University of Southern California Dissertations and Theses

Development of composite oriented strand board and structures

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Development of composite oriented strand board and structures

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Content 1 DEVELOPMENT OF COMPOSITE ORIENTED STRAND BOARD AND STRUCTURES by Bo Cheng Jin 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 (AEROSPACE AND MECHANICAL ENGINEERING) December 2017 Copyright 2017 Bo Cheng Jin 2 但使龙城飞将在，不教胡马渡阴山。 3 DEDICATION To My Family 4 ACKNOWLEDGEMENTS I would like to thank my advisors Professors Steven R. Nutt, Javier LLorca, Carlos D. Gonzalez, Stephen W. Tsai, Oussama Safadi, Shiv Joshi, Geoffrey Shiflett, Geoffrey Spedding, Julian Domaradzki, Marijan Dravinski, Assimina Pelegri, Ellis Dill, for all their patient guidance and instructions. Without them I would not have been able to get through all the obstacles. Their ability as scientists and advisors, and more importantly, their professional work ethics have affected me in a long way. I would also like to thank my colleagues, Limin Jin, Lessa Grunenfelder, Atui Jain, Timotei Centea, Ming-Sung Wu, Miguel Herraez, William Edwards, Mark Anders, Yinghui Hu, Nik Kar, Sarah Katz, Daniel Zebrine, Ruchir Shanbhag, David Bender, Jung Hwan Shin, Lee Hamill, Yijia Ma, Wei Hu, Yixiang Zhang, Yunpeng Zhang, Yuzheng Zhang, Daniel Kim, Rohan Panikar, Gaurav Nilakantan, Jonathan Lo, these people helped me grown. The undergraduate and M.S. students worked with me, Rodrigo Mier, Junbo Wang, Billy Shen, Bing Su, Seungjong Lee, Jing Peng, Antonio Raul Perez, Cliff Lester, Gus Lang, forced me to become a better teacher. Finally, to my sweetheart Xiaochen, who has made me a better person. 5 TABLE OF CONTENTS Dedication 3 Acknowledgements 4 Motivation 6 Part I Manufacturing and Characterization of COSB 8 Part II Simulation (FEA), Fiber Level Micro-Scale 36 Part III Simulation (FEA), Coupon Level, Meso-Scale 64 Part IV Simulation (FEA), Fiber Level, Macro-Scale 82 Part V Future Work 125 6 MOTIVATION Composite Oriented Strand Boards (COSB) are a bulk molding compound type of random fiber composites (RaFC) comprised of pre-impregnated strand tapes. This type of material has numerous applications such as: 1. In recycling expired composite materials, 2. In re-use of composite scraps generated from manufacturing work in automotive and aerospace industry. 3. In making composites tooling, because both the mold and curing part would have the same coefficient of thermal expansion. 4. When the strand aspect ratio is low, it has good drapability and is idea for compression molding of small complex parts such as brackets and hinges, where varying wall thickness, tight radii and rib feathers are common. It is therefore a good candidate to replace complex metallic parts that are commonly attached to carbon fiber reinforced polymers primary structures in modern aircrafts. Previous work in the field included exploring the possibility of using COSB to manufacture different structures that can be used in daily life e.g. cell phone case, skateboard, or as a cheaper replacement of some existed composite parts e.g. as the face sheet of the sandwich panels, or to replace hat stiffener made with virgin unidirectional prepreg composites. However, the mechanical properties of this type of material have not been systematically reported. A numerical tool is needed in predicting the behavior of COSB RaFC materials, and to replace years of mechanical testing work. 7 In this work, there are mainly three goals: 1. Till present, there’s still no standards in testing or measuring this type of materials’ various mechanical properties including tensile and compression modulus and strength, fracture toughness, strength after impact damage, flexural bending strength, short beam shear strength etc. To conclude a complete report of COSB RaFC’s mechanical properties will take more than decades of mechanical destructive testing work, and numerous of funding and human resources. In this work, we aimed at investigating the possibility of using geometric modeling and Finite Element Method (both fiber level micro-scale and coupon level meso-scale) to predict COSB material’s microstructure and mechanical properties. 2. The FEA modeling results were experimentally validated via advanced manufacturing of composites and structures. 3. In order to support future work of making COSB material into 3D contoured structures that can replace some of the existing expensive ones, we aimed at establishing a set of higher order abstract structural elements using parametric finite element analysis (part level macro-scale) to define the design sensitivity of composite hat stiffened panels, a widely used structure in aerospace industry. 8 PART I Optimization of Microstructures and Mechanical Properties of Composite Oriented Strand Board from Reused Prepreg A prepreg strand layup method (Mat-Stacking) is presented to enhance the microstructure and mechanical properties of composite oriented strand board (COSB) produced with re- used prepreg scraps. Eight COSB panels were produced using two layup methods and four prepreg strand aspect ratios (1:1, 2:1, 5:1, and 10:1). All COSB panels were compression molded with the same carbon/epoxy system and process parameters, including cure cycle, temperature, and mold pressure. COSB void content, morphology, and distribution were characterized using microscopy and X-ray computed tomography (XCT). Tensile properties and failure modes of COSB panels exhibited a strong dependence on the strand layup method and the strand aspect ratio. Results demonstrated that COSB with lower coefficient of variation and useful mechanical properties can be produced with the proposed layup method and judicious selection of strand aspect ratio, yielding stiffness similar to continuous quasi-isotropic composites with up to 50% of the strength. 1. Introduction In recent years, the commercial aircraft industry has relied increasingly on composite materials to produce lighter and more durable aircraft. For example, a Boeing 787 airplane contains 50% by weight of composites, which is about 32,000 kg of carbon fiber reinforced polymer (CFRP). In 2015, Boeing projected a demand of 38,050 new airplanes at a total 9 value of $5.6 trillion [1] over the next 20 years, an increase of 3.5 percent from the previous year’s forecast. Currently, Boeing and Airbus each generate ~450,000 kg (~1 million lb) of cured and uncured prepreg waste annually from airplane production (primarily 787 and A350 XWB) [2]. If the entire supply chain for these planes is included, the total prepreg waste is closer to 1,814,369 kg (4 million lb)/year. With the automotive industry poised to consume more carbon fiber (and generate additional production scrap), recycling and reuse of composite production waste will soon be essential [3]. The technical community has been seeking viable methods and processes to convert in- process waste into useful composite parts. Efforts have focused on converting prepreg scrap into composite products, including oriented strand board [4-6], skateboard decks, and hat stiffeners [7], by cutting waste prepreg into rectangular strands and curing them by compression molding and Vacuum Bag Only (VBO) processes. Structural characterization studies have focused on the elastic behavior and failure response of COSBs produced by a “mechanical-agitation” layup method [8-11]. In these studies, failure was dominated by inter-strand matrix events with little or no fiber breakage, and yielded a high coefficient of variation (CoV) in the measured properties (the CoV in modulus values was as large as 50%). In other studies [12-14], thermoplastic COSBs were investigated to determine the effects of processing conditions on defect formation and properties. A 2D FE model was built [15] to predict the squeeze flow behavior, and stochastic and analytical models [16, 17] were developed to predict the modulus, strength and fracture path. 10 Despite these studies, the issue of high CoV of mechanical properties has persisted, and a more thorough characterization of mechanical properties is required for design of components using this material. In the present work, a “mat-stacking” layup method was employed to produce laminates from prepreg strands, yielding higher values of tensile modulus, strength, and strain-to-failure with lower values of CoV than COSB panels produced previously using the "mechanical-agitation” approach. The concept was subsequently validated using experimental data from tensile tests. The design of COSB specimens, together with manufacturing, NDT, and experimental techniques, are introduced in Section 2. Results and discussion appear in Section 3, while the conclusions are presented in Section 4. 2. Manufacturing and characterization techniques of COSB COSB panels were produced from unidirectional (UD) thermoset prepreg strands distributed in random orientations. These rectangular strands were cut from expired OoA (Out of Autoclave) carbon fiber-epoxy prepreg. The COSBs were formed using compression molding with heated platens [6], although other methods can be used, such as autoclave, and Vacuum Bag Only (VBO) OoA techniques [18]. Parameters that can differentiate between materials and manufacturing methods were not considered because this issue was beyond the scope of this study. The COSB design variables considered in this study included aspect ratio (AR) of prepreg strands and the planar distribution of strands within the board resulting from layup methods. We will show that these variables strongly affect the mechanical performance of COSBs. 11 2.1. Material The prepreg strands selected for producing the COSBs were cut from unidirectional carbon/epoxy prepreg (CYCOM T40-800B/5320-1, Cytec Co., Ltd.) designed for OoA manufacture of aerospace structures. The prepreg consisted of a toughened epoxy resin reinforced with carbon fibers (cure temperature of 121º C) with an elastic modulus of 57.6 GPa and strength of 931 MPa (quasi-isotropic layup), elastic modulus of 156 GPa and strength of 2703 MPa (0 o fiber direction), 0.137 mm cured ply thickness, 1.31 g/cm 3 cured resin density, 220 g/m 2 and 145 g/m 2 of areal density for prepreg and dry fibers, respectively, and 67% nominal fiber volume fraction. All prepregs used in this work were two years beyond specified shelf life, and thus the mechanical properties were compromised compared to a fresh prepreg system. 2.2. Manufacturing techniques The fabrication procedure involved strand cutting, lay-up, and heated plate compression molding. Care was taken in the process to ensure (a) that the cuts on strand ends did not damage adjacent fibers, (b) a controllable orientation and distribution of strands during lay- up procedure and an acceptable thickness variation of final part, and (c) the surface and bulk void contents were eliminated/minimized. Mechanical properties were benchmarked to those of quasi-isotropic laminates. 12 2.2.1. Strand cutting Prepreg sheets were cut into strands using a razor blade, taking care to avoid shearing of fiber ends in cuts parallel to the fiber direction. However, cuts across fibers and cuts through resin rich areas presented challenges with regard to avoiding shearing of fiber ends. Cutting tools such as slitting knives (rolling wheel blade) and shear cutters with scissor action were suitable for clean cuts. Paper shear cutters also provided clean cuts for strands with rectangular shapes. An automated cutting machine and a semi-automatic feeding system were designed for this purpose. Fully automated cutting systems will be required for large scale production of COSB products. 2.2.2. Strand geometry and distribution methods The aspect ratio (AR) of each rectangular composite strand is defined as the strand length to width ratio. Strands with AR = 1, 2, 5 and 10 were prepared, and all had a width of 10 mm. Controlling the length of shorter strands (AR 1:1 in Figure 1(a)) proved difficult. While COSB panels with lower AR strands are expected to yield inferior tensile strength due to limited fiber continuity, such panels may have manufacturing advantages. For example, reduced AR can be expected to facilitate molding of contoured parts with complex shapes and offer superior drapability (assuming a COS prepreg sheet). Such AR strands can be readily procured, because scraps collected from manufacturing settings are in random shapes and can more readily be cut into low AR strands. In contrast, COSBs with higher AR strands would yield superior mechanical performance because of longer 13 fibers and fewer strand ends (crack initiation/pathways). A hybrid blend of strands with various AR could result in COSBs with balanced mechanical performance and formability. An optimal strand geometry that considers processing challenges can be obtained from experimental and numerical simulations. Also, strand sizes and shapes used for OSB in the wood industry could help inform choices for COSB. Figure 1. (a) Four different strand AR 1:1, 2:1, 5:1 and 10:1. (b) the “mechanical-agitation” layup method. Two lay-up methods were used to produce COSB panels. In the first method, a “randomly distributed” layout was created by a “mechanical-agitation” method (Figure 1(b)). In this method, UD strands of 250 g were placed in an open box (215.9 mm × 215.9 mm × 200 mm) and manually shaken. Strands were then pressed using a heated press to achieve a near-uniform layup. Fresher strands tended to mutually adhere on initial contact, restricting redistribution and sliding during shaking. Strands with more than 1-2 weeks out-time showed increased sliding mobility because of reduced tack and were hence used with the mechanical-agitation method. 14 Though the "mechanical-agitation" method provided a rapid method to produce COSB, the mass distribution was not homogeneous, and strands tended to cluster, creating regions with high and low fiber concentrations. To address this, a uniform layout was created by “mat-stacking” layup (Figure 2), in which multiple thin layers (mats of UD prepreg strands) were formed first as a COS prepreg sheet, then stacked, and finally pressed. Each strand of UD prepreg was attached to an aluminum base plate coated with demolding release agent. During the stacking process, each strand was deposited to fill the largest opening in the array of strands. This “fill-in-the-blanks” process was considered complete when openings in the mat were no longer evident. A mat produced in this manner consisted of a single layer of COSB strand prepreg and constituted the structural unit in this method. The final mat-stacked COSB consisted of six layers of prepreg strand mats (each 215.9 × 215.9 mm mat weighing 41.7g) and had a total weight of 250 g (regardless of strand AR), equivalent to the total weight of a COSB produced by mechanical-agitation. This method resulted in 893 g/m 2 of areal weight per layer as compared with the 145 g/m 2 of the raw UD prepreg and indicates the degree of surface coverage by strand overlapping obtained with the proposed "mat-stacking" method. 15 Figure 2. (a)-(d) The “mat-stacking” layup method. (e) side view of mat-stacking layers. 2.2.3. Curing All COSB panels were cured by compression molding in a heated platen press (Wabash). High consolidation pressure was required to achieve low porosity and suitable resin bleed rate. The compression force was 3.4 MPa, and the curing cycle was 3 hours at 121 o C with a ramp rate of 2.8 o C/minute, followed by a 2-hour freestanding postcure at 177 o C. Following the procedures described, 8 COSB panels of 216 × 216 mm were produced. The panels belonged to two groups depending of the lay-up methods (mat-stacking and mechanical-agitation) and each group included four values of strand AR (1, 2, 5 and 10). 16 Figure 3. COSB manufactured using (a) mechanical-agitation layup (b) mat-stacking layup. 