum sulfate with the same
composition that was used for bronze powder were used for titanium powder as
inhibitor. The SEM images of the titanium powder with and without salt/Sucrose,
and also before and after sintering are shown in Figures 9.1 through 9.4. Based on
these SEM images it can be observed that the decomposition of salt crystals and
sucrose plays an essential role in preventing metal particles from being properly
fused in the course of sintering.

Figure 9.1. Initial stage sintering (left) and final stage of sintering (right) for titanium

Figure 9.2. Printed aluminum sulfate (left) and Sucrose (right) on titanium powder before
sintering
Aluminum Sulfate
salt crystals
Sucrose (carbohydrate)
crystals

130

Figure 9.3. Decomposed Aluminum Sulfate (Left) and Sucrose (Right) on titanium powder
after sintering

Figure 9.4. Two sample titanium parts that was used for testing
5. Fabrication of steel parts is another future work for this research. Preliminary
results showed success in 440C and diffused alloy Steel (Fe-Ni-C) powder with a -
100/325 mesh size. Separation with Aluminum Sulfate showed success in diffused
alloy steel. However two stage of sintering is necessary for this process. The first
stage is for removing the printed sections from the non-printed sections which
requires a lower duration of sintering and the second stage is carried out to improve
the pa rt’ s mec h a nica l p ro pe rt y .

Figure 9.5. Loose powder sintered 440C (right) diffused alloy Steel (Fe-Ni-C) (left)

131

Figure 9.6. Initial and intermediate stage sintering stage for 440C stainless Steel powder
(left) and intermediate stage sintering stage for irregular shaped diffused
alloy Steel (Fe-Ni-C) powder (right)

132

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136

Appendix A: The DOE Results
Minitab results from our DOE for the four parameters T1, t1, T2 and t2 are written
below:
Regression model for surface hardness:
Surface hardness = 2.875 + 0.0958333 Temperature - 44.125 Time + 0.0625
Temperature*Time
Coefficients
Term Coef SE Coef T P
Constant 2.8750 36.8137 0.07810 0.945
Temperature 0.0958 0.0466 2.05718 0.176
Time -44.1250 28.5158 -1.54739 0.262
Temperature*Time 0.0625 0.0361 1.73205 0.225
Summary of Model
S = 1.44338 R-Sq = 97.70% R-Sq(adj) = 94.24%
PRESS = 56.25 R-Sq(pred) = 68.89%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 176.667 176.667 58.8889 28.2667 0.034362
Temperature 1 60.167 8.817 8.8167 4.2320 0.175939
Time 1 110.250 4.988 4.9884 2.3944 0.261843
Temperature*Time 1 6.250 6.250 6.2500 3.0000 0.225403
Error 2 4.167 4.167 2.0833
Total 5 180.833
Regression Equation
Shrinkage = -0.146583 + 0.000208333 Temperature - 0.11125 Time + 0.000175
Temperature*Time
Coefficients
Term Coef SE Coef T P
Constant -0.146583 0.201099 -0.728912 0.542
Temperature 0.000208 0.000254 0.818683 0.499

137

Time -0.111250 0.155770 -0.714192 0.549
Temperature*Time 0.000175 0.000197 0.887808 0.468
Summary of Model
S = 0.00788458 R-Sq = 96.39% R-Sq(adj) = 90.97%
PRESS = 0.0016785 R-Sq(pred) = 51.23%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 0.0033177 0.0033177 0.0011059 17.7891 0.053691
Temperature 1 0.0003527 0.0000417 0.0000417 0.6702 0.498997
Time 1 0.0029160 0.0000317 0.0000317 0.5101 0.549212
Temperature*Time 1 0.0000490 0.0000490 0.0000490 0.7882 0.468312
Error 2 0.0001243 0.0001243 0.0000622
Total 5 0.0034420
Regression Equation
Shrinkage = -0.146583 + 0.000208333 Temperature - 0.11125 Time + 0.000175
Temperature*Time
Coefficients
Term Coef SE Coef T P
Constant -0.146583 0.201099 -0.728912 0.542
Temperature 0.000208 0.000254 0.818683 0.499
Time -0.111250 0.155770 -0.714192 0.549
Temperature*Time 0.000175 0.000197 0.887808 0.468

Summary of Model
S = 0.00788458 R-Sq = 96.39% R-Sq(adj) = 90.97%
PRESS = 0.0016785 R-Sq(pred) = 51.23%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 0.0033177 0.0033177 0.0011059 17.7891 0.053691
Temperature 1 0.0003527 0.0000417 0.0000417 0.6702 0.498997
Time 1 0.0029160 0.0000317 0.0000317 0.5101 0.549212

138

Temperature*Time 1 0.0000490 0.0000490 0.0000490 0.7882 0.468312
Error 2 0.0001243 0.0001243 0.0000622
Total 5 0.0034420
General Regression Analysis: Printed-Shrinkage versus Temperature, Time
Regression Equation
Printed-Shrinkage = -0.093 + 0.000133333 Temperature - 0.08325 Time +
0.000125 Temperature*Time

Coefficients
Term Coef SE Coef T P
Constant -0.0930000 0.106187 -0.87581 0.473
Temperature 0.0001333 0.000134 0.99228 0.426
Time -0.0832500 0.082252 -1.01213 0.418
Temperature*Time 0.0001250 0.000104 1.20096 0.353

Summary of Model
S = 0.00416333 R-Sq = 97.06% R-Sq(adj) = 92.66%
PRESS = 0.000468 R-Sq(pred) = 60.37%

Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 0.0011462 0.0011462 0.0003821 22.0417 0.043712
Temperature 1 0.0001602 0.0000171 0.0000171 0.9846 0.425633
Time 1 0.0009610 0.0000178 0.0000178 1.0244 0.418009
Temperature*Time 1 0.0000250 0.0000250 0.0000250 1.4423 0.352702
Error 2 0.0000347 0.0000347 0.0000173
Total 5 0.0011808