2.3. Microstructure 2.3.1. Thickness and flatness The COSB panels exhibit near-isotropic in-plane material distribution, and in that regard, they resemble quasi-isotropic layups. Nevertheless, a fair comparison between COSBs with quasi-isotropic laminates may not be realistic. Unlike traditional UD composite laminates, the internal structure (strand layout) of COSBs is irregular and differs from what appears on the surface. The three dimensionality of this material is apparent: the internal prepreg strands interact with adjacent strands in the z direction, perpendicular to the surface. The substantial overlap of strands resulted in mechanical performance similar to woven composites in some aspects, e.g., mode I fracture behavior. When exploring the elastic modulus and ultimate tensile strength of COSB, thicker samples yielded more representative values. A COSB panel with 250 g of prepreg is equivalent in mass to a quasi- 17 isotropic laminate panel with 25 unidirectional prepreg layers and a total thickness of ≈ 3 mm, which fits the general requirements of ASTM [19] (> 2.5 mm). To assess panel thickness uniformity, a long arm caliper gauge was used to perform thickness measurements of 100 equidistance points (10 by 10) on each edge-trimmed COSB panel. Figure 4. Thickness profile of (a) mechanical-agitation and (b) mat-stacking COSBs (c) average thickness values and (d) thickness spans of COSBs with two layup methods and four strand AR. 2.3.2. Void content and morphology Type A, B and C ultrasound scans were performed to reveal the overall void and strand distribution. All samples were scanned in water using a NDT ultrasound system (Mistras 18 NDT) with a 10 MHz transducer. A quasi-isotropic laminate produced with identical prepreg (CYCOM 5320-1 UD prepreg) was cured in an autoclave to serve as a reference panel. The reference panel had a void content < 0.5%. Ultrasonic A-scans were first performed on both COSB panels and the reference panels. To carry out the scans, the ultrasound transducer was fixed in position at the center of specimen, and a pulse-echo mode was used to identify defects. Figure 5. Ultrasonic c-scan results of “mechanical-agitation” layup (a) AR=2. (b) AR=10. “mat-stacking” layup (c) AR=2. (d) AR=10. (e) quasi-isotropic reference panel, compression molding cured. (f) quasi-isotropic reference panel, autoclave cured. For ultrasonic C-scans, a 20 MHz transducer was used to increase resolution. C-scans were performed on COSBs with AR=2 and AR=10 for mat-stacking and mechanical-agitation layup methods. A quasi-isotropic reference panel was produced by compression molding, and another quasi-isotropic reference panel was autoclave cured. Both reference panels 19 were fabricated using the same prepreg (Cytec 5320-1) and had void contents less than 0.5%. Figure 6. Void morphology and distribution of: (a) “mechanical-agitation” layup (AR=2). (b) “mat-stacking” layup (AR=2). (c)&(d):close-up views of (a)&(b). (e)&(f): side views of (a)&(b). X.-ray computed tomography (XCT) was performed on samples of 50 × 30 × 3.5 mm extracted from the center and edges of each COSB panel. XCT scans were acquired using a tomographic system (GE Phoenix Nanotom) to obtain void contents and morphology in 20 two COSB groups. XCT settings were 80 kV and 150 uA, with a 500 ms exposure time, yielding a resolution of 13 µ m/pixel. Initial scans showed that clear boundaries between strands could not be resolved using X-ray absorption tomography, even at the highest resolution. However, by viewing continuous frames of scanned images, animation revealed strand boundaries. This observation was helpful in identifying the shape of deformed strands and stitching together multiple volumes for further post processing and analysis. Multiple adjacent samples in all COSB groups were scanned, and XCT images and volumes were stitched and rendered using a user developed image post processing code to reveal void content and morphology. Figure 7. Number of voids for each size level: “mechanical-agitation” vs.”mat-stacking”, AR=2. 21 2.4. Mechanical characterization Static tensile tests were performed to determine the influence of layup methods and strand AR. All specimens were loaded to failure at 2 mm/min (0.05 inch/min) using a load frame (INSTRON) equipped with a digital image correlation (DIC) system. Quasi-isotropic fiberglass/epoxy tabs were bonded to the ends of each specimen to prevent slipping and stress concentrations during tensile tests. Elastic modulus, strain-to-failure, and ultimate tensile strength were measured. Because there was no standardized coupon dimension for this material, ASTM D-3039 [19] was selected as the most suitable standard. Specimen dimensions were 25 × 200 mm, and the thickness varied with strand AR and layup methods. For COSB panels with 10mm strand width, the coupon width would have to be greater than 20 mm to ensure representativeness. Failed specimens were inspected to characterize failure modes. Approximately 15 images were obtained from each failed sample to assemble a full-scale montage of the cross-section. 3. Results and discussion 3.1. Surface finish and resin bleed The two groups of COSB panels are shown in Figure 3. The mechanical-agitation COSB panels exhibited surface porosity and neglibible resin bleed at edges, while the mat- stacking panels showed excellent surface finish and extensive resin bleed, especially at higher strand AR (5:1 and 10:1). This effect was attributed to the difference in internal 22 structural configuration: the strands in mat-stacking COSB panels were organized spatially with less three-dimensional twist and zigzags, thus provided channels for resin flow. 3.2. Thickness and flatness The thickness and flatness of composite laminates depended on the amount of reinforcement and the relative amount of resin included. For COSB panels produced with similar quantities of prepreg, laminates with higher fiber volume fractions were thinner than those with lower fiber volume fractions. After hot-pressing, each COSB panel was trimmed to a square (200 mm × 200 mm) to remove irregular edges resulting from resin bleeding and strand sliding. The thickness profiles of both groups are shown in Figures 4 (a) and (b). The mat-stacking layup method yielded greater control of panel thickness t and flatness (variation of thickness over the panel surface). The average panel thickness t was generally 20-40% less when using the mat-stacking method, leading to two general observations. First, the average COSB panel thickness generally increased with AR (particularly from 1- 2 to 5-10) for both types of layups. Strands with low AR fit more easily into interstices, while the number of strands decreased and fewer strand ends existed within the structure with high AR. Thus, more strand “stacked area” was generated and the COSB overall thickness increased. Secondly, the thickness did not increase monotonically with the strand AR for the mechanical-agitation method. The thickness of panels produced with AR=2 strands was 3.7% less than that of the corresponding thickness for AR=1, and the thickness 23 of the panel with AR=10 was 2.9% less than that of AR=5. These small differences indicated resin-rich volumes were more randomly generated due to the intrinsic randomness of the mechanical-agitation layup method. The mat-stacking method increased COSB flatness, as shown in Figure 4 (d). For each strand AR, the difference between the maximum and the minimum thickness, 𝛿 , and the standard deviation (SD, values in brackets) was measured. The 𝛿 values were 0.2 mm (7.73%), 0.25 mm (7.37%), 0.3 mm (9.45%), and 0.3 mm (9.16%) for mat-stacking, and 0.4 mm (12.18%), 0.4 mm (12.33%), 1.0 mm (22.67%), and 0.6 mm (14.01%) for mechanical-agitation. These values reflected the statistical dispersion of the local thicknesses and provided a measure of overall flatness. 3.3. Non-destructive testing Two-dimensional maps of panel quality were produced using C-scan with a conventional pulse-echo or pulsed through-transmission system. The C-scans from COSB panels with AR=2 and AR=10 for both layup methods are shown in Figure 5, together with those obtained from quasi-isotropic laminates produced with the same process parameters. The gate range of the ultrasound wave signal was set to the thickness of each COSB, and the color scale bar indicates the signal attenuation level (which is related to the void content). Aluminum bars used to hold the COSB panels produced highest signal attenuation (dark red). Two general observations are noted. First, COSB panels exhibited high signal attenuations (max ~ 90%) compared to continuous fiber laminates (max ~ 10% to 20%), 24 reflecting the much higher void contents compared to the reference panels (porosity < 0.5%). Secondly, the mass distribution in COSB panels was more uneven than in the continuous quasi-isotropic laminates, as shown in Figures 5 (a) to (d). The uneven distribution of mass can be attributed to the different layup methods and to the lower resin mobility compared to continuous prepreg. For instance, the C-scan image of the mechanical-agitation COSB panel with AR=2 in Figure 5 (a) shows that most of the voids were trapped at the central and left-center regions. The mat-stacking COSB panel with strand AR=10 (Figure 5 (d)) exhibited a more uniform void distribution. The larger AR strands and the mat-shaking layup method led to a more uniform distribution of the strands and consequently, lower porosity level. For a given layup method, the use of higher AR strands led to lower overall void contents. In all cases, the mechanical-agitation COSB panels showed more uneven distribution of strands and voids. 3.4. XCT: void distribution content and morphology XCT provided additional insights into global distributions of voids and morphologies. Multiple scans (4-6) were performed on regions from each sample to cover the entire volume. The volumes obtained were reconstructed and stitched using a user-defined image post-processing algorithm. A segmentation method was used to extract the void content and spatial distribution of two COSBs produced by the two methods with strand AR=2. The rendered results are presented in Figure 6, in which the color scale indicates different void sizes, red being largest. 25 The total void content measured with the XCT images was ≈10% and ≈2.5% for the panels produced using the mechanical-agitation and mat-stacking methods, respectively. From visual inspection (Figure 6), the spatial distributions of voids differed substantially, and mechanical-agitation panels exhibited greater numbers of small (< 10 4 μm 3 ) and large (>10 5 μm 3 ) voids (Figure 7), both of which were heterogeneously distributed. Typically, the larger voids were a consequence of the uneven distribution of strands during the stacking process, producing bridges and gaps that were only partially filled with resin during consolidation. Some of the smaller voids were cylindrical and elongated along the fiber direction of the individual strands. In contrast, the porosity in the mat-stacking panels showed a finer dispersion of voids. The shape of the voids in both panels presented important differences (Figures 6 (a)-(d)). In the mechanical-agitation panels, the voids were irregular, while in mat-stacking panels, voids were mostly acicular. The final fiber crimping obtained with the two methods warrants comment because of the effect on mechanical properties. Figures 6 (e) and (f) show cross-sections of the two COSB panels. Judging from the morphology of the voids, the strands in the mechanical-agitation COSB panel exhibited greater curvature and undulation than the strands in the mat-stacking panel. The crimping effect will affect mechanical properties, especially those of panels with the highest AR. In addition, the strand gaps and bridges were precursors to resin pockets and voids that adversely affect mechanical properties. 26 3.5. Mechanical behavior Figure 8. Stress-strain curves of: “mechanical-agitation” and “mat-stacking” COSBs with AR=1. (b) AR=2. (c) AR=5. (d) AR=10. Tensile specimens produced by the two methods and with different strand aspect ratios were subjected to tensile deformation up to failure, and the stress-strain curves are summarized in Figure 8. The shapes of the stress-strain curves exhibited differences in elastic modulus, ultimate tensile strength, strain-to-failure, and experimental scatter. The stress-strain curves of mechanical-agitation COSB samples deviated early from linearity, and this was attributed to the presence of internal defects introduced during fabrication. In general, the mat-stacking COSB panels showed superior mechanical properties for a given 27 AR, and these properties generally increased with the length of the strand. The mat- stacking COSB panels also exhibited much lower coefficients of variation (CoV) compared to those of mechanical-agitation panels, indicating benefits of the more controlled manufacturing route. Figure 9. Modulus, strength, strain-to-failure of “mechanical-agitation” and “mat-stacking” COSBs. 28 Mechanical properties are summarized in Figure 9, in which each group of columns represents six tensile coupons cut from one COSB panel. Three general observations can be made. First, the elastic modulus, strength, and strain-to-failure generally increased with AR for both methods. For each AR, all mat-stacking COSB materials showed superior properties compared to mechanical-agitation COSB (for AR=10, there was a 138% increase in strength and 74% increase in strain-to-failure). Second, the average elastic modulus of the COSB materials with large AR was similar to one of the standard quasi- isotropic panels. For the AR=10 mat-stacking COSB, coupons showed an average modulus of 61.7 GPa, which was larger than that of the quasi-isotropic panel (57.6 GPa), and was slightly less than the modulus of aluminum (69 GPa). Finally, the mat-stacking materials yielded data with much lower values of standard deviation (SD) and coefficient of variation (CoV) (Figure 10). COSB panels produced by the mechanical-agitation method exhibited larger scatter, a result of the non-homogeneous strand, void, and resin distribution shown by ultrasound inspection in Figure 5(a) and (b). In contrast, mat-stacking materials exhibited more homogeneous signal attenuation in ultrasound inspection, resulting in more homogeneous values of modulus, strength and strain-to-failure (Figure 9). 29 Figure 10. Mat-stacking layup markedly reduced the coefficient of variation of elastic modulus. Four types of failure modes were observed, and the associated damage mechanisms stemmed from the void characteristics noted above. The fracture of mechanical-agitation COSBs featured wedge pullout, while mat-stacking COSBs showed both strand pullout (with smaller AR strands), and strand breaking (with larger AR strands). The fourth failure mode was a mixed mode of both strand pullout and strand breaking. Figures 11 (a) – (d) show that the mechanical-agitation COSB specimens split into two fracture surfaces that slid relative to one another. Multiple cracks were observed through the specimen thickness, indicating that the fracture followed a tortuous path of least resistance linking the void 30 clusters. In most of the mechanical-agitation specimens, wedge pullout consisted of multiple strands through the thickness that were pulled out, resulting in the non-linear stress-strain behavior. Figure 11. Failure mechanisms: “mechanical-agitation” COSBs with (a) AR=1, (b) AR=2, (c) AR=5, (d) AR=10, and, “mat-stacking” COSBs with (e) AR=1, (f) AR=2, (g) AR=5, (h) AR=10. The mat-stacking specimens showed different types of failure modes. Strand pullout occurred in COSB samples with lower AR strands, as shown in Figures 11 (e) and (f). Strands pulled out and cracks tended to follow strand edges. The load (even at peak) was not sufficient to break the strands, and cracks tended to follow resin-rich areas as in the case of mechanical-agitation materials. On the other hand, mat-stacking specimens with higher AR strands exhibited strand breaking or mixed mode failure (Figures 11 (f) – (h)) and, as a result, superior properties compared to the other materials. In these cases, longer prepreg strands were the main load carrying elements, and these were controlled by the carbon fiber strength. The longer strands through thickness were eventually broken into 31 segments (Figure 11 (h)). As a result, mat-stacking COSB coupons showed greater values of ultimate strength and strain-to-failure compared to mechanical-agitation COSB coupons. 