139

0.0050 0.0025 0.0000 -0.0025 -0.0050
99
90
50
10
1
Residual
Percent
0.05 0.04 0.03 0.02 0.01
0.004
0.002
0.000
-0.002
Fitted Value
Residual
0.004
0.003
0.002
0.001
0.000
-0.001
-0.002
-0.003
2.0
1.5
1.0
0.5
0.0
Residual
Frequency
6 5 4 3 2 1
0.004
0.002
0.000
-0.002
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Printed-Shrinkage

Nonlinear Regression: Printed-Shrinkage = Theta1 - ...
Method
Algorithm Gauss-Newton
Max iterations 200
Tolerance 0.00001

Starting Values for Parameters
Parameter Value
Theta1 1
Theta2 2
Theta3 3
Equation
Printed-Shrinkage = 0.148125 - 0.136125 * exp(-0.129212 * Time)
Parameter Estimates
Parameter Estimate SE Estimate
Theta1 0.148125 0.889067

140

Theta2 0.136125 0.886932
Theta3 0.129212 0.958311
Printed-Shrinkage = Theta1 - Theta2 * exp(-Theta3 * Time)
Lack of Fit
The number of distinct predictor combinations equals the number of parameters,
so there are no degrees of freedom for lack of fit.
Minitab cannot do the lack of fit test based on pure error.
Summary
Iterations 17
Final SSE 0.0002185
DFE 3
MSE 0.0000728
S 0.0085342
Regression Equation
Printed-Hardness = 35.3333 + 0.05 Temperature + 4.5 Time - 5.42004e-017
Temperature*Tim
Coefficients
Term Coef SE Coef T P
Constant 35.3333 52.0625 0.678672 0.567
Temperature 0.0500 0.0659 0.758947 0.527
Time 4.5000 40.3274 0.111587 0.921
Temperature*Time -0.0000 0.0510 -0.000000 1.000

Summary of Model
S = 2.04124 R-Sq = 91.26% R-Sq(adj) = 78.15%
PRESS = 112.5 R-Sq(pred) = -18.01%
Analysis of Variance
Source DF Seq SS Adj SS Adj MS F P
Regression 3 87.0000 87.0000 29.0000 6.96000 0.12821
Temperature 1 6.0000 2.4000 2.4000 0.57600 0.52713
Time 1 81.0000 0.0519 0.0519 0.01245 0.92134
Temperature*Time 1 0.0000 0.0000 0.0000 0.00000 1.00000

141

Error 2 8.3333 8.3333 4.1667
Total 5 95.3333
Nonlinear Regression: Printed-Hardness = Theta1 - Theta2 * exp(-Theta3 * Time)
Method
Algorithm Gauss-Newton
Max iterations 200
Tolerance 0.00001

Starting Values for Parameters
Parameter Value
Theta1 1
Theta2 2
Theta3 3

Equation
Printed-Hardness = 83.8 - 9.8 * exp(-1.25276 * Time)
Parameter Estimates
Parameter Estimate SE Estimate
Theta1 83.8000 2.26310
Theta2 9.8000 2.40865
Theta3 1.2528 0.82685
Printed-Hardness = Theta1 - Theta2 * exp(-Theta3 * Time)
Lack of Fit
The number of distinct predictor combinations equals the number of parameters,
so there are no degrees of freedom for lack of fit.
Minitab cannot do the lack of fit test based on pure error.
Summary
Iterations 7
Final SSE 6
DFE 3
MSE 2
S 1.41421

142

Factorial Fit: Hardness, shrinkage

* NOTE * Data in the worksheet do not appear to match the center point column.
* NOTE * This design has some botched runs. It will be analyzed using a
regression approach.

Factorial Fit: Hardness versus Temp1, Time1, Temp2, Time2
Estimated Effects and Coefficients for Hardness (coded units)
Term Effect Coef SE Coef T P
Constant 64.375 5.822 11.06 0.002
Temp1 -3.375 -1.687 2.911 -0.58 0.603
Time1 -0.750 -0.375 2.911 -0.13 0.906
Temp2 4.125 2.063 2.911 0.71 0.530
Time2 1.125 0.563 2.911 0.19 0.859
Temp1*Time1 4.625 2.313 2.911 0.79 0.485
Temp1*Temp2 -0.000 -0.000 2.911 -0.00 1.000
Temp1*Time2 2.000 1.000 2.911 0.34 0.754
Time1*Temp2 2.125 1.063 2.911 0.37 0.739
Time1*Time2 -4.875 -2.438 2.911 -0.84 0.464
Temp2*Time2 -5.000 -2.500 2.911 -0.86 0.454
Temp1*Time1*Temp2 3.250 1.625 2.911 0.56 0.616
Temp1*Time1*Time2 0.250 0.125 2.911 0.04 0.968
Temp1*Temp2*Time2 6.625 3.312 2.911 1.14 0.338
Time1*Temp2*Time2 -6.750 -3.375 2.911 -1.16 0.330
Temp1*Time1*Temp2*Time2 7.625 3.813 2.911 1.31 0.282
Ct Pt 1.125 6.509 0.17 0.874

S = 11.6431 PRESS = *

143

R-Sq = 72.51% R-Sq(pred) = *% R-Sq(adj) = 0.00%

Analysis of Variance for Hardness (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 120.94 120.938 30.234 0.22 0.909
2-Way Interactions 6 314.69 314.688 52.448 0.39 0.851
3-Way Interactions 4 400.31 400.312 100.078 0.74 0.624
4-Way Interactions 1 232.56 232.563 232.563 1.72 0.282
Curvature 1 4.05 4.050 4.050 0.03 0.874
Residual Error 3 406.69 406.687 135.562
Pure Error 3 406.69 406.687 135.562
Total 19 1479.24