4. Conclusions We have presented a mat-stacking method to lay up strands to produce COSB panels. Thickness profiles, microstructures, mechanical properties and failure mechanisms for different strand AR (1, 2, 5, and 10) were studied. The process modification we demonstrated yielded COSB panels with more controllable thickness and flatness, and with significantly enhanced microstructure that has less amount of voids. As a result, mechanical property levels of mat-stacking COSB panels were markedly improved (e.g. for AR=10, a 138% increase in tensile strength and 74% increase in strain-to-failure), and CoV values decreased from ~20% to ~5%. The mat-stacking method utilized the concept of lamination and aimed at an even distribution of strands and internal voids (with improved morphology). When properly laminated, structural loads were shared by more prepreg strands, and failure modes advanced from “Wedge-Pullout” to a mixed mode of “Strand-Pullout” and “Strand-Breaking”. The work performed here provides a potential solution to prepreg production scraps with enhanced quality assurance. However, the improvements in mechanical performance come at significant cost of processing time and labor, unless the arrangement of strands can be automated in a continuous process. In this study, a semi-automatic feeding and cutting machine was designed. In the future, systems for fully automated strand cutting and 32 placement will be required for large-scale production of COSB products. Producers of composite parts that use hand layup constantly generate large amount of prepreg skeletons that could be material source of future COSB productions. In this regard, incorporating scraps of different types of prepregs (e.g. various fabric, shape, epoxy formulations, areal weight, aged level) from various producers could be a challenge. Meanwhile, out-time related steps such as collection, logistics, and storage of the prepreg scraps will be some of the hurdles. Lastly, building a market that uses COSB products will require quality assurance, property uniformity, and complete property databases. The study also establishes a basis for future efforts to develop a parametric design space. Logical extension of this work should focus on simulation models [20] to understand the progressive failure mechanisms, and extending the flat stacking approach to fabrication of contoured parts. Ac k n ow ledgem e n ts This research was supported by NSF G8 Initiative “Sustainable Manufacturing of Composite Materials” (Award # CMMI-1229011) and Airbus Institute for Engineering Research (AIER) program. The finantial support from the Comunidad de Madrid through the program DIMMAT (S2013/MIT-2775) is also gratefully acknowledgeded. Authors appreciate Prof. Stephen Tsai for his warm discussions and helpful suggestions. 33 References [1]. Current Market Outlook. Report. Boeing Commercial Airplanes. 2015. [2]. Jeff Sloan. Composites recycling becomes a necessity. 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Mechanical properties of randomly oriented strands thermoplastic composites. Conference procedding. 19th Int. Conf Compos Mater. Montreal, Canada. 2013;1:480-8. [13]. Landry B, Hubert P. Experimental study of defect formation during processing of randomly-oriented strand carbon/PEEK composites. Compos Part A 2015;77:301-9. [14]. LeBlanc D, Landry B, Levy A, Hubert P, Roy S, Yousefpour A. Study of processing conditions on the forming of ribbed features using randomly oriented strands thermoplastic composites. J Am Helicopter Soc 2015;60. [15]. Picher-Martel G-P, Levy A, Hubert P. Compression molding of carbon/PEEK randomly-oriented strands composites: a 2D finite element model to predict the squeeze flow behavior. Compos Part A: Appl Sci Manuf 2016;81:69–77. [16]. Feraboli P, Cleveland T, Stickler P, Halpin J. Stochastic laminate analogy for simulating the variability in modulus of discontinuous composite materials. Compos Part A: Appl Sci Manuf 2010;41:557-570. 35 [17]. 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J Eng Mater Technol 2011;133:041014. 36 PART II Numerical Simulation and Finite Element Analysis of Complex Geometry Random Fiber Composites at Fiber Level with High Volume Fraction and High Aspect Ratio Fiber reinforced composites with innumerable fiber strand orientation and distribution and fiber and matrix geometries are abundantly available in several natural and synthetic structures. Carbon fiber composites have been introduced to numerous applications due to their economical fabrication and tailored structural properties. Numerical characterization of such composite material systems is necessitated due to their intrinsic statistical nature, which renders extensive experimentation prohibitively time consuming and costly. To predict various mechanical behavior and characterizations of Uni-Directional Fiber Composites (UDFC) and Random Fiber Composites (RaFC), we numerically developed Representative Volume Elements (RVE) with high accuracy and efficiency and with complex fiber geometric representations encountered in unidirectional and random fiber composites. In this work, the numerical simulations of unidirectional RaFC fiber strand RVE models (VF>70%) are first presented by programming in ABAQUS PYTHON. Secondly, when the cross sectional aspect ratios (AR) of the second phase fiber inclusions are not necessarily one, various types of RVE models with different cross sectional shape fibers are simulated and discussed. A modified random sequential absorption algorithm is applied to enhance the volume fraction number (VF) of the RVE, which the mechanical properties 37 represents the composite material. Thirdly, based on a Spatial Segment Shortest Distance (SSSD) algorithm, a 3-Dimentional RaFC material RVE model is simulated in ABAQUS PYTHON with randomly oriented and distributed straight fibers of high fiber aspect ratio (AR=100:1) and volume fraction (VF=31.8%). Fourthly, the piecewise multi-segments fiber geometry is obtained in MATLAB environment by a modified SSSD algorithm. Finally, numerical methods including the polynomial curve fitting and piecewise quadratic and cubic B-spline interpolation are applied to optimize the RaFC fiber geometries. Based on the multi-segments fiber geometries and aforementioned techniques, smooth curved fiber geometries depicted by cubic B-spline polynomial interpolation are obtained and different types of RaFC RVEs with high fiber filament aspect ratio (AR>3000:1) and high RVE volume fraction (VF>40.29%) are simulated by ABAQUS scripting language PYTHON programming. 1. Introduction In view of the increasing demand in aerospace and automotive industries for cheaper materials with lower density and superior strength-to-weight and modulus-to-weight ratios, fiber reinforced composites (FRCs) have been introduced to numerous applications due to their supreme strength and stiffness properties along with their lightweight characteristics [1–5]. However, the cost of traditional FRC materials is still considerable. Random fiber reinforced composites (RaFC) have a promising alternative for their low cost, light weight structure, and efficient production capability [5]. In the last four decades finite element 38 methods (FEMs) have successfully become the prevalent computational analysis technique of designing RaFC materials with optimized physical properties [6]. Important contributors on the overall composite material behavior are the fiber dimensions and geometry [6,7] among others. Cendre et al. [8] used high-resolution X-ray synchrotron microtomography to measure two samples of unidirectional glass fiber composites with 55% volume fraction (VF) and reported 3D computerized tomography (CT) images, which demonstrated the irregular fiber distribution and the varying glass fiber diameters ranging from 0.0102 mm to 0.0234 mm. The commercial and industrial use carbon fibers have diameters in the range of [0.0050–0.0100] mm [9]. Fang [10] experimentally investigated the diameter effects associated with a single glass fiber filament strength and a glass fiber composite bending strength and determined that the average strengths of single glass fiber filaments decrease from 2.52*10 3 MPa to 1.81*10 3 MPa as their average diameters increase from 0.0136 mm to 0.0298 mm. In contrast, the bending strength of dry-state glass fiber composites reduced from 1070 MPa to 848 MPa with an average fiber diameter reduction from 0.023 mm to 0.008 mm. The identification of a representative volume element (RVE) is obvious in laminate [11] and woven composite materials [12,13] due to the repeatable structure of the architecture. However, in composite materials with random fiber reinforcements the numerical simulation of an RVE is not straightforward. Similar to the RVE definition of those composites that have a repeatable structure, the RaFC RVE, of which fiber reinforcement inclusions have random orientation distribution and location, additionally requires a 39 statistical representation of its characteristics. There are five key methods that have been used for numerical generation of RVEs of composite materials, namely, molecular dynamics, Voronoi tessellation scheme [14], Monte Carlo (MC) procedure (mechanical contraction method), random sequential adsorption (RSA) method[12,13], and image reconstruction technique. One of the earliest methods was based on molecular dynamics using an equilibrium fluid as a starting point. The shortcoming of this approach by Williams and Philipse [14] pertains to the resulting physical interference of the inclusions. Another novel method used by Hinrichsen et al. [15] was to form a Voronoi tessellation around some inclusions, which are all then moved to the center of their Voronoi cell, and the RVE volume was reduced until a pair of inclusions came into contact with each other. The procedure was repeated until the RVE could no longer be reduced in volume. Related to the Voronoi tessellation method, MC simulations have been widely used in RVE generation. The MC two-step procedure starts with a configuration of arbitrary fiber locations and orientations within a large box and their rearrangement, without accepting physical intersections, until a predetermined desired orientation state is reached. The MC method has been widely used by Gusev [16] and Gusev et al. [17,18] for studying the short FRC material properties. The RSA schemes [12,19] are very popular in studying sphere [14,20–22], spherocylinder [14,20], ellipsoid, and rod [14,20,21,23] packing schemes during RVE generation of composites. In RSA method, inclusions are added to the RVE by randomly generating its location and orientation angle. In the case of fiber reinforcing, the newly introduced fibers 40 cannot intersect with any of the previously generated ones. Boehm et al. [20] applied the modified RSA method and achieved 15% VF in generating metal matrix composite RVEs with random short fibers of AR=5 aspect ratio. Fibers are not allowed to overlap in RSA, thus a minimum distance between any two fibers is set with regard to the side length of the RVE model. Geometrical periodicity is usually applied with the RSA scheme to enhance the VF. Tu et al. [21], Iorga et al. [24], and Pan et al. [25] applied modified RSA algorithm and achieved RVEs with AR=7 for spherical particles and AR=10 (with VF=13.5%) for random chopped fibers, respectively. It should be noted that the VF achievable through RSA is much smaller than that predicted by existing analytical models; Widom [12] refers to this phenomenon as “Jamming Effect.” To overcome the jamming effect, Kari et al. [23] used fibers of different sizes and deposited them inside the RVE in a descending manner. A recent method applied in RVE generation is the 3D image reconstruction via X-ray tomography and image processing technique. Some good examples on FRCs and wood fiberboard based on the CT image reconstruction are presented by Redenbach and Vecchio [26] and Faessel et al. [27]. The 3D fiber networks of the samples are reconstructed and generated based on X-ray absorption radiographs using specialized software. However, this method is challenging in that the obtained geometry cannot be modified for different composite architectures, thus its appeal is limited. While the 3D CT application appears attractive for the random fiber networks, modeling of composites with straight fibers of fixed aspect ratio using Monte Carlo and RSA procedures [12,13] results in low fiber volume fractions. When the fibers are modeled as 41 short straight cylinders with small aspect ratio lower than 10, the VF of the RVE is generally found to be less than 25%. For fibers with aspect ratio 20, the relation between the fiber aspect ratio and the maximum achievable fiber VF is 20% as illustrated by Evans and Gibson [28], 30% by Parkhouse and Kelly [29], 18.5% by Toll [30], and 27% by Williams and Philipse [14]. However, their results not only indicate that the increase of the fiber aspect ratio will result in decrease of the maximum achievable fiber volume fraction but also that the volume fractions as predicted by their RVE models are still relatively small compared to the composites used in industry, which have volume fractions larger than 40% [25]. Modeling RaFC materials with high fiber filament aspect ratios (AR>20:1) and high fiber volume fractions (VF>20%) in PYTHON is challenging. Nevertheless, PYTHON cannot only access ABAQUS model databases to automatically establish complex geometries and apply material properties in its CAE modulus but, more importantly, is also able to merge FEM procedures within the programmed codes and perform FEA tests in ABAQUS Standard/Explicit automatically. In this work, a 3D RaFC RVE model with AR=100:1 and VF>31.8% is simulated for illustration purposes by taking advantage of the PYTHON scripting capabilities and the automatic complex geometries generation in ABAQUS. 2. RVE Generation of Unidirectional Filaments A typical specimen of fiber RaFC in a polyurethane matrix is illustrated in Fig. 1. The RaFC specimen consists of 50 mm long and 1 mm wide randomly distributed fibers. These 42 dimensions are statistically determined by sampling the specimens throughout various sections. Cendre et al. [8] applied X-ray tomographic microscopy (XTM) as a nondestructive characterization technique, which ensures high-resolution images of heterogeneous materials, enabling the distinction of individual fibers and matrix in composites. As a result, the irregular fiber distribution and varying fiber diameters are easily detected. The top right corner of Fig. 1 illustrates a 3D XTM view of a unidirectional composite specimen with 55% fiber volume fraction. The cross section (c/s) perpendicular to the fibers not only explicates the irregular fiber distribution but also clearly indicates the varying fiber diameter dimensions. In order to accurately represent the geometry of the specimen to be simulated, cross sections perpendicular to the longitudinal direction of the elliptical fibers (composed of numerous filaments with circular c/s) are examined with a scanning electron microscope (SEM) and characterized, as shown in Fig. 2. The semi- major axis length of the ellipse’s c/s is defined as “a” and the semi-minor axis length of the ellipse’s c/s is defined as “b.” Note that the major axis of the elliptical c/s, which in Fig. 2 is marked as the length “2a,” is also the 1 mm fiber width shown in Fig. 1. In this study, we statistically determined that the average semi-minor axis length of the elliptical c/s is 0.03 mm, while the average semi minor axis length of the cross section (c/s) ellipse is 0.50 mm resulting in fiber c/s aspect ratio of 2a/2b=16.67:1. The length and the width of the fiber (elliptical cylinder in Fig. 2) equals to 100a and 2a, respectively, ensuing a 100a/2a fiber aspect ratio of AR=100. The cross sections of the fiber filaments (marked with black ink in Fig. 2) are of circular shape and their radii are in the range of 0.010 mm (10 lm) to 0.025 mm (25 lm), with an average radius of 0.016 mm (16 lm). All filaments are unidirectionally aligned along the longitudinal direction of each fiber. 43 Fig. 1 Glass fiber RaFC specimen and the manufacturing process of Reused Carbon fiber RaFC panel. 