Unusual Observations for Hardness
St
Obs StdOrder Hardness Fit SE Fit Residual Resid
1 1 82.0000 82.0000 11.6431 0.0000 * X
2 2 76.0000 76.0000 11.6431 0.0000 * X
3 3 57.0000 57.0000 11.6431 0.0000 * X
4 4 66.0000 66.0000 11.6431 0.0000 * X
5 5 71.0000 71.0000 11.6431 0.0000 * X
6 6 66.5000 66.5000 11.6431 0.0000 * X
7 7 63.0000 63.0000 11.6431 0.0000 * X
8 8 73.0000 73.0000 11.6431 0.0000 * X
9 9 68.0000 68.0000 11.6431 0.0000 * X
10 10 50.0000 50.0000 11.6431 0.0000 * X
11 11 59.0000 59.0000 11.6431 0.0000 * X
12 12 70.0000 70.0000 11.6431 0.0000 * X
13 13 59.0000 59.0000 11.6431 0.0000 * X

144

14 14 69.0000 69.0000 11.6431 0.0000 * X
15 15 65.5000 65.5000 11.6431 0.0000 * X
16 16 53.0000 53.0000 11.6431 0.0000 * X

X denotes an observation whose X value gives it large leverage.

Factorial Fit: shrinkage versus Temp1, Time1, Temp2, Time2
Estimated Effects and Coefficients for shrinkage (coded units)
Term Effect Coef SE Coef T P
Constant 0.105451 0.013911 7.58 0.005
Temp1 0.004521 0.002260 0.006955 0.32 0.767
Time1 -0.008787 -0.004393 0.006955 -0.63 0.572
Temp2 0.006551 0.003275 0.006955 0.47 0.670
Time2 0.021659 0.010829 0.006955 1.56 0.217
Temp1*Time1 0.011433 0.005716 0.006955 0.82 0.471
Temp1*Temp2 0.006765 0.003382 0.006955 0.49 0.660
Temp1*Time2 -0.000498 -0.000249 0.006955 -0.04 0.974
Time1*Temp2 0.000114 0.000057 0.006955 0.01 0.994
Time1*Time2 0.001504 0.000752 0.006955 0.11 0.921
Temp2*Time2 -0.001218 -0.000609 0.006955 -0.09 0.936
Temp1*Time1*Temp2 -0.000892 -0.000446 0.006955 -0.06 0.953
Temp1*Time1*Time2 -0.007429 -0.003715 0.006955 -0.53 0.630
Temp1*Temp2*Time2 -0.003483 -0.001742 0.006955 -0.25 0.818
Time1*Temp2*Time2 -0.001469 -0.000735 0.006955 -0.11 0.923
Temp1*Time1*Temp2*Time2 0.016008 0.008004 0.006955 1.15 0.333
Ct Pt 0.002589 0.015553 0.17 0.878

S = 0.0278219 PRESS = *
R-Sq = 65.90% R-Sq(pred) = *% R-Sq(adj) = 0.00%

145

Analysis of Variance for shrinkage (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.00243866 0.00243866 0.00060967 0.79 0.602
2-Way Interactions 6 0.00072188 0.00072188 0.00012031 0.16 0.974
3-Way Interactions 4 0.00028114 0.00028114 0.00007029 0.09 0.979
4-Way Interactions 1 0.00102506 0.00102506 0.00102506 1.32 0.333
Curvature 1 0.00002145 0.00002145 0.00002145 0.03 0.878
Residual Error 3 0.00232217 0.00232217 0.00077406
Pure Error 3 0.00232217 0.00232217 0.00077406
Total 19 0.00681036
St
Obs StdOrder shrinkage Fit SE Fit Residual Resid
1 1 0.088126 0.088126 0.027822 -0.000000 * X
2 2 0.131762 0.131762 0.027822 -0.000000 * X
3 3 0.112101 0.112101 0.027822 0.000000 * X
4 4 0.125093 0.125093 0.027822 -0.000000 * X
5 5 0.130428 0.130428 0.027822 0.000000 * X
6 6 0.119758 0.119758 0.027822 0.000000 * X
7 7 0.102656 0.102656 0.027822 0.000000 * X
8 8 0.118425 0.118425 0.027822 -0.000000 * X
9 9 0.113239 0.113239 0.027822 -0.000000 * X
10 10 0.104005 0.104005 0.027822 0.000000 * X
11 11 0.078767 0.078767 0.027822 -0.000000 * X
12 12 0.105354 0.105354 0.027822 -0.000000 * X
13 13 0.108053 0.108053 0.027822 0.000000 * X
14 14 0.098796 0.098796 0.027822 -0.000000 * X
15 15 0.119947 0.119947 0.027822 -0.000000 * X
16 16 0.072122 0.072122 0.027822 0.000000 * X

146

X denotes an observation whose X value gives it large leverage.
Factorial Fit: Hardness versus Temp1, Time1, Temp2, Time2

Estimated Effects and Coefficients for Hardness (coded units)

Term Effect Coef SE Coef T P
Constant 64.375 5.822 11.06 0.002
Temp1 -3.375 -1.687 2.911 -0.58 0.603
Time1 -0.750 -0.375 2.911 -0.13 0.906
Temp2 4.125 2.063 2.911 0.71 0.530
Time2 1.125 0.563 2.911 0.19 0.859
Temp1*Time1 4.625 2.313 2.911 0.79 0.485
Temp1*Temp2 -0.000 -0.000 2.911 -0.00 1.000
Temp1*Time2 2.000 1.000 2.911 0.34 0.754
Time1*Temp2 2.125 1.063 2.911 0.37 0.739
Time1*Time2 -4.875 -2.438 2.911 -0.84 0.464
Temp2*Time2 -5.000 -2.500 2.911 -0.86 0.454
Temp1*Time1*Temp2 3.250 1.625 2.911 0.56 0.616
Temp1*Time1*Time2 0.250 0.125 2.911 0.04 0.968
Temp1*Temp2*Time2 6.625 3.312 2.911 1.14 0.338
Time1*Temp2*Time2 -6.750 -3.375 2.911 -1.16 0.330
Temp1*Time1*Temp2*Time2 7.625 3.813 2.911 1.31 0.282
Ct Pt 1.125 6.509 0.17 0.874