44 The effective elastic properties of FRC materials depend on the elastic properties of their constituents as well as on the geometry of their reinforcing phases [31–33]. Moreover, in contrast to circular c/s filament reinforcements, Zhao and Weng [34] derived the elastic moduli in terms of c/s aspect ratio and fiber volume fraction. The analysis indicates that fibers with ribbon shaped c/s are far more effective in terms of packing than the traditional circular cylindrical filament reinforcements. In order to capture the characteristics of the material structure observed above (Figure 1), a 3D RaFC fiber RVE model was generated. We developed a fiber RVE material model based on PYTHON (an ABAQUS scripting language) using the RSA scheme. Fiber collision and interpenetration were not permitted throughout the process as reflected in our protocol, which is summarized in Sec. 2.1. The collision detection algorithms and a modified RSA scheme are applied to enhance the volume fraction of the RVE model and are discussed in Sec. 2.2. In Sec. 2.3, a spatial segment shortest distance (SSSD) algorithm is developed and a RaFC RVE model in 3D space is simulated. Finally, the element properties and material direction information from the 3D model are extracted and input into a simplified 2D model, which has the same material configuration with the manufactured carbon fiber RaFC samples. The predicted modulus results are validated using experimental testing and proved to be accurate. 45 Fig. 2 Microscopic images of cross sections of a fiber strand from a RaFC specimen. Note the damage and removal of fiber filaments (due to cutting and polishing) on the left corner of the elliptical cross section. 2.1 Numerical Modeling of a Fiber RVE. The term data structure in PYTHON language is referred to as the term “Dictionary,” the array is referred as the term “List.” The tree data structure is applied throughout the algorithm. The RVE list includes multiple “FIBER” dictionaries (each FIBER dictionary in the algorithm is defined as including integer, or float), variables and matrices (such as fiber-number, fiber-volume, fiber-translate-matrix, and fiber-rotation-matrix), and subdictionaries (such as fiber-type-dictionary and segment-dictionary). Two subdictionaries are illustrated here as examples: (a) fiber-type-dictionary, which includes a cylindrical-fiber-filament-dictionary with a final subdictionary of the cross sectional radius “r,” and an elliptical-fiber-filament-dictionary with a final subdictionary of semi- 46 major axis a and semi-minor axis b; and (b) segment-dictionary, which encompasses variables such as segment-number, part-name, instance-name, layer-number, and last level subdictionary like segments-end-points. The last level subdictionary segments-end-points are defined as spatial Cartesian coordinate points, {‘x1’; ‘y1’; ‘z1’} and {‘x2’; ‘y2’; ‘z2’}. The filament lengths are identical in one fiber and a cross section perpendicular to the fiber longitudinal direction represents the geometry of the fiber RVE. In order to overcome the jamming difficulty in generating a time efficient RVE with high fiber volume fraction, a value of 50*r is set as the side length of the square shaped RVE. In what follows, the protocol to generate the fiber RVE is described. (1) At the beginning of each iteration, a filament with either circular c/s of radius r, or with elliptical cross section of semi-major axis a and semi-minor axis b, is generated along z- axis in ABAQUS. (2) A random rotation matrix is generated and applied to the current filament. Note that the current fiber along the z-axis will be randomly rotated about the z-axis only. (3) A random translation matrix is generated and applied to the current rotated filament, allowing the current fiber to be translated within x-y plane only. (4) The current filament is filtered with the compatibility collision detection algorithm (Sec. 2.2). If any physical collision of the current filament with existing local ones is detected, the current filament will be either moved to a vacant space and go through the iteration procedure until generated or will be simply discarded if iterations overflow a 47 predetermined value. Otherwise, the examined filament will be generated at this new collision free position. (5) If the filament is successfully generated, its volume will be calculated and added to the current total fiber volume within the RVE. (6) At the end of each iteration, the current total fiber volume fraction is calculated and compared to the requested volume fraction. The algorithm will continue unless it meets either of the following conditions: the current fiber volume fraction reaches or exceeds the requested volume fraction value; or when additional attempts do not provide any meaningful improvements, that is, the total iteration number overflows or exceeds a preset experience based value. (7) RVE is successfully generated. Calculate and output all necessary parameters, such as filament separation distances, filament volume fractions, etc. 2.2 Modified RSA Scheme with Collision Detection Algorithm. In order to increase the efficiency of our algorithm, the RVE is divided into 625 second level subsquares with each side length of 2*r, as shown in Fig. 3. When the center point of a newly introduced filament is located on the edge of any second level square, filament collision check is performed to the filaments located within up to four (4) neighboring squares, as shown in the blue region in the lower right corner of Fig. 3. When the center point of a newly introduced filament is located within a certain second level square, the collision check of this filament is performed to the filaments located within eight second level squares around the current location, as shown in the green region in the top left corner 48 of Fig. 3. For any two filaments checked for physical collision, a geometric compatibility test follows. The filaments discussed in this work are of circular and elliptical cross sections. Fig. 3 Spatial division of the RVE. Green region: collision check area for new filament located at center of second level square. Blue region: collision check area for new filament located on the edge of second level square. 2.2.1 Circular Cross Section Filaments. In previous studies on unidirectional FRC materials, filament cross sections have been mostly treated as circular. For circular cross section filaments, the calculated x-y plane distance from the new filament’s center position to the center position of the existing filament, should fit the criterion dcriterion < 2 * r + dmin (1) 49 where dmin is the preset minimum tolerable distance between any two filaments and r is the filament’s radius. Following collision detection criterion of Eq. (1) a unidirectional RVE model of RaFC fiber, with 60% fiber volume fraction, is generated and presented in Fig. 4(a). Each filament has the same radius r and aspect ratio of l/r=100 (l=filament length). Additionally, by applying proper boundary conditions the real fiber configuration in the RaFC specimen can be achieved as shown in Figs. 4(b) and 4(c). The shape of the RVE is described by the canonical implicit elliptical equation 𝑥 2 𝑎 2 + 𝑦 2 𝑏 2 < 1 (2) According to the experimental observations in Sec. 2, the radii of the filaments are not identical. Filament radii in RaFC structures range from 0.010 mm (10 um) to 0.025 mm (25 um), with an average radius of 0.016 mm (16 um). Based on the above observation, the RSA algorithm is modified and the collision detection criterion of the cylindrical filaments is expressed as dcriterion < r1 + r2 + dmin (3) where r1 and r2 are the filament radii involved in the collision detection. While the filament radii can vary, the volume fraction of the RVE may theoretically reach 100%. A RVE model consisting of filaments with a variety of radii is presented in Figs. 4(d) and 4(e), with volume fractions of 65% and 70%, respectively. 50 Fig. 4 Unidirectional fiber RVEs with filament aspect ratio of l/r=100. (a) Square c/s and, (b), (c) elliptical c/s fiber with VF of 60%; each filament has the same radius r. (d), (e) Square c/s fibers with 65% and 70% VF, respectively, and (f) elliptical c/s fiber with 70% VF; filaments have a variety of radii sizes to increase packing capability (higher density fibers). 51 2.2.2 Elliptical Cross Section Filaments. When the filament c/s is elliptical such that the aspect ratio a/b (thickness to width ratio) is a/b=1, the moduli of the fiber, thus the composite, will be different since elliptical filaments present higher packing capacity as well as more anisotropy. In this RVE, the filament’s elliptical c/s, see Fig. 5, is defined as a set of points (X, Y) of the Cartesian plane that satisfy the implicit ellipse equation AX 2 + BXY + CY 2 + DX + EY + F = 0 (4) provided that B 2 -4AC<0. Two collision detection algorithms are proposed. 2.2.2.1 Algorithm 1 - Polygon Method. In order to be computationally efficient during collision detection, we approximate the filament elliptical c/s with polygons. In this polygon collision detection algorithm, two ellipses are considered as “collision free” if the two polygons surrounding them do not interfere with, or included in, one another. The detection of two polygons can be reduced to the collision detection of the polygons’ edges. So as to avoid the situation in which one polygon is included into another, two points in each polygon are picked randomly and tested to see if they exist in both polygons. Figure 5 illustrates the elliptical c/s as approximated by a square, a hexagon, and an octagon. During execution of the polygon method, the algorithm’s efficiency heavily depends on the ellipse’s cross sectional aspect ratio a/b; in particular when a/b approaches zero, that is, 52 ribbon shaped filaments, the packing efficiency is increased. Furthermore, employment of the polygon method results in overall reduction of the fiber volume in the RVE since the available space for generation of new fibers is limited. For instance, in the case of approximating a circular c/s filament (a/b=1) using a rectangular polygon the maximum volume fraction is 78.54%. Fig. 5 The polygon method for elliptical cross section fiber reinforcement 2.2.2.2 Algorithm 2 - Minimum Collision Distance Method. The minimum acceptable distance between two elliptical filament c/s is calculated according to Fig. 6 where the green ellipse represents an existing filament with center point OA and the red ellipse represents the introduced filament with center point OB, which is required to be checked for collision compatibility. The critical value of collision distance is presented as distance OAOC between the green and blue ellipses and calculated according to 2D analytical geometry; note that OAOC includes a minimum tolerance segment between any two elliptical filaments. The collision criterion, therefore, is obviously described as OAOB>OAOC. New elliptical filaments will be generated when this collision criterion fits, or, will be discarded otherwise. Figure 4(f) illustrates a fiber generated using the minimum 53 collision distance method where x 2 /a 2 + y 2 /b 2 < 1 is employed as the boundary condition of the RVE shape. Fig. 6 Collision detection of elliptical fiber reinforcement. The green ellipse is an existing filament (center point OA), and the red ellipse is the introduced filament (center point OB) to be checked for collision compatibility. 2.3 Numerical Modeling of Random Fiber Composites Using Cylindrical Fiber RVE. Based on the aforementioned technique, a SSSD algorithm is developed in PYTHON (ABAQUS scripting language) and applied in simulating RVEs of RaFCs. The process is depicted in the flowchart in Fig. 7. The SSSD algorithm calculates the 3D shortest distance between any two random limited length segments in space. When calculating the two endpoint coordinates of the common perpendicular segment between two fiber axes, the cylindrical fiber with circular c/s is defined algebraically as the solution set of a linear system. For the nth new fiber in the RVE, n*1 calculations need to be performed with every existing fiber, that is 54 Ax < b (5) where A is a real 3n*3n matrix, b is a real 3n*1 vector, and x is a 3n*1 vector including the information of 3D spatial point coordinates of each pair of fibers to be tested. Note that when the current fiber is the 103rd in sequence, the coordinate vector x may reach the order of 104, while the element number of matrix A is in the order of 106. To solve the linear system, we apply a modified LU decomposition algorithm Pn-1……P2P1AQ1Q2……Qn-1=A’ (6) The system is then determined by A’ = PAQ (7) where P and Q are the symmetric and orthogonal permutation matrices. Thereafter, Eq. (4) can be rewritten as PAQQ T X < Pb (8) The numerical solution of the linear system is then obtained by applying LU decomposition on the new system with A’ matrix LUx’ < b’ (9) 55 The 3D collision criterion of the fibers is similar to the introduced 2D unidirectional fiber simulation: when the shortest distance between any two fibers is larger than a preset minimum collision free distance, the two fibers will be generated in the 3D space. The RVE size is chosen based on results from previous studies for straight fiber RVEs with varying sizes [25], which suggests that satisfactory results are given when the ratio of RVE side length to fiber length is 2:1. Fig. 7 Flow chart of a RaFC RVE generation using an SSSD algorithm is developed in PYTHON 56 Although industrial applications usually require RaFCs with high aspect ratios and high volume fractions, Boehm et al. [20] used the RSA method to generate a 15% VF RVE with fiber aspect ratio of AR=5. Tu et al. [21] also used the RSA approach for fibers of AR=7:1. Iorga et al. [24] applied the modified RSA algorithm for a RaFC with fiber AR=10:1 and achieved composites with VF=13.5%. For fibers with larger aspect ratio AR=20, the relation between the fiber AR and the achievable fiber VF has been reached to 20% by Evans and Gibson [28], to 30% by Parkhouse and Kelly [29], to 18.5% by Toll [30], and to 27% by Williams and Philipse [14]. In contrast to these studies, all filaments in the present investigation are simulated as cylinders with AR=100:1. Figure 8 illustrates a random fiber composite RVE generated with three layers of straight cylindrical fibers of high aspect ratio, AR=100:1, and high volume fraction, VF=31.8%, which is within the range of the values employed in industry. 57 Fig. 8 Random fiber composite RVE with AR=100:1 and VF=31.8% The model (with no spatial collision) is thus consider as representative compare to the manufactured RaFC samples. The model is then trimmed into 25mm by 200mm coupons, with all the element orientation and material properties information transferred to a 2D simplified model with two types of distributions (Figure 9 upper). Realistic boundary condition (fix the left end) and loading condition (uniaxial loading on the right end) are applied, and equivalent modulus are predicted using Finite Element Methods, and compared to experimented measured values (Figure 9 lower). 58 3. Results and Discussion In this work, a 3D RaFC RVE geometry model with AR=100:1 and VF>31.8% is simulated by PYTHON. This scripting code can currently access the ABAQUS model database to automatically establish complex geometries and apply material properties in ABAQUS/CAE modulus. Single filaments were modeled as straight cylinders with circular and elliptical cross sections, and longitudinal aspect ratio of AR=100:1, so as to study the packing capacity of a single fiber with respect to the cross sectional geometry of the filaments. The attained AR values were comparable to the ones employed in industrial applications and are a significant improvement to current research efforts in RaFCs. Moreover, from studying a variety of filament packing geometries, it was concluded that the elliptical c/s filaments produce higher density (tighter packed) fibers. A modified RSA algorithm was applied to enhance fiber volume fraction. Fibers with volume fractions as high as VF=70% were achieved in the cases of circular cross section filaments with an assortment of radii values (Figs. 4(d)–4(f)). Moreover, based on a SSSD algorithm, a 3D RaFC material RVE model was simulated in ABAQUS PYTHON with randomly oriented and distributed, high aspect ratio (AR 100:1) straight fibers to attain a volume fraction of VF=31.8%, which is comparable to the ones used in RaFC industrial applications. To expedite the simulation speed, the 3D models are transferred into 2D version for fast calculation. The predicted modulus value of the RaFC material are reasonably close to the experimental measured value. 