S = 11.6431 PRESS = *
R-Sq = 72.51% R-Sq(pred) = *% R-Sq(adj) = 0.00%

Analysis of Variance for Hardness (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 120.94 120.938 30.234 0.22 0.909

147

2-Way Interactions 6 314.69 314.688 52.448 0.39 0.851
3-Way Interactions 4 400.31 400.312 100.078 0.74 0.624
4-Way Interactions 1 232.56 232.563 232.563 1.72 0.282
Curvature 1 4.05 4.050 4.050 0.03 0.874
Residual Error 3 406.69 406.687 135.562
Pure Error 3 406.69 406.687 135.562
Total 19 1479.24
St
Obs StdOrder Hardness Fit SE Fit Residual Resid
1 1 82.0000 82.0000 11.6431 0.0000 * X
2 2 76.0000 76.0000 11.6431 0.0000 * X
3 3 57.0000 57.0000 11.6431 0.0000 * X
4 4 66.0000 66.0000 11.6431 0.0000 * X
5 5 71.0000 71.0000 11.6431 0.0000 * X
6 6 66.5000 66.5000 11.6431 0.0000 * X
7 7 63.0000 63.0000 11.6431 0.0000 * X
8 8 73.0000 73.0000 11.6431 0.0000 * X
9 9 68.0000 68.0000 11.6431 0.0000 * X
10 10 50.0000 50.0000 11.6431 0.0000 * X
11 11 59.0000 59.0000 11.6431 0.0000 * X
12 12 70.0000 70.0000 11.6431 0.0000 * X
13 13 59.0000 59.0000 11.6431 0.0000 * X
14 14 69.0000 69.0000 11.6431 0.0000 * X
15 15 65.5000 65.5000 11.6431 0.0000 * X
16 16 53.0000 53.0000 11.6431 0.0000 * X

X denotes an observation whose X value gives it large leverage.

Factorial Fit: shrinkage versus Temp1, Time1, Temp2, Time2

148

Estimated Effects and Coefficients for shrinkage (coded units)
Term Effect Coef SE Coef T P
Constant 0.105451 0.013911 7.58 0.005
Temp1 0.004521 0.002260 0.006955 0.32 0.767
Time1 -0.008787 -0.004393 0.006955 -0.63 0.572
Temp2 0.006551 0.003275 0.006955 0.47 0.670
Time2 0.021659 0.010829 0.006955 1.56 0.217
Temp1*Time1 0.011433 0.005716 0.006955 0.82 0.471
Temp1*Temp2 0.006765 0.003382 0.006955 0.49 0.660
Temp1*Time2 -0.000498 -0.000249 0.006955 -0.04 0.974
Time1*Temp2 0.000114 0.000057 0.006955 0.01 0.994
Time1*Time2 0.001504 0.000752 0.006955 0.11 0.921
Temp2*Time2 -0.001218 -0.000609 0.006955 -0.09 0.936
Temp1*Time1*Temp2 -0.000892 -0.000446 0.006955 -0.06 0.953
Temp1*Time1*Time2 -0.007429 -0.003715 0.006955 -0.53 0.630
Temp1*Temp2*Time2 -0.003483 -0.001742 0.006955 -0.25 0.818
Time1*Temp2*Time2 -0.001469 -0.000735 0.006955 -0.11 0.923
Temp1*Time1*Temp2*Time2 0.016008 0.008004 0.006955 1.15 0.333
Ct Pt 0.002589 0.015553 0.17 0.878

S = 0.0278219 PRESS = *
R-Sq = 65.90% R-Sq(pred) = *% R-Sq(adj) = 0.00%

Analysis of Variance for shrinkage (coded units)
Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 0.00243866 0.00243866 0.00060967 0.79 0.602
2-Way Interactions 6 0.00072188 0.00072188 0.00012031 0.16 0.974
3-Way Interactions 4 0.00028114 0.00028114 0.00007029 0.09 0.979
4-Way Interactions 1 0.00102506 0.00102506 0.00102506 1.32 0.333
Curvature 1 0.00002145 0.00002145 0.00002145 0.03 0.878
Residual Error 3 0.00232217 0.00232217 0.00077406

149

Pure Error 3 0.00232217 0.00232217 0.00077406
Total 19 0.00681036
St
Obs StdOrder shrinkage Fit SE Fit Residual Resid
1 1 0.088126 0.088126 0.027822 -0.000000 * X
2 2 0.131762 0.131762 0.027822 -0.000000 * X
3 3 0.112101 0.112101 0.027822 0.000000 * X
4 4 0.125093 0.125093 0.027822 -0.000000 * X
5 5 0.130428 0.130428 0.027822 0.000000 * X
6 6 0.119758 0.119758 0.027822 0.000000 * X
7 7 0.102656 0.102656 0.027822 0.000000 * X
8 8 0.118425 0.118425 0.027822 -0.000000 * X
9 9 0.113239 0.113239 0.027822 -0.000000 * X
10 10 0.104005 0.104005 0.027822 0.000000 * X
11 11 0.078767 0.078767 0.027822 -0.000000 * X
12 12 0.105354 0.105354 0.027822 -0.000000 * X
13 13 0.108053 0.108053 0.027822 0.000000 * X
14 14 0.098796 0.098796 0.027822 -0.000000 * X
15 15 0.119947 0.119947 0.027822 -0.000000 * X
16 16 0.072122 0.072122 0.027822 0.000000 * X

X denotes an observation whose X value gives it large leverage.

150

3 2 1 0 -1 -2 -3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Not Significant
Significant
Effect Type
ABCD
AB
D
Normal Plot of the Standardized Effects
(response is shrinkage, Alpha = 0.50)
2.5 2.0 1.5 1.0 0.5 0.0
98
95
90
85
80
70
60
50
40
30
20
10
0
Absolute Standardized Effect
Percent
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Not Significant
Significant
Effect Type
ABCD
AB
D
Half Normal Plot of the Standardized Effects
(response is shrinkage, Alpha = 0.50)
2.5 2.0 1.5 1.0 0.5 0.0
98
95
90
85
80
70
60
50
40
30
20
10
0
Absolute Standardized Effect
Percent
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Not Significant
Significant
Effect Type
ABCD
BCD
ACD
CD
BD
AB
Half Normal Plot of the Standardized Effects
(response is Hardness, Alpha = 0.50)

151

3 2 1 0 -1 -2 -3
99
95
90
80
70
60
50
40
30
20
10
5
1
Standardized Effect
Percent
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Not Significant
Significant
Effect Type
ABCD
BCD
ACD
CD
BD
AB
Normal Plot of the Standardized Effects
(response is Hardness, Alpha = 0.50)
AC
ABD
B
D
AD
BC
ABC
A
C
AB
BD
CD
ACD
BCD
ABCD
1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Term
Standardized Effect
0.765
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Pareto Chart of the Standardized Effects
(response is Hardness, Alpha = 0.50)
BC
AD
ABC
CD
BCD
BD
ACD
A
C
AC
ABD
B
AB
ABCD
D
1.6 1.4 1.2 1.0 0.8 0.6 0.4 0.2 0.0
Term
Standardized Effect
0.765
A Temp1
B Time1
C Temp2
D Time2
Factor Name
Pareto Chart of the Standardized Effects
(response is shrinkage, Alpha = 0.50)

152

Factorial Fit: Shrinkage versus Temp1, time1, Temp2, time2
Estimated Effects and Coefficients for Shrinkage (coded units)
Term Effect Coef
Constant 6.2313
Temp1 0.0875 0.0437
time1 -0.2875 -0.1437
Temp2 2.4375 1.2187
time2 1.1125 0.5562
Temp1*time1 0.0875 0.0437
Temp1*Temp2 0.1625 0.0813
Temp1*time2 -0.1625 -0.0812
time1*Temp2 0.3875 0.1938
0.04 0.02 0.00 -0.02
99
90
50
10
1
Residual
Percent
0.14 0.12 0.10 0.08
0.04
0.02
0.00
-0.02
Fitted Value
Residual
0.03 0.02 0.01 0.00 -0.01 -0.02 -0.03
16
12
8
4
0
Residual
Frequency
20 18 16 14 12 10 8 6 4 2
0.04
0.02
0.00
-0.02
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for shrinkage
10 0 -10
99
90
50
10
1
Residual
Percent
80 70 60 50
10
0
-10
Fitted Value
Residual
10 5 0 -5 -10 -15
16
12
8
4
0
Residual
Frequency
20 18 16 14 12 10 8 6 4 2
10
0
-10
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Hardness

153

time1*time2 -0.1375 -0.0687
Temp2*time2 0.0875 0.0437
Temp1*time1*Temp2 0.1625 0.0813
Temp1*time1*time2 -0.1625 -0.0813
Temp1*Temp2*time2 -0.0875 -0.0438
time1*Temp2*time2 -0.2625 -0.1312
Temp1*time1*Temp2*time2 -0.0875 -0.0438

Analysis of Variance for Shrinkage (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 29.0775 29.0775 7.2694 * *
Temp1 1 0.0306 0.0306 0.0306 * *
time1 1 0.3306 0.3306 0.3306 * *
Temp2 1 23.7656 23.7656 23.7656 * *
time2 1 4.9506 4.9506 4.9506 * *
2-Way Interactions 6 0.9487 0.9487 0.1581 * *
Temp1*time1 1 0.0306 0.0306 0.0306 * *
Temp1*Temp2 1 0.1056 0.1056 0.1056 * *
Temp1*time2 1 0.1056 0.1056 0.1056 * *
time1*Temp2 1 0.6006 0.6006 0.6006 * *
time1*time2 1 0.0756 0.0756 0.0756 * *
Temp2*time2 1 0.0306 0.0306 0.0306 * *
3-Way Interactions 4 0.5175 0.5175 0.1294 * *
Temp1*time1*Temp2 1 0.1056 0.1056 0.1056 * *
Temp1*time1*time2 1 0.1056 0.1056 0.1056 * *
Temp1*Temp2*time2 1 0.0306 0.0306 0.0306 * *
time1*Temp2*time2 1 0.2756 0.2756 0.2756 * *
4-Way Interactions 1 0.0306 0.0306 0.0306 * *
Temp1*time1*Temp2*time2 1 0.0306 0.0306 0.0306 * *
Residual Error 0 * * *
Total 15 30.5744

154

Estimated Coefficients for Shrinkage using data in uncoded units
Term Coef
Constant -15.2500
Temp1 -6.36464E-14
time1 264.100
Temp2 0.0250000
time2 -12.5750
Temp1*time1 -0.648500
Temp1*Temp2 8.00210E-17
Temp1*time2 3.95416E-14
time1*Temp2 -0.350000
time1*time2 -104.000
Temp2*time2 0.0175000
Temp1*time1*Temp2 0.000850000
Temp1*time1*time2 0.263500
Temp1*Temp2*time2 -5.01110E-17
time1*Temp2*time2 0.140000
Temp1*time1*Temp2*time2 -3.50000E-04