59 It is expected, that the automatic formulation of complex geometry models will greatly enhance the accuracy and efficiency of both 3D and 2D analytical simulations and optimization of RaFC structures, once they are adopted into the FEM procedures in ABAQUS Standard/Explicit. This modeling work has brought infinite possibilities to the research work in predicting various mechanical properties and parametric design of the mentioned random strand fiber composites, saving years of experimental investigation time by means of accurate and efficient computer simulations. 4. Conclusions Representative volume elements (RVEs) accurately depicting-per industrial standards-the geometry, volume fraction, and aspect ratios are developed for unidirectional and random fiber composites. Geometry characterization is determined by optical and SEM studies. PYTHON programming is used in order to automatically generate the RVEs in ABAQUS. Single fiber RVEs composed of filaments with circular or elliptical cross sections and a variety of radii are composed to study their packing capacity, resulting to unidirectional fibers with 70% volume fraction. Based on an RSA algorithm combined with an in-house developed SSSD algorithm using modified LU decomposition we developed a 3D RVE model for a random fiber composite material in ABAQUS PYTHON with randomly distributed and orientated fibers of high fiber aspect ratio (AR=100:1) and high volume fraction (VF>31.8%). Coding in PYTHON as a scripting language for ABAQUS has greatly enhanced the accuracy and efficiency of the geometric representation of RaFC structures. Details such as 3D architectural and interfacial information of filaments and 60 fibers, which otherwise are lost due to the resolution of the numerical methods used, can now be easily carried to ABAQUS for further finite element analysis. References [1] Harris, C. E., Starnes, J. H., and Shuart, M. J., 2002, “Design and Manufacturing of Aerospace Composite Structures, State-of-the-Art Assessment,” J. Aircr., 39, pp. 545–560. [2] Soutis, C., 2005, “Carbon Fiber Reinforced Plastics in Aircraft Applications,” Mater. Sci. 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A., 1997, “Representative Volume Element Size for Elastic Composites: A Numerical Study,” J. Mech. Phys. Solids, 45, pp. 1449–1459. [17] Gusev, A. A., Heggli, M., Lusti, H. R., and Hine, P. J., 2002, “Orientation Averaging for Stiffness and Thermal Expansion of Short Fiber Composites,” Adv. Eng. Mater., 4(12), pp. 927–931. [18] Gusev, A. A., Hine, P. J., and Ward, I. M., 2000, “Fiber Packing and Elastic Properties of a Transversely Random Unidirectional Glass/Epoxy Composite,” Compos. Sci. Technol., 60(4), pp. 535–541. 62 [19] Wang, Z., Wang, X., Zhang, J., Liang, W., and Zhou, L., 2011, “Automatic Generation of Random Distribution of Fibers in Long-fiber-Reinforced Composites and Mesomechanical Simulation,” Mater. Des., 32(2), pp. 885–891. [20] Boehm, H. J., Eckschlager, A., and Han, W., 2002, “Multi-Inclusion Unit Cell Models for Metal Matrix Composites With Randomly Oriented Discontinuous Reinforcements,” Comput. Mater. Sci., 25(1–2), pp. 42–53. [21] Tu, S. T., Cai, W. Z., Yin, Y., and Ling, X., 2005, “Numerical Simulation of Saturation Behavior of Physical Properties in Composites With Randomly Distributed Second-Phase,” J. Compos. Mater., 39(7), pp. 617–631. [22] Coelho, D., Thovert, J. F., and Adler, P. M., 1997, “Geometrical and TransportProperties of Random Packings of Spheres and Aspherical Particles,” Phys. Rev. E, 55(2), pp. 1959–1978. [23] Kari, S., Berger, H., and Gabbert, U., 2007, “Numerical Evaluation of Effective Material Properties of Randomly Distributed Short Cylindrical Fibre Composites,” Comput. Mater. Sci., 39(1), pp. 198–204. [24] Iorga, L., Pan, Y., and Pelegri, A. A., 2008, “Numerical Characterization of Material Elastic Properties for Random Fiber Composites,” J. Mech. Mater. Struct., 3(7), pp. 1279– 1298. [25] Pan, Y., Iorga, L., and Pelegri, A. A., 2007, “Analysis of 3D Random Chopped Fiber Reinforced Composites Using FEM and Random Sequential Adsorption,” Comput. Mater. Sci., 43(3), pp. 450–461. [26] Redenbach, C., and Vecchio, I., 2011, “Statistical Analysis and Stochastic Modeling of Fibre Composites,” Compos. Sci. Technol., 71(2), pp. 107–112. 63 [27] Faessel, M., Delise´ e, C., Bos, F., and Caste´ ra, P., 2005, “3D Modeling of Random Cellulosic Fibrous Networks Based on X-Ray Tomography and Image Analysis,” Compos. Sci. Technol., 65(13), pp. 1931–1940. [28] Evans, K. E., and Gibson, A. G., 1986, “Prediction of the Maximum Packing Fraction Achievable in Randomly Orientated Short-Fibre Composites,” Compos. Sci. Technol., 25(2), pp. 149–162. [29] Parkhouse, J. G., and Kelly, A., 1995, “The Random Packing of Fibers in Three Dimensions,” Proc. R. Soc. London, Ser. A, 451(1943), pp. 737–746. [30] Toll, S., 1998, “Packing Mechanics of Fiber Reinforcements,” Polym. Eng. Sci., 38(8), pp. 1337–1350. [31] Jones, B. F., 1971, “Further Observations Concerning the Effect of Diameter on the Fracture Strength and Young’s Modulus of Carbon and Graphite Fibres Made from Polyacrylonitrile,” J. Mater. Sci., 6(9), pp. 1225–1227. [32] Ramsteiner, F., and Theysohn, R., 1985, “The Influence of Fibre Diameter on the Tensile Behavior of Short-Glass-Fibre Reinforced Polymers,” Compos. Sci. Technol., 24(3), pp. 231–240. [33] Miwa, M., and Horiba, N., “Effects of Fibre Length on Tensile Strength of Carbon/Glass Fibre Hybrid Composites,” J. Mater. Sci., 29(4), pp. 973–977. [34] Zhao, Y. H, and Weng, G. J., 1990, “Effective Elastic Moduli of Ribbon-Reinforced Composites,” ASME J. Appl. Mech., 57(1), pp. 158–167 64 PART III Prediction of the Stiffness of Reused Carbon Fiber/Epoxy Composite Oriented Strand Board at Coupon Level using Finite Element Methods There is growing interest for the reused composite oriented strand board (COSB) for stiffness-critical and contoured applications. COSBs are made of rectangular shape prepreg strands that are randomly oriented within the structure. Development of this product form could markedly reduce the scrap generated during aerospace manufacturing processes. COSBs retain high modulus and drapability during processing and manufacturing. However, before any material can be deployed in industrial applications, the mechanical properties must be well understood so that proper design analysis can be performed. COSB has complex structure due to the randomly oriented prepreg strands, and this makes it difficult to model the stiffness using conventional methods. In general, a purely experimental hit and trial approach is used to design components out of such material. In this paper, a finite element based modelling approach to predict the stiffness of COSB is presented. A number of finite element models are developed using different meshing and contact techniques including orphan meshing, embedded elements, tie constraints and cohesive surface and cohesive elements. The model is validated with experimentally determined stiffness of COSB samples manufactured using Out of Autoclave (OoA) heated tool compression molding. 65 1. Introduction In 2015, Boeing projected a demand of 38,050 new airplanes at a total value of $5.6 trillion [1] over the next 20 years, an increase of 3.5 percent from previous year’s forecast. In recent years, the commercial aircraft industry has increased their reliance on composite materials to produce lighter and more durable aircraft: a Boeing 787 aircraft contains 50% by weight of composites, which is about 32,000 kg of carbon fiber reinforced polymer (CFRP). Typically, composites are produced by cutting prepreg into the desired shape and using a combination of temperature and pressure to achieve compaction. In current aerospace and automotive production lines, more than 20% of virgin carbon fiber reinforced prepreg sheets eventually became production waste (Figure 1). Also, waste is generated due to disposing prepreg rolls that have exceeded storage lifetimes. Increasing use of composites in various applications will also lead to increase in the amount of scrap generated from the manufacturing process. The total combined volume of end of life and production waste generated by thermoset composites market in Europe is expected to reach about 304,000 tons by 2015 [2]. The question of how to dispose of production waste is growing in importance. Current traditional disposal routes include landfill and incineration, both of which have limitations due to the costs incurred (both financial and environmental). Industries, composites companies and customers are looking for more sustainable solutions for reusing and recycling composite materials [3-7]. 66 Figure 1. Motivation and potential applications of the composite oriented strand board (COSB), top left corner shows the scrap generated during manufacturing, the scrap is trimmed to rectangular strands (center) and subsequently used for a variety of applications (bottom row and right column). The M.C. Gill Composites Center at the University of Southern California has been actively seeking viable methods and processes to turn in-process waste to useful composites [4-7]. Efforts have focused on turning prepreg scraps into reused composites products (Figure 1) including reused skateboard [8], reused composite oriented strand board, and reused hat stiffeners, by cutting the waste prepregs into rectangular strands and curing them using out of autoclave (OoA) and Vacuum Bag Only (VBO) technologies. 67 Although significant work has been carried out, a thorough mechanical property characterization is still required for design of components using this new material. The research work presented in this paper initiated from the NSF G8 Research Council funded project on “Sustainable Manufacturing through Out-of-Autoclave Processing” [11]. The first phase of the project focused on evaluating the manufacturing feasibility, commercial aspects and the influence of the microstructure of reused composites on its properties. One of the conclusions of the above said project was that a purely empirical experimental approach to designing composites is not feasible due to the large number of variables such as strand size and shape, layup methods, processing parameters etc. In this paper, various finite element (FE) approaches to predict the modulus of a composite oriented strand board (COSB) are presented. COSB panels are created using prepreg scrap using OoA [9] and heated compression molding techniques. The predictions of the FE calculations are subsequently validated using experimental data derived from tensile tests. The outline of this paper is as follows: In Section 2, we describe the finite element analysis of the COSB. In Section 3, the manufacturing and experimental measurements of the COSB is introduced. Results and discussion are in Section 4 and the conclusions are summarized in Section 5. 2. Finite Element Analysis In this study, FE calculations are used to predict the effective properties of COSB composites. Using a finite element method to calculate the effective stiffness generally consists of building a representative model with the details of the micro-structure and interactions between the different components correctly accounted for. This model is then 68 subjected to specific boundary conditions, and the average response of the model to the boundary conditions is calculated. The effective properties of the model are then calculated as a function of the applied load and corresponding response. In the following sections, the different aspects of the analysis described above is presented, giving special attention to the meshing and contact schemes, since they are the first and probably most important step towards use of FE to determine the effective stiffness of COSB. 2.1 Meshing and Contact Schemes for Composite Strands and Epoxy Matrix In this sub-section, the different meshing and contact schemes between the strand and the matrix are explained using the example of a single strand and the matrix. The advantages and disadvantages of the different meshing and contact schemes are listed. These insights will be used to build a “full” model containing multiple strands and different orientations. The finite element models developed for this work consisted of single composite strands in resin. Models were built using commercially available FEA software (SIMULIA ABAQUS [12]). Several meshing and contact set ups were examined. These set ups included meshing schemes of orphan mesh and embedded mesh, tie constraints, general contact with cohesive surface behavior, and cohesive elements for fiber/resin contacts. The general geometric assembly of the single strand model is shown in Figure 2. The rectangular strand (10mm by 20mm, 150 elements) is placed at the center of a surrounding resin matrix (20mm by 30mm). S4R elements were used in all models developed. S4R elements are robust and general purpose 4-node quadrilateral shell elements with uniformly reduced integration that avoids shear and membrane locking. Because of the geometric 69 complexity of COSB, several finite element approaches were considered involving a range of techniques. The pros and cons of these approaches are discussed below. Figure 2. General geometric assembly scheme of a single strand in a resin matrix The orphan meshing scheme (Figure 3 Left) contains no feature information and is defined by a collection of nodes, elements, surfaces, and sets. No geometric features can be added to an orphan meshed part, but nodes and elements can be edited. The main advantage of orphan meshing is the ability to apply certain loads to a specific number of elements. To achieve this, creating partitions is not necessary. Instead, coordinate nodes and elements are assigned before applying the mesh, a task which can be performed relatively easily using a programming language such as PYTHON or FORTRAN. 70 COSB is composed of multiple layers of randomly oriented strands. To model this material, it is important to create an orphan mesh that is independent of the overall part due to large number of strands and possible different strand shapes in future design. The orphan mesh must also have the ability to adjust to the assembly. This means when placing the strand into surrounding resin, the vertical distance between the strands and resin matrix decreases and the elements in between are able to stretch correspondingly. Figure 3. Orphan Meshing of Composite Strand and Resin Matrix (left). Embedded Elements and Embedded Region (right) 71 A second mesh type, the embedded mesh, can be used to provide connection between the carbon fiber strand and the epoxy resin matrix. The embedded meshing scheme (Figure 3 Right) allows a region to be embedded within another “host” region of the model. The geometric relationships between the nodes of the embedded elements and the host elements are identified during calculation, and if a node of an embedded element lies within a host element, the translational degrees of freedom at the nodes are eliminated and they become “embedded nodes”. When embedding the fiber strands into the resin matrix, constraints with respect to fitting different strand shapes into matrix meshes are eliminated. However, there are limitations for the embedded element technique: (1) the host region must be a solid region when the strands to be embedded are defined with composite element properties, thus shell elements cannot be used; (2) elements with rotational degrees of freedom cannot be used as host elements. Embedded elements are allowed to have rotational degrees of freedom, but the rotations are not constrained by embedding. In other words, there are no viable rotational degrees of freedom within the model; (3) Embedded elements generate volume redundancy within the model, leading to error in the predicted stresses in the embedded region. 72 Figure 4. FE model of singular strand in a matrix: Boundary conditions (top), Tie Constraints, yellow dots indicate the tied surface (middle) and stress mismatch in the strand due to difference in stiffness properties (bottom). Finally, the tie constraint (Figure 4) is one of the simpler and more commonly used surface based constraints. It can be used to model both translational and rotational motion, as well as all other active degrees of freedom for a pair of surfaces. Nodes are tied only where the two surfaces (strand and resin, or strand and strand) are close to one another. One surface in the constraint is designated to be the slave surface, and the other surface is the master surface. Considering the large number of contact surfaces when modeling multiple strands in COSB, the limitations of utilizing tie constraints include (1) a slave node of the tie 73 constraint cannot act as a slave node of another constraint (2) when performing damage analysis, there is no cohesive behavior when using a tie constraint. Figure 5. Cohesive Elements setup between Strand and Resin Cohesive elements are ideal for modeling damage in composites, as they can be connected to adjacent components via shared nodes and via mesh tie constraints. Large displacement analyses are also possible. Limitations to cohesive element models include: (1) 2D cohesive elements are only available for 2D planar models with no out of plane stresses or displacements; (2) As a result of this, cohesive surface and 2D and 3D cohesive elements have complicated interaction relationships and compatibility issues with different element types including 2D shell, 3D shell, and 3D solid for both fiber strands and resins. 74 The combination of techniques chosen to enable future damage analysis of COSB, included the use of tie constraints with cohesive elements between the fiber strands and resin matrix (Figure 5). Cohesive elements are typically used to model adhesives between two components or to model interfacial de-bonding using a cohesive zone framework. Element compatibility study and observations were carried out and listed in Table 1 and Table 2. Table 1. Conclusions for different Element Interaction Type. Table 2. Element Compatibility Study for Modeling Strands and Resin in COSB. 75 After a careful assessment of the different contact possibilities in commercial finite element software, we decided to use a combination of tie and cohesive zone elements. This decision was taken on the basis of wide range of applicability and the possibility to increase the scope of modelling by including damage and other sources of non-linearity. Using the newly developed models just described, a standard size tensile testing coupon (25mm × 200mm, ASTM D3039) was built (Figure 6) in FEA package ABAQUS. The position of the strands was random, a total of about 125 strands were made to constitute a coupon. The boundary conditions and loads are applied in such a way that they replicate closely the conditions placed in the coupon during tensile testing. Figure 6. Configuration of Coupon Size COSB Finite Element Model Material properties were assigned to the model based on the manufacturer’s data sheet for the prepreg used in the experimental portion of the study (Cytec CYCOM 5320-1 and UD IM T40/800B) [13]. The relevant properties of unidirectional laminates made from this material – tensile properties, elastic modulus, Poisson’s ratio, and shear modulus are listed in Table 3. Table 3. Mechanical Properties of Prepregs used in this Study. E11 E22 12 23 G12=G23 156 GPa 9.7 GPa 0.344 0.350 4.5 GPa 76 3. Manufacturing and Mechanical Testing A COSB panel (Figure 7) was fabricated to validate the FE model proposed in the previous sections. Fresh prepregs (IM Fiber UD Tape T40/800B with Cytec CYCOM 5320-1 epoxy resin System) were first manually cut into rectangular strands (10 mm by 20 mm) and distributed evenly on an aluminum plate. These strands were then cured using a compression molding hot press (Wabash) into a flat COSB panel measuring 215.9 mm × 215.9 mm. A CNC milling machine with a diamond cutting wheel was used to fabricate the COSB into 7 individual plain tensile specimens (25 mm by 200 mm) in accordance with the ASTM D3039 standard [14] for tensile testing. Fiberglass end-tabs were attached to the ends of each sample using epoxy adhesive. End-tabs were added to prevent slipping and stress concentrations during tensile testing. 6 coupons were subject to quasi-static loading in an INSTRON loading frame and elastic modulus was determined from the resulting load-displacement curve. The remaining coupon (prepared from the center of the COSB) was cut into smaller pieces for non-destructive evaluation (NDE) using high resolution micro-CT, the details of which are presented elsewhere [5]. 77 Figure 7. Composite Oriented Strand Board (COSB, left), similar to wood OSB (right) 4. Results and Discussion The modulus values measured from the 6 COSB plain tensile coupons are displayed in Figure 9. The average modulus obtained from experiments is 51.7 GPa. The difference between the maximum (56.4 GPa) and minimum (47.8 GPa) measured moduli values is 8.6 GPa, or 16.6% of the averaged modulus. This degree of scatter in the measured properties is not unexpected and is probably due to the stochastic distribution of strands, their orientation, and other defects. The orientation of strands is random, and variability is expected from coupon to coupon. One coupon with larger fraction of strands with orientations close to 90-degree of loading direction will have lower stiffness compared to another coupon with more axially aligned strands. The simulated deformed shape of the tensile coupon size model is shown in Figure 8. A qualitative observation of the stress contour shows that the strands oriented along the tensile loading axis of the specimen apparently carry the majority of the stresses. This is not surprising, because unidirectional composites are transversely isotropic with high 78 stiffness in the axial direction, and most of the load is carried along the fiber direction. The distribution of stresses is quite random throughout the test coupon, with several zones of high and low stresses. The local stress concentrations depend on local strand interactions, local volume fraction, and orientations of the strands in the immediate neighborhood. The equivalent coupon elastic modulus obtained by averaging the stress response to the applied strain was 48.5 GPa, consistent with the average measured value of 51.7 GPa. This agreement with the predicted value validates the FEA model and confirms that the model can be implemented to accurately predict future COSB designs. Figure 8. Simulation of Deformed Shape of Coupon Size COSB Finite Element Model Figure 9. Measured and FEA Predicted Modulus of COSB Coupons 79 5. Conclusion A finite element model was developed to simulate the complex geometry of composite oriented strand board. Lab scale COSB samples were manufactured, and the FEA prediction for elastic modulus was validated experimentally. The model described in this work provides an accurate and efficient way to predict the equivalent elastic modulus of COSB material. The work presented will be used as a guideline and design strategy for future optimization of COSB. FEA models will also be used to guide the development of test protocols for this unique material, as ASTM testing standards for COSB are not currently available. By implementing finite element modeling in the optimization of COSB design and testing, we move closer to our ultimate goal - to reduce the time and resources required for expansive experimental efforts with large test matrices. Increased understanding of the relation between the fabrication methods and the mechanical properties of the COSB can lead to more widespread deployment of such materials. This can potentially solve the problem of scrap disposal by creating useful products with materials currently discarded as production waste. Current and future research activities are concentrated in this field. A parametric study on strand locations and orientations will be carried out in future work. Other research directions include building a 3D model [10] to further understand the damage mechanism and other mechanical behavior of COSB, such as the residual strength after damage. 80 6. Acknowledgements The authors are grateful to NSF G8 program and to Airbus Institute for Engineering Research (AIER) program for supporting this research. M.C. Gill Composites Center in Los Angeles, CA, and IMDEA Materials Institute in Madrid, Spain are thanked for supporting this work. Vanesa Martinez, Jose Luis Jimenez, Miguel De La Cruz Pacha, Dr. Claudio Lopes, Dr. Federico Sket, Dr. Ignacio Romero, and Dr. Lessa Grunenfelder are thanked for their useful suggestions and warm discussions in the summer of 2015. 7. References [1]. Current Market Outlook 2015-2034. Report. Boeing Commercial Airplanes. 2015. [2]. Fons Harbers, Annual Report of the European Composite Recycling Services Company. 2015. [3]. Feraboli P, Cleveland T, Ciccu M, Stickler P, DeOto L. Defect and Damage Analysis of Advanced Discontinuous Carbon/Epoxy Composite Materials. J of Composites: Part A 41 (2010) 888-901. [4]. Jin B, Li X, Jain A, Wu M, Mier R, Herraez M, Gonzalez C, LLorca J, Nutt S. Design, Manufacturing, NDT, and Mechanical Properties of Reused OoA VBO UD Carbon Fiber/Epoxy Composite Oriented Strand Board. Submitted to J of Composites Science and Technology. [5]. Jin B, Li X, Jain A, Grunenfelder L, Wu M, Zhang Y, Jormescu A, Gonzalez C, LLorca J, Nutt S. Nondestructive testing and evaluation of conventional and reused carbon fiber composites using ultrasonic scan and Micro-CT. Proceeding. SAMPE 2016, Long Beach, 2016. 81 [6]. Jain A, Jin B, Li X, Nutt S. Stiffness Predictions of Random Chip Composites by Combining Finite Element Calculations with Inclusion Based Models. Proceeding. SAMPE 2016, Long Beach, 2016. [7]. Nilakantan G, Olliges R, Su R, Barnhart J, Nutt S. Reuse Strategies for Out-of- Autoclave Vacuum-Bag-Only Carbon Fiber-Epoxy Prepreg Scrap. Proceeding. CAMX (The Composites and Advanced Materials Expo) Orlando, FL, 2014. [8]. Reused Carbon Fiber Skateboard. Startup Company. www.121cboards.com. [9]. Nutt S, Centea T. Sustainable Manufacturing using OoA Prepregs. Proceeding. CAMX 2014, Orlando, FL, United States, October 13–16; 2014. [10]. Jin B, Pelegri A. Three-dimensional numerical simulation of random fiber composites with high aspect ratio and high volume fraction. 133:41014. J Eng Mater Technol 2011. [11]. NSF G8 Research project “Sustainable Manufacturing through Out-of-Autoclave Processing” http://composites.usc.edu/G8composites [12]. ABAQUS. A Gen Finite Elem Software, ABAQUS Inc, Pawtucket RI, USA 2005. [13]. Technical Data Sheet. CYCOM 5320-1 Epoxy Resin System. Cytec Engineered Materials. AECM-00017. 19 March 2012. [14]. D 3039/D 3039M – 00. Standard Test Method for Tensile Properties of Polymer Matrix Composite Materials. ASTM International. 82 PART IV Parametric Modeling, Higher Order FEA and Experimental Investigation of Hat-Stiffened Composite Panels Sizing of hat-stiffened composite panels presents challenges because of the broad design hyperspace of geometric and material parameters available to designers. Fortunately, design tasks can be simplified by performing parameter sensitivity analysis a priori and by making design data available in terms of a few select parameters. In the present study, we describe parametric modeling and design sensitivity analyses performed on hat stiffener elements for both single and multiple-hat-stiffened panels using parametrically defined scripting finite element analysis (FEA) models and an idealized analytical solution. We fabricated a composite skin panel and 4 hat stiffeners using out of autoclave (OoA) and vacuum bag only (VBO) techniques. The stiffeners were subsequently bonded to the skin to form a multi-hat-stiffened panel. To validate the FEA and analytical solutions, multi- point deflections were measured using different loading conditions. The analytical solution provided upper and lower bounds for the center-point deflections of the panels, values potentially useful for hat-stiffened composite panels. The detailed FEA results accurately revealed the design sensitivities of relevant geometric parameters of hat-stiffened composite panels. The findings constitute a first step towards a structural and scripted FEA framework to speed the development and qualification of composite aircraft structures. The framework has the potential to reduce design cost, increase the possibility of content reuse, and improve time-to-market. 83 1. Introduction To produce lighter and more durable aircraft, the aircraft industry in recent years has increased reliance on carbon fiber composite materials. The higher strength-to-weight ratio of the materials relative to traditional metallic alloys offer the prospect of reducing aircraft weight and increasing fuel efficiency. Composites also offer the potential for reducing part count, increased fatigue resistance, and reduced maintenance frequency. Modern aerospace structures are frequently appended with stiffener components to increase efficiency in terms of stiffness, strength, and weight-optimization. Among the various stiffener configurations, which include L, I, C, T, box, and hat shapes, hat-stiffened composite panels are widely used in the design of large commercial airplanes because of multiple attributes, including ease of manufacture, high specific stiffness and strength, fatigue resistance, and design feasibility. Such laminated composite stiffened panels are extensively used in aircraft structures and can withstand severe service environments that include dynamic loads. Advances in manufacturing and global and local finite element analyses have made it possible to determine with confidence the strength, durability, failure modes and damage tolerance of stiffened composite panels [1-2]. When investigating the parametric design of stiffened composite panels, a first parameter to consider could actually be the manufacturing methods (and associated defects) that will affect the mechanical properties of the parts, and details such as void content, thickness variations, and corner smoothness. In a parametric study of stiffened composite panels, Kim et al. [3] investigated the effects of different curing and bonding processes such as co-curing, co-bonding, and secondary bonding. When co-curing the stiffeners and the skin panel, the authors used a steel mold, 84 an inflatable mold, and a rubber mold, and evaluated the mechanical properties of the parts produced with different bonding techniques. Geometric accuracy was assessed using 3-D measurement and an ultrasonic tester. Additional parameters in the design of stiffened panels include varying loading conditions over the panel surface, and varying fiber orientations (in-plane) of individual plies. Kristinsdottir et al. [8] presented an optimization methodology termed “blending” for the design of large sandwich skin stiffened panels when loads are not constant and vary over the panel surface. Coburn et al. [9] recently studied blade-stiffened variable angle tow (VAT) panels, where the variation in fiber orientation of a single ply was achieved by automated fiber laying technologies. Detailed analysis and modeling of isotropic stiffened panels can be traced back to early last century when FEA method became popular [1]. In recent decades, researchers have begun to focus on composite stiffened panels [2-11]. When modeling stiffened composite panels, simulation approaches can be grouped into two types based on handling of the stiffeners. The first approach utilizes the classic laminate theory (CLT) and “smears” the skin plus stiffener structure into a thick orthotropic laminate panel where the equivalent stiffness is defined by A, B, D matrices. One limitation of this approach is that it can be applied only to panels with closely spaced stiffeners and simple boundary/loading conditions. When the distance between stiffeners is increased, the system becomes a “sparse” stiffened panel, the equivalent stiffness matrix is no longer representative, and thus the analytical solution becomes irrelevant. A second approach involves high-accuracy finite elements to simulate both the skin and stiffeners as meshed discrete elements. This high-accuracy approach has no restrictions on boundary/loading conditions or on the spacing between stiffeners [9]. In addition, the high-accuracy approach enables detailed interaction and manipulation on 85 individual nodes and elements so one can post-process local effects between stiffeners and the skin when investigating strain energy distribution for progressive failure analysis. Although the latter method delivers robust and reliable results, the computational cost as well as model setup time is high. A review of work on static and dynamic analysis of isotropic stiffened panels was reported in 2000 by Sinha et al. [4]. Several publications with direct relevance to the work reported in this manuscript have been published since then. For example, Kumar and Mukhopadhyay [7] formulated a stiffened plate element and performed FEA of Hat/I- section/rectangular beam-stiffened plates, allowing them to use fewer degree of freedom (d.o.f.) compared to the conventional discrete plate and beam models. Prusty [6] analyzed composite stiffened panels by a finite element formulation based on the concept of equal displacements at the shell–stiffener interface. Most of these studies were performed using first-order shear deformation theory. Bhar et al.