Least Squares Means for Shrinkage
Mean
Temp1
500 6.188
600 6.275
time1
0.0000 6.375
0.5000 6.088
Temp2
770 5.013
810 7.450

155

time2
1 5.675
2 6.787
Temp1*time1
500 0.0000 6.375
600 0.0000 6.375
500 0.5000 6.000
600 0.5000 6.175
Temp1*Temp2
500 770 5.050
600 770 4.975
500 810 7.325
600 810 7.575
Temp1*time2
500 1 5.550
600 1 5.800
500 2 6.825
600 2 6.750
time1*Temp2
0.0000 770 5.350
0.5000 770 4.675
0.0000 810 7.400
0.5000 810 7.500
time1*time2
0.0000 1 5.750
0.5000 1 5.600
0.0000 2 7.000
0.5000 2 6.575
Temp2*time2
770 1 4.500
810 1 6.850
770 2 5.525

156

810 2 8.050
Temp1*time1*Temp2
500 0.0000 770 5.350
600 0.0000 770 5.350
500 0.5000 770 4.750
600 0.5000 770 4.600
500 0.0000 810 7.400
600 0.0000 810 7.400
500 0.5000 810 7.250
600 0.5000 810 7.750
Temp1*time1*time2
500 0.0000 1 5.750
600 0.0000 1 5.750
500 0.5000 1 5.350
600 0.5000 1 5.850
500 0.0000 2 7.000
600 0.0000 2 7.000
500 0.5000 2 6.650
600 0.5000 2 6.500
Temp1*Temp2*time2
500 770 1 4.500
600 770 1 4.500
500 810 1 6.600
600 810 1 7.100
500 770 2 5.600
600 770 2 5.450
500 810 2 8.050
600 810 2 8.050
time1*Temp2*time2
0.0000 770 1 4.900
0.5000 770 1 4.100
0.0000 810 1 6.600

157

0.5000 810 1 7.100
0.0000 770 2 5.800
0.5000 770 2 5.250
0.0000 810 2 8.200
0.5000 810 2 7.900
Temp1*time1*Temp2*time2
500 0.0000 770 1 4.900
600 0.0000 770 1 4.900
500 0.5000 770 1 4.100
600 0.5000 770 1 4.100
500 0.0000 810 1 6.600
600 0.0000 810 1 6.600
500 0.5000 810 1 6.600
600 0.5000 810 1 7.600
500 0.0000 770 2 5.800
600 0.0000 770 2 5.800
500 0.5000 770 2 5.400
600 0.5000 770 2 5.100
500 0.0000 810 2 8.200
600 0.0000 810 2 8.200
500 0.5000 810 2 7.900
600 0.5000 810 2 7.900

Alias Structure
I
Temp1
time1
Temp2
time2
Temp1*time1
Temp1*Temp2
Temp1*time2

158

time1*Temp2
time1*time2
Temp2*time2
Temp1*time1*Temp2
Temp1*time1*time2
Temp1*Temp2*time2
time1*Temp2*time2
Temp1*time1*Temp2*time2
Tabulated statistics: Temp2, time2
Columns: Temp2 / time2

770 810 All
1 2 1 2 All

4 4 4 4 16

Cell Contents: Count

General Regression Analysis: Shrinkage versus time1, time2, Temp1, Temp2
Regression Equation

Shrinkage = -1.85148 - 12.2573 time1 - 13.1887 time2 - 0.0225013 Temp1 +
0.00794954 Temp2 + 46.9635 time1*time2 - 0.153471 time1*Temp1 +
0.018337 time2*Temp2 + 2.86469e-005 Temp1*Temp2 - 0.0512135
time1*Temp2*time2 - 0.00651603 Temp1*time1*time2 + 0.000223052
Temp1*time1*Temp2 - 1.09461e-007 Temp1*Temp2*time2 - 7.98863e-006
Temp1*time1*Temp2*time2

Coefficients

159

Term Coef SE Coef T P
Constant -1.8515 28.9311 -0.06400 0.955
time1 -12.2573 6.6485 -1.84361 0.207
time2 -13.1887 5.3019 -2.48755 0.131
Temp1 -0.0225 0.0508 -0.44328 0.701
Temp2 0.0079 0.0367 0.21664 0.849
time1*time2 46.9635 50.2765 0.93410 0.449
Temp1*Temp2 0.0000 0.0001 0.44484 0.700
time1*Temp1 -0.1535 0.0446 -3.44457 0.075
time2*Temp2 0.0183 0.0070 2.63372 0.119
Temp1*time1*Temp2 0.0002 0.0001 4.10561 0.055
Temp1*time1*time2 -0.0065 0.0939 -0.06937 0.951
Temp1*Temp2*time2 -0.0000 0.0000 -0.03213 0.977
time1*Temp2*time2 -0.0512 0.0635 -0.80704 0.504
Temp1*time1*Temp2*time2 -0.0000 0.0001 -0.06737 0.952

Summary of Model

S = 0.190396 R-Sq = 99.76% R-Sq(adj) = 98.22%
PRESS = 8.66285 R-Sq(pred) = 71.67%

Analysis of Variance

Source DF Seq SS Adj SS Adj MS F P
Regression 13 30.5019 30.5019 2.34630 64.7242 0.015313
time1 1 0.3306 0.1232 0.12321 3.3989 0.206555
time2 1 4.9506 0.2243 0.22432 6.1879 0.130669
Temp1 1 0.0306 0.0071 0.00712 0.1965 0.700902
Temp2 1 23.7656 0.0017 0.00170 0.0469 0.848582
time1*time2 1 0.0756 0.0316 0.03163 0.8725 0.448861

160

Temp1*Temp2 1 0.1056 0.0072 0.00717 0.1979 0.699945
time1*Temp1 1 0.0306 0.4301 0.43012 11.8651 0.074931
time2*Temp2 1 0.0306 0.2515 0.25145 6.9365 0.118979
Temp1*time1*Temp2 1 0.6420 0.6110 0.61104 16.8560 0.054520
Temp1*time1*time2 1 0.2112 0.0002 0.00017 0.0048 0.951006
Temp1*Temp2*time2 1 0.0000 0.0000 0.00004 0.0010 0.977284
time1*Temp2*time2 1 0.3284 0.0236 0.02361 0.6513 0.504361
Temp1*time1*Temp2*time2 1 0.0002 0.0002 0.00016 0.0045 0.952418
Error 2 0.0725 0.0725 0.03625
Total 15 30.5744

Factorial Fit: Hardness (HRB) versus Temp1, time1, Temp2, time2

Estimated Effects and Coefficients for Hardness (HRB) (coded units)

Term Effect Coef
Constant 93.8125
Temp1 -0.3750 -0.1875
time1 0.6250 0.3125
Temp2 7.3750 3.6875
time2 2.8750 1.4375
Temp1*time1 -0.3750 -0.1875
Temp1*Temp2 -0.6250 -0.3125
Temp1*time2 0.3750 0.1875
time1*Temp2 0.3750 0.1875
time1*time2 -0.1250 -0.0625
Temp2*time2 1.1250 0.5625
Temp1*time1*Temp2 -0.6250 -0.3125
Temp1*time1*time2 0.3750 0.1875

161

Temp1*Temp2*time2 0.6250 0.3125
time1*Temp2*time2 0.1250 0.0625
Temp1*time1*Temp2*time2 0.6250 0.3125
Analysis of Variance for Hardness (HRB) (coded units)

Source DF Seq SS Adj SS Adj MS F P
Main Effects 4 252.750 252.750 63.188 * *
Temp1 1 0.562 0.562 0.562 * *
time1 1 1.563 1.562 1.562 * *
Temp2 1 217.563 217.563 217.563 * *
time2 1 33.063 33.063 33.063 * *
2-Way Interactions 6 8.375 8.375 1.396 * *
Temp1*time1 1 0.562 0.562 0.562 * *
Temp1*Temp2 1 1.563 1.563 1.563 * *
Temp1*time2 1 0.563 0.563 0.563 * *
time1*Temp2 1 0.562 0.562 0.562 * *
time1*time2 1 0.063 0.063 0.063 * *
Temp2*time2 1 5.062 5.062 5.062 * *
3-Way Interactions 4 3.750 3.750 0.937 * *
Temp1*time1*Temp2 1 1.562 1.562 1.562 * *
Temp1*time1*time2 1 0.562 0.562 0.562 * *
Temp1*Temp2*time2 1 1.562 1.562 1.562 * *
time1*Temp2*time2 1 0.062 0.062 0.062 * *
4-Way Interactions 1 1.562 1.562 1.562 * *
Temp1*time1*Temp2*time2 1 1.562 1.562 1.562 * *
Residual Error 0 * * *
Total 15 266.438

Hardness SE St
Obs StdOrder (HRC) Fit Fit Residual Resid
1 7 98.000 98.000 * 0.000 *

162

2 16 100.000 100.000 * 0.000 *
3 15 100.000 100.000 * 0.000 *
4 13 99.000 99.000 * 0.000 *
5 12 91.000 91.000 * 0.000 *
6 6 95.000 95.000 * 0.000 *
7 10 91.000 91.000 * 0.000 *
8 3 89.000 89.000 * 0.000 *
9 11 91.000 91.000 * 0.000 *
10 1 89.000 89.000 * 0.000 *
11 14 99.000 99.000 * 0.000 *
12 8 94.000 94.000 * 0.000 *
13 9 91.000 91.000 * 0.000 *
14 2 89.000 89.000 * 0.000 *
15 5 95.000 95.000 * 0.000 *
16 4 90.000 90.000 * 0.000 *

Estimated Coefficients for Hardness (HRB) using data in uncoded units
Term Coef
Constant 10.0000
Temp1 4.81981E-13
time1 -2137.50
Temp2 0.100000
time2 -36.5000
Temp1*time1 3.89000
Temp1*Temp2 -6.04497E-16
Temp1*time2 -3.02780E-13
time1*Temp2 2.75000
time1*time2 1049.50
Temp2*time2 0.0500000
Temp1*time1*Temp2 -0.00500000
Temp1*time1*time2 -1.94500
Temp1*Temp2*time2 3.82294E-16

163

time1*Temp2*time2 -1.35000
Temp1*time1*Temp2*time2 0.00250000

Least Squares Means for Hardness (HRB)
Mean
Temp1
500 94.00
600 93.63
time1
0.0000 93.50
0.5000 94.13
Temp2
770 90.13
810 97.50
time2
1 92.38
2 95.25
Temp1*time1
500 0.0000 93.50
600 0.0000 93.50
500 0.5000 94.50
600 0.5000 93.75
Temp1*Temp2
500 770 90.00
600 770 90.25
500 810 98.00
600 810 97.00
Temp1*time2
500 1 92.75
600 1 92.00
500 2 95.25
600 2 95.25

164

time1*Temp2
0.0000 770 90.00
0.5000 770 90.25
0.0000 810 97.00
0.5000 810 98.00
time1*time2
0.0000 1 92.00
0.5000 1 92.75
0.0000 2 95.00
0.5000 2 95.50
Temp2*time2
770 1 89.25
810 1 95.50
770 2 91.00
810 2 99.50
Temp1*time1*Temp2
500 0.0000 770 90.00
600 0.0000 770 90.00
500 0.5000 770 90.00
600 0.5000 770 90.50
500 0.0000 810 97.00
600 0.0000 810 97.00
500 0.5000 810 99.00
600 0.5000 810 97.00
Temp1*time1*time2
500 0.0000 1 92.00
600 0.0000 1 92.00
500 0.5000 1 93.50
600 0.5000 1 92.00
500 0.0000 2 95.00
600 0.0000 2 95.00
500 0.5000 2 95.50