[5] performed finite element analysis of laminated composite stiffened plates using first-order shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT) and demonstrated that HSDT produces accurate structural response of such stiffened configuration. In these studies of the stiffened composite panels, the finite element method was used extensively due to its reliability and the ease of manipulating individual nodes/elements while applying complicated loading/bounday conditions. The method can be relatively accurate, but the fine meshes required for improving accuracy and performing the parametric model variations make it computationally costly and time consuming. Although numerous analytical solutions and FEM analyses have been employed to study the static and dynamic responses of hat- stiffened composite panel to loading, the geometrical design sensitivities remain 86 unexploited. Some studies [10, 11] focusing on the stiffener plate joints examined the key aspects defining the performance characteristics. In particular, Shenoi and Hawkins [12] reported an initial attempt to understand design sensitivity of composite hat stiffeners and hat-stiffened panels. The hat shape is a common structure in aerospace design as it affords greater design flexibility and is more easily manufactured compared to other stiffener shapes. Systematic computational work must be focused on sensitivity of the hat stiffener to geometric parameters. A first step to achieve this objective is to use parametric modeling in FEA to determine the sensitivities of the load-deflection behavior of hat-stiffened composite panels to simple geometric design variables. Thus, the objectives of the work described herein are to: 1. Explore the design space and use the Finite Element Method (FEM) to analyze the parametrical sensitivity of hat stiffened panel design. 2. Develop an analytical solution and explore the utility in preliminary design 3. Manufacture hat-stiffened composite panels and compare the measured mechanical response with FEA model predictions. This work will provide the aviation industry with a parametric database of hat stiffener design and analysis. We organize our narrative into sections. In Section 2, we introduce the configuration and design parameters for structural components. Section 3 describes the finite element analysis of stiffened panels. In Section 4, we introduce the analytical solution and the construction of the higher order abstract structural element. Section 5 presents the 87 manufacturing and experimental measurements of stiffened panel’s deformation behavior for validation. Results and discussion follow these sections. 2. Basic Structural Element Configuration In this study, we consider stiffened composite panels built from equispaced laminated composite hat stiffeners and a laminated composite plate. Orthotropic ply material properties, laminating stacking sequence, and ply thickness constitute design variables for both hat stiffener and plate structural elements. In addition, length and width of the plate and several geometric parameters for the hat stiffener are considered. These parameters are shown in Figures 1(a) and (b). The distance between stiffeners is a geometric parameter at the structural component level. Most composite stacking sequences correspond to quasi-isotropic layups, and thus, only quasi-isotropic layups using 0, 90 and 45 angle unidirectional plies are considered in the parametric sensitivity analyses with Finite Element Method (FEM). A stiffened panel can be formed by bonding multiple hat stiffeners to the base plate using different types of manufacturing methods, including co-curing, co-bonding, and secondary bonding [2]. We do not consider parameters that can differentiate between these bonding methods, an issue that is beyond the scope of this study. Hat stiffener, associated geometric parameters, a repetitive unit of hat-stiffened plate and the composite panel stiffened with multiple hat- stiffeners is shown in Figures 1(a) to (d), respectively. Figure 1 (e) shows the edge view of the panel showing the distance a between the stiffeners. 3. Finite Element Analysis 3.1. FEM modeling 88 The investigation of parametric sensitivities of hat-stiffened panel design for static deformation is performed in three steps. First, finite element parametric modeling is performed using user-defined scripts (written in C++ [13], MATLAB [14] and PATRAN Command Language (PCL) [15]), which automatically generate FEA finite element model input decks with information including part geometry, meshing element and density, material properties, stacking order of composite laminates, structural boundary/loading conditions, etc. Treating the structure as groups of individual detailed discrete elements allows capture of the local interaction between skin and stiffener elements for energy analysis, and this high-accuracy approach has no restrictions on the system boundary/loading conditions or on spacing between the stiffeners. The application of user- defined scripting langauge programming enables high performace computing and greatly expedites the FEA simulation process by reducing the time spent on manually generating multiple input decks. 89 Figure 1. Geometric parameters of hat stiffeners. (a) A hat stiffener. (b) Geometric parameters. (c) Single- hat-stiffened composite panel. (d) A four-hat-stiffened panel with hat spacing parameter “a”. Laminated plate, hat-stiffener, hat-stiffener bonded to a skin plate were modeled (MSC NASTRAN and PATRAN). The FEM modeling procedure for laminated composite plates is routine and therefore not described here. The model for the hat stiffener (with and without a plate to which it is bonded) incorporates geometric parameters, including the height of the stiffener web (h), width of the stiffener cap (W1), bottom width in between stiffener 90 flanges (W2), width of the stiffener flange (due to symmetry, the left and right width are both L1), as well as the ply thickness, ply orientation, and the stacking sequence. The length of the hat stiffener is 508 mm (20 inches). Figures 2 (a) and (b) present geometric models with fine meshes, and these models feature configurations identical to the hat stiffeners in Figures 1 (a) and (c). Figure 2. Fine meshed finite element models of (a) single hat stiffener, (b) single-hat stiffened composite panel, and (c) four-hat stiffened composite panel. The prepreg properties used in this work for modeling hat-stiffened panels were based on a commercial material (Cytec CYCOM 5320 unidirectional ply), and were taken from a commercial data sheet. The relevant properties of the unidirectional laminates - tensile properties, elastic modulus, Poisson’s ratio, and shear modulus - are listed in Table 1. 91 Table1 Mechanical properties of unidirectional prepreg laminates E 11 E 22 ν 12 G 12=G 23 1.59E5 MPa 9.3E3 MPa 0.336 5.6E3 MPa 3.2. Parametric simulations and sensitivity analysis To determine the sensitivity of hat-stiffener geometric parameters, a first set of simulation models were created for hat-stiffeners without a skin plate, as shown in Figure 2 (a). To construct the parametric design space, this structural element (hat-stiffener) was parametrically modeled and analyzed (using MSC NASTRAN and PATRAN). Design parameters were defined for hat stiffeners as described previously. We selected a commonly used plate element defined in the commercial code (NASTRAN CQUAD4), a four-noded isoparametric flat plate element that behaves well even for irregular shapes. The element selected can be used for either plane strain or plane stress and has in-plane penalty bending stiffness terms in the stiffness matrix to account for transverse shear flexibility and for membrane bending coupling. We used classical laminate theory to compute the properties of the laminate from the properties defined for the individual lamina and the material angle of each lamina. Input cards including element property (PCOMP) and material property (MAT8) were prepared to define the properties of the lamina, and the stresses associated with a plane stress state were recovered at the mid-point of each ply. The upward uniform pressure of 6.89E-2 MPa (10 psi) was applied on each of the two bottom flange surfaces for the hat-stiffener simulation. The two longitudinal edges (cross-sections at the end of the stiffener) of the model were free to rotate but not translate (Tx = Ty = Tz = 0), and the two transverse edges were free to rotate 92 and translate. These longitudinal edge boundary conditions represented fixed edges rather than simply supported, because edge cross sections were constrained from translation. Similar boundary conditions for flat plates represent simply supported conditions. For the second set of simulation models of single-hat-stiffened panels, 16 groups of single hat stiffener configurations were chosen and each was bonded to a skin plate, as shown in Figure 2 (b). The same magnitude of pressure was applied on the added laminate skin plate to which the single hat-stiffener was bonded. The skin plate included the same number of plies and stacking sequence as the hat stiffener and was 4L1+W2 in width, or 2L1 wider than the stiffener itself. Longitudinal edges (the two edges of the skin plate only, not including hat stiffener web and top cap) were simply supported as Tx = Ty = Tz = 0 for a hat stiffener bonded to the skin plate. The transverse edges of the plate were subjected to the boundary conditions Tx = Ry = Rz = 0, corresponding to all four edges simply supported. These boundary conditions were chosen to demonstrate extreme sensitivity of the structural response to hat-stiffener end boundary conditions. The effects of different boundary conditions on the mechanical behavior of the structure were not negligible, as described in the Results and Discussion section. To better understand and predict the mechanical behavior of the structure, a third set of parametric FEA models for one skin panel with multiple hat-stiffeners were analyzed (using MSC NASTRAN and PATRAN). One of the models is shown in Figure 2 (c). This particular model has the same geometric configuration as the multi-hat-stiffened panel shown in Figure 1 (d). Identical composite ply material properties that were used in modeling single hat open and bonded elements were selected (from Cytec CYCOM 5320 prepreg data sheet) to create the model and generate the database. All NASTRAN models 93 were built using scripting language PCL and were easily modified to incorporate hat stiffener parameters and stiffener spacing. Models with increasing numbers of bonded hat- stiffeners (equal in length to the plate) were thus built, ranging from a two hat-stiffened to a five hat-stiffened panel. Note that when the skin panel had a small number of hat- stiffeners attached, e.g. only two stiffeners, we referred to the structure as a “sparse” hat- stiffened panel, because the equal distance “a” between stiffeners exceeded 3 times the width of a single hat stiffener, that is to say, greater than 3*(2L1+W2). The geometric configuration of the multi-hat stiffened panel model, corresponding to the panel fabricated for experimental measurements, consisted of a base plate of in-plane dimensions 304.8 mm (12 in) by 863.6 mm (34 in) with four identical hat stiffeners attached, each separated by an equal distance of 85.725 mm (3.37 in). The bottom total width of the hat stiffener was approximately 86.36 mm (3.4 in), with 61 mm (2.4 in) between the lower two corners of the hat stiffeners and 12.7 mm (0.5 in) overhang (i.e., two bottom flanges) on either side. The base skin panel had 8 plies of 5320 unidirectional prepreg stacked in a quasi-isotropic layup [90/-45/+45/0]s. Each of the 4 hats also consisted of 8 unidirectional fiber plies in the same quasi-isotropic layup. All multi-hat-stiffened panel models were subjected to simply supported boundary conditions on the four edges of the skin panel, and were uniformly loaded corresponding to the actual test load applied to the structure, as described in the Experiments section. Simulation of hat-stiffened panel requires understanding of global and local effects of the parameters. We expect local maximum deflection to occur between the stiffeners on the panel, and that deflection will be a dominant parameter for satisfying deformation constraints in aircraft wing section design. 94 4. Analytical Solution In addition to the detailed FEM modeling for the study of design sensitivities, we derived and programmed a proof-of-concept analytical model (using C++ and MATLAB 2014a) consisting of a rectangular plate stiffened by multiple hat stiffeners. We modified the classical laminate theory (CLT) and analytically smeared the material properties of a single-hat-stiffened panel to construct an equivalent thick orthotropic laminate plate. The composite stiffener was replaced with several orthotropic laminate layers to represent a higher order abstract structural element. Figure 3 shows the equivalency between a single hat-stiffened plate and the smeared laminated plate higher order abstract structural element. Figure 3. Equivalent orthotropic plate for hat-stiffened skin. The analytical solution derived in this section is representative of the panel with hat- stiffeners when the spacing “a” between stiffeners is less than a critical value, which is defined as: a < 3*(2L1+W2) (1) When the stiffened panel is wide and has multiple equispaced stiffeners satisfying constraint represented by eq. (1), the equivalent A, B, D matrices provide reasonable global behavior of the panel. When predicting static deformation, the analytical solution yields 95 lower bounds of the deflection values, which are useful reference and guidance to designers and establish the first order validity of the FEA results. The upper deflection bound can be obtained by considering the plate between the stiffeners as a simply supported plate. We obtain orthotropic plate properties by scaling, homogenizing, and distributing stiffener properties over the spaces between hat-stiffeners. We assume that a hat stiffener only modifies the longitudinal (along the length of the stiffener) stiffness of the plate. Thus, the stiffener contributes to the D11 term primarily for bending deformation. However, depending on the geometric design variables, D22, D12 and D66 terms can contribute to the deformation. Therefore, all elements of the ABD matrix were calculated. Note that because of the smearing of a hat-stiffener ply, the abstract plate structure becomes asymmetric, but the B matrix contribution to deformation is negligible. 