165

600 0.5000 2 95.50
Temp1*Temp2*time2
500 770 1 89.00
600 770 1 89.50
500 810 1 96.50
600 810 1 94.50
500 770 2 91.00
600 770 2 91.00
500 810 2 99.50
600 810 2 99.50
time1*Temp2*time2
0.0000 770 1 89.00
0.5000 770 1 89.50
0.0000 810 1 95.00
0.5000 810 1 96.00
0.0000 770 2 91.00
0.5000 770 2 91.00
0.0000 810 2 99.00
0.5000 810 2 100.00
Temp1*time1*Temp2*time2
500 0.0000 770 1 89.00
600 0.0000 770 1 89.00
500 0.5000 770 1 89.00
600 0.5000 770 1 90.00
500 0.0000 810 1 95.00
600 0.0000 810 1 95.00
500 0.5000 810 1 98.00
600 0.5000 810 1 94.00
500 0.0000 770 2 91.00
600 0.0000 770 2 91.00
500 0.5000 770 2 91.00
600 0.5000 770 2 91.00

166

500 0.0000 810 2 99.00
600 0.0000 810 2 99.00
500 0.5000 810 2 100.00
600 0.5000 810 2 100.00

Alias Structure
I
Temp1
time1
Temp2
time2
Temp1*time1
Temp1*Temp2
Temp1*time2
time1*Temp2
time1*time2
Temp2*time2
Temp1*time1*Temp2
Temp1*time1*time2
Temp1*Temp2*time2
time1*Temp2*time2
Temp1*time1*Temp2*time2

* NOTE * Could not graph the specified residual type because MSE = 0 or the
degrees of freedom for error = 0.

Regression Analysis: Shrinkage versus Temp1, time1, Temp2, time2
The regression equation is
Shrinkage = - 43.9 + 0.00087 Temp1 - 0.575 time1 + 0.0609 Temp2 + 1.11 time2

167

Predictor Coef SE Coef T P
Constant -43.916 3.794 -11.58 0.000
Temp1 0.000875 0.001844 0.47 0.644
time1 -0.5750 0.3689 -1.56 0.147
Temp2 0.060938 0.004611 13.22 0.000
time2 1.1125 0.1844 6.03 0.000

S = 0.368890 R-Sq = 95.1% R-Sq(adj) = 93.3%

Analysis of Variance
Source DF SS MS F P
Regression 4 29.0775 7.2694 53.42 0.000
Residual Error 11 1.4969 0.1361
Total 15 30.5744

Source DF Seq SS
Temp1 1 0.0306
time1 1 0.3306
Temp2 1 23.7656
time2 1 4.9506

Unusual Observations

Obs Temp1 Shrinkage Fit SE Fit Residual St Resid
12 600 7.6000 6.7937 0.2062 0.8063 2.64R

R denotes an observation with a large standardized residual.

168

1.0 0.5 0.0 -0.5
99
90
50
10
1
Residual
Percent
8 7 6 5 4
0.5
0.0
-0.5
Fitted Value
Residual
0.8 0.6 0.4 0.2 0.0 -0.2 -0.4
6.0
4.5
3.0
1.5
0.0
Residual
Frequency
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
0.5
0.0
-0.5
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Shrinkage

The regression equation is
Hardness (HRC) = - 54.4 - 0.00375 Temp1 + 1.25 time1 + 0.184 Temp2 + 2.88 time2

Predictor Coef SE Coef T P
Constant -54.41 11.47 -4.74 0.001
Temp1 -0.003750 0.005577 -0.67 0.515
time1 1.250 1.115 1.12 0.286
Temp2 0.18438 0.01394 13.22 0.000
time2 2.8750 0.5577 5.15 0.000

S = 1.11549 R-Sq = 94.9% R-Sq(adj) = 93.0%

Analysis of Variance

Source DF SS MS F P
Regression 4 252.750 63.188 50.78 0.000
Residual Error 11 13.688 1.244
Total 15 266.438

169

Source DF Seq SS
Temp1 1 0.563
time1 1 1.563
Temp2 1 217.563
time2 1 33.063
Hardness
Obs Temp1 (HRB) Fit SE Fit Residual St Resid
12 600 94.000 96.188 0.624 -2.188 -2.37R

R denotes an observation with a large standardized residual.

Residual Plots for Hardness (HRB)
2 1 0 -1 -2
99
90
50
10
1
Residual
Percent
100 95 90
1
0
-1
-2
Fitted Value
Residual
1.5 1.0 0.5 0.0 -0.5 -1.0 -1.5 -2.0
3
2
1
0
Residual
Frequency
16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1
1
0
-1
-2
Observation Order
Residual
Normal Probability Plot Versus Fits
Histogram Versus Order
Residual Plots for Hardness (HRC)

170

Appendix B: XRD Settings
Settings for the X-Ray diffraction and the related results:

171

XRD-raw results for bronze aluminum sulfate after sintering:

Abstract (if available)

Abstract The Selective Inhibition Sintering (SIS) process is an additive manufacturing (AM) technology which builds parts on a layer-by-layer basis. The principle idea of the SIS process is based on the prevention of selected segments of each powder layer from sintering. The purpose of this research is to investigate the fundamentals of the Selective Inhibition Sintering (SIS) process for the fabrication of metallic parts. A SIS-Metal process has been developed based on the microscopic mechanical inhibition principle. In this process the inhibitor, which is a salt solution or a carbohydrate solution (sucrose), is printed in the selected areas of each metal powder layer

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