𝜃 in Eq. (2, 3 and 5) is the angle between the principal structural coordinate x-axis (stiffener width direction in this case) and the ply fiber orientation. Overbar represents the transformation of the ply stiffness coefficients from the ply principal material coordinate system to the structural coordinate system. Superscript j represents the ply number in the laminate. Subscripts bf and tf represent the bottom and top flange, respectively. L1, W1, W2, and h are defined in Figure 1(b). The reduced stiffness coefficient contribution to the abstract structural element follows. For bottom flange: 𝑄 ̅ 11𝑏𝑓 𝑗 = 2𝐿 1 𝑎 [𝑄 11 𝑗 𝑐𝑜𝑠 4 𝜃 + 𝑄 22 𝑗 𝑠𝑖𝑛 4 𝜃 + 2(𝑄 12 𝑗 + 2𝑄 66 𝑗 ) 𝑠𝑖𝑛 2 𝜃 𝑐𝑜𝑠 2 𝜃 ] (2) For top flange: 96 𝑄 ̅ 11𝑡𝑓 𝑗 = 𝑤 1 𝑎 [𝑄 11 𝑗 𝑐𝑜𝑠 4 𝜃 + 𝑄 22 𝑗 𝑠𝑖𝑛 4 𝜃 + 2(𝑄 12 𝑗 + 2𝑄 66 𝑗 ) 𝑠𝑖𝑛 2 𝜃 𝑐𝑜𝑠 2 𝜃 ] (3) For webs, we define: cos𝑥 = ℎ [( 𝑤 2 −𝑤 1 2 ) 2 +ℎ 2 ] 1 2 (4) Therefore, the contributions from the two hat stiffener web sections are: 𝑄 ̅ 11𝑤𝑒𝑏 𝑗 = 2 𝑎 cos 𝑥 ∑ 𝑡 𝑗 𝑛 𝑗 =1 [𝑄 11 𝑗 𝑐𝑜𝑠 4 𝜃 + 𝑄 22 𝑗 𝑠𝑖𝑛 4 𝜃 + 2(𝑄 12 𝑗 + 2𝑄 66 𝑗 ) 𝑠𝑖𝑛 2 𝜃 𝑐𝑜𝑠 2 𝜃 ] (5) These equivalent 𝑄 ̅ 11 𝑗 contributions can be used in classical ABD matrix construction. Similarly, other reduced stiffness matrix components can be calculated. These components are used to calculate the classical ABD matrix. As mentioned before, when symmetric layups are used for the plate and hat, the B matrix elements are negligibly small and the in- plane and bending stiffness of the abstract plate element are not coupled. The D matrix components are calculated according to 𝐷 𝑖𝑗 = 1 3 ∑ (𝑄 ̅ 𝑖𝑗 ) 𝑘 (ℎ 3 𝑘 − ℎ 3 𝑘 −1 ) 𝑗 𝑘 =1 (6) where hk is the thickness direction coordinates of ply interfaces for the abstract plate laminate. Assuming [B] = 0, simplifies the differential equation to obtain the deformation of the abstract plate structure. The solution procedure is straightforward for simply supported and uniformly loaded plate [16]. The expression of the deflection is then given by: w = b 4 π 4 ∑ ∑ 𝑎 𝑚𝑛 (sin 𝑚𝜋𝑥 𝑎 sin 𝑛𝜋𝑦 𝑏 )/(𝐷 1 ( 𝑚 𝑐 ) 4 + 2𝐷 3 𝑛 2 ( 𝑚 𝑐 ) 2 + 𝐷 2 𝑛 4 ) ∞ 𝑛 =1 ∞ 𝑚 =1 (7) 97 where D1, D2, D3 are the components of the D stiffness matrix and are defined as: 𝐷 1 = 𝐷 11 (8) 𝐷 2 = 𝐷 22 (9) 𝐷 3 = 𝐷 12 + 2𝐷 33 (10) amn is defined as: 𝑎 𝑚𝑛 = 16𝑝 𝜋 2 ∗ 1 𝑚𝑛 (11) for all m, n =1, 3, 5, …; where p is the applied pressure, the load per unit area, and 𝑎 𝑚𝑛 = 0 (12) for all other m and n. The analytical solution of the equivalent panel was input into a code (MATLAB 2014a) to predict the center point deflection. Note that for the analytical solution for a large panel with a sparse distribution of stiffeners, although these relationships may not be valid, they can provide bounding values for the possible deflection of points on the plate. 5. Manufacturing and Experiments To validate the FEA and analytical solutions, a four-hat-stiffened composite panel (Figure 4) was fabricated and cured out-of-autoclave (OoA). The stiffeners and skin were manually laid ply-by-ply, vacuum bagged and cured separately. Cured parts, plate and hat-stiffeners are bonded together after curing. The dimensions of the panel were used in FEM modeling. The deflection response of the simply supported panel was measured by applying discrete incremental loads. 98 Figure 4. (a) Secondary bonding of four hat stiffeners and a skin plate. (b) A four-hat-stiffened composite panel for experimental validating. 5.1. Manufacturing of multi-hat-stiffened composite panel A composite plate and hat stiffeners were fabricated from unidirectional prepreg material. VBO and OoA curing was used to fabricate the composite plate and hat-stiffeners separately. The components were attached using a secondary bonding technique. The prepreg material (CYCOM T40-800b/5320-1) used in this work was a carbon fiber toughened epoxy resin system. The volume fraction of fiber was 67% by weight and the fabric areal weight was 145 gsm. The resin (5320-1) was formulated for OoA manufacturing and reportedly can achieve autoclave-quality parts with VBO curing. 99 Vacuum debulking cycles were not required to eliminate voids for flat or mildly contoured parts, but doing so eliminates wrinkles and bridging of materials in highly contoured parts. The plate and hat stiffeners were cured in a convective air-heating oven. Standard room- temperature vacuum hold prior to curing was applied to evacuate the air in the system and achieve fine part quality. The manufacturer recommends three different cure cycles [17]. In this work, a combined cure and post-cure procedure was performed on the part, consisting of a ramp to 132.2 C (250 F), a 1-hour hold, and then a ramp to 176.6 C (350 F) and a hold for another 2 hours. The recommended ramp rate of 1-5 degree per minute was applied. Secondary bonding is a method in which cured parts are bonded together using an adhesive and may require further curing. The four hats and the composite skin plate were cured separately, and they were secondary bonded together by a high viscosity epoxy adhesive (Henkel Loctite E-120HP Hysol) [18]. Once two parts were mixed, the two-component epoxy cured at room temperature (RT) and formed a tough, amber-beige bond line with excellent resistance to peel and impact. The adhesive was allowed to cure at room temperature for one week to achieve full strength. The stacking sequence for both hat stiffeners and the skin plate (8 layers of unidirectional laminates) was a quasi-isotropic layup of [90/-45/+45/0]s stacking sequence. The 90-degree layer, which had the same fiber direction as the hat stiffener longitudinal direction, was placed as the top surface ply of the hat. As the drapability of unidirectional laminates is generally inferior to woven composites, superior corner lamination quality was obtained when the 90-degree ply was laid up as the first plies on the tool surface. 100 5.2. Experimental testing The four-hat-stiffened composite panel was supported at the edges to mimic simply supported boundary conditions, as shown in Figure 5(a). The panel deflection was measured under near-uniform loading. Discrete four levels of incremental loadings were chosen to keep all tests within low linear deformation regime so there was little possibility of damage occurring in the structure. The maximum loading was kept below 6.89 kPa (1 psi) as shown in Figure 5(c). The loading was kept as close as possible to uniform loading by using combinations of barbells and bags filled with lead beads. Near-uniform loadings of 68 kg (150 lbs), 104.3 kg (230 lbs), 138.3 kg (305 lbs) and 179.2 kg (395 lbs) total were applied to the stiffened panel in ascending order. 101 Figure 5. (a) The simply support boundary condition set up on a granite optical table. (b) Positioning and translation of the LVDT measuring unit. (c) A simply supported hat-stiffened composite panel under near-uniform loading of 395 lbs. 102 An LVDT (Omega LD621-5) was used to record the deflection at pre-marked locations on bays and stiffeners. A UPS voltage current regulator was connected between wall power socket and LVDT to reducing the noise generated by the power source. The LVDT had a maximum measurement range from -2.5 mm to +2.5 mm and was configured to provide a DC voltage output ranging from -5 VDC to +5 VDC. As shown in Figure 5 (b), the LVDT was clamped and positioned on a precision machining tool block underneath the hat stiffened panel to form a measuring unit that can be traversed freely on the flat marble table surface. While moving the measuring unit, deflection data in the z direction were recorded. The spring-loaded LVDT tip was traversed over all marked points on the unloaded panel to assure contact between the tip and the panel surface. The vertical positions of marked points on the unloaded panel were used as reference measurements to obtain deflections at these points when the panel was loaded. 6. Results and Discussion Results of parametric finite element simulations, analytical estimation and experimental results are discussed in this section. 6.1. Parametric finite element simulations Parametric FEM models of hat stiffeners were analyzed first to understand the sensitivity of deflection to independent geometric parameters (L1, W2, W1, h, n, stacking sequence) for the hat-stiffener element. The relative effect of boundary conditions and strain energy shared between the hat-stiffener and plate were analyzed next. The parametric range and increments used in this study covered most of the practical design exploration space and are summarized in Table 2. 103 Table 2 Hat-stiffener parametric design space Parameter Minimum Value Maximum Value Variation Step Bottom Flange (L 1) 12.7 mm (0.5 inch) 38.1 mm (1.5 inch) 6.35 mm (0.25 inch) Bottom Hat Width (W 2) 25.4 mm (1 inch) 63.5 mm (2.5 inch) 12.7 mm (0.5 inch) Top Flange Width (W 1) 12.7 mm (0.5 inch) 50.8 mm (2.0 inch) 12.7 mm (0.5 inch) Hat Height (h) 12.7 mm (0.5 inch) 50.8 mm (2.0 inch) 6.35 mm (0.25 inch) Number of Plies (n) 8 plies 24 plies 8 plies Stacking Sequence [90/-45/+45/0] s [90/-45/+45/0] 3s Single Ply Thickness 0.127 mm (0.005 inch) The parametric variations represent 1680 finite element models and corresponding design points. A smaller set of parameter combinations was analyzed to determine the design trends and is shown in Table 3. This set of parametric groups was selected based on four heights h: 12.7 mm (0.5 in), 25.4 mm (1 in), 38.1 mm (1.5 in), and 50.8 mm (2 in). For each height h, 4 sets of W1 and W2 combinations were selected and are presented in Table 3. In these 16 groups, number of plies, bottom flange length L1 and stacking sequence were set constant at 8 plies, 12.7 mm (0.5 in) and [90/-45/+45/0]s, respectively. We explored the maximum specific bending rigidity contribution of hat-stiffeners to a membrane skin that is generally designed to carry torsional shear. A representative 6.89E-2 MPa (10 psi) uniform pressure loading and simply supported boundary conditions on a 508 mm (20 inches) long hat cross section beam was analyzed. The cross sectional area of hat-stiffeners varies with design parameters. For reference, a baseline configuration with minimum cross sectional area was chosen to illustrate the effect of parameters on bending. This 104 configuration consisted of 12.7 mm (0.5 in) for bottom flange length L1, 25.4 mm (1 in) for bottom hat width W2, 12.7 mm (0.5 in) for top flange width W1, 12.7 mm (0.5 in) for hat height h, 0.127 mm (0.005 in) single ply thickness. Results are presented for 8 plies with [90/-45/+45/0]s laminate stacking order. All hat stiffeners had a fixed length of 508 mm (20 in). Stacking sequence and therefore corresponding laminate thickness were held constant. The ratio of top and bottom hat widths was fixed at 0.5 for all parametric variations. Table 3 Parameter combinations for design of hat-stiffened panels h (mm) W 1 (always<W 2) (mm) W 2 (mm) Number of Plies L 1 (mm) 12.7 12.7 25.4 8 12.7 12.7 25.4 38.1 8 12.7 12.7 38.1 50.8 8 12.7 12.7 50.8 63.5 8 12.7 25.4 12.7 25.4 8 12.7 25.4 25.4 38.1 8 12.7 25.4 38.1 50.8 8 12.7 25.4 50.8 63.5 8 12.7 105 38.1 12.7 25.4 8 12.7 38.1 25.4 38.1 8 12.7 38.1 38.1 50.8 8 12.7 38.1 50.8 63.5 8 12.7 50.8 12.7 25.4 8 12.7 50.8 25.4 38.1 8 12.7 50.8 38.1 50.8 8 12.7 50.8 50.8 63.5 8 12.7 Figure 6 consolidates the results spanning the design space defined by the parameters. Curves in the figure represent variations of bottom flange length, top flange width (and corresponding bottom hat width because the ratio was constant) and hat height, while other variables were held constant. The longitudinal maximum fiber stress and the maximum deflection of the hat, which occurs at the midpoint along the length of the stiffener for uniform loading, are presented for the three independent variables mentioned above. The maximum stress and deflection are plotted as percentage change from the reference configuration shown at the top left corner. The variations are plotted against the relative cross sectional areas of the hat stiffeners, which changes while the geometrical parameters are varying, and other ones such as material properties and stacking sequences were kept constant. 106 Figure 6. Single hat stiffener bending behavior and parameter design sensitivity analysis. The variation in hat-stiffener height had the greatest effect on the maximum stress and deflection of the beam under uniform loading. Reductions in maximum stress of 80% and maximum deflection of 70% were achieved by a 1.8 times change in cross-sectional area (corresponding to tripling the height), respectively. Note that cross-sectional area corresponds directly to the structural weight, and minimizing structural weight is a common design objective. As expected, the contribution of the bottom flange length L1 to both maximum stress and deflection of the stiffener was minimal. In contrast, the top flange width (1.2 to 1.4 area change) had a significant effect on the maximum stress initially, although further doubling the width produced a mere 20% decrease in stress. The same change in flange width changed the maximum deflection by only 20%. Based on these results, height should be maximized first within the design constraints, while the flange 107 width should be the second choice. The bottom flange length should be decided based on the minimum needed to achieve full load transfer to the stiffener - it has negligible effect on the maximum stress and deflection, despite almost doubling the structural weight. This parametric modeling method and the trends discovered can be used to reduce the design parameters and can be coded to automatically select a near-optimum combination without the need to explore the complete design space. Figure 7. Deformed shapes of: (a) a single-hat-stiffened composite panel, ID 16, and (b) a four-hat- stiffened composite panel. 108 Figure 7 illustrates the local effect of a hat stiffener, showing results for the geometric parameters of ID 16 given in Table 4. Figure 7(a) shows deformation of a plate 2L1 wider than the hat stiffener and simply supported on the ends and the free lateral edges. Note that because the plate edges as well as the hat stiffener are simply supported, the closed cross section is effectively fixed. The deformation in Figure 7(a) reflects effective fixed end conditions by zero slopes at the ends. The hat stiffener imparts significant bending rigidity to the plate. The maximum deflection of the plate alone was 395 times greater than the stiffened plate (67.30 mm/0.17 mm) under the same uniform pressure loading. Figure 7(b) shows the plate deformation with four equidistant hat stiffeners, the plate that was fabricated and tested. End bays (3 and 5 in Figure 4(b)) showed greater and slightly asymmetric deflection compared to middle bays (1,2 and 4) due to the fact that end bays were subjected to three simply supported edges and one (stiffener side) partially fixed edge. Other bays had partially fixed support from the hat stiffeners with high torsional rigidity. The maximum deflection of the plate alone was 485 times greater than the plate stiffened with four hats (757mm/1.56mm) under identical loading. Table 4 Design parameters for hat stiffener with monotonically increasing material usage ID Hat Cross Sectional Area (mm 2 ) Plate Cross Sectional Area (mm 2 ) Relative Material Usage (Hat/Whole Structure) h (mm) W 1 (always<W 2) (mm) W 2 (mm) 1 67.6 77.4 46.60% 12.7 12.7 25.4 109 2 80.5 90.3 47.11% 12.7 25.4 38.1 3 91.9 77.4 54.28% 25.4 12.7 25.4 4 93.4 103.2 47.49% 12.7 38.1 50.8 5 104.8 90.3 53.71% 25.4 25.4 38.1 6 106.3 116.1 47.78% 12.7 50.8 63.5 7 117.2 77.4 60.22% 38.1 12.7 25.4 8 117.7 103.2 53.28% 25.4 38.1 50.8 9 130.1 90.3 59.02% 38.1 25.4 38.1 10 130.6 116.1 52.94% 25.4 50.8 63.5 11 142.7 77.4 64.83% 50.8 12.7 25.4 12 143.0 103.2 58.08% 38.1 38.1 50.8 13 155.6 90.3 63.28% 50.8 25.4 38.1 14 156.0 116.1 57.31% 38.1 50.8 63.5 15 168.5 103.2 62.02% 50.8 38.1 50.8 16 181.4 116.1 60.98% 50.8 50.8 63.5 The set of 16 parametric groups was ordered with monotonically increasing material usage in the hat stiffener, and ID numbers were assigned for referencing (see Table 4). Maximum stress and maximum deflection of 16 sets were modeled for only plate ends simply 110 supported, and for plate and hat stiffener ends simply supported. Figure 8 shows a comparison of maximum stress and deflection between the two groups. First, note that the parametric design sensitivity trend remains similar for both cases. Second, FEA results for hat stiffener only, (e.g., for ID1 parameters) show a maximum deflection of 2.81 mm, while the single-hat-stiffened panel FEA results in 7.33 mm. This difference is attributed to the different boundary condition - the hat-only models were fixed on all translation and rotation on their cross sections, while the single-hat-stiffened panel models were only simply supported on the bottom flange of the stiffener/skin plate. Hat stiffener height h significantly affects stiffened plate deflection, as evident from results of IDs 1, 3, 7, 11; 2, 5, 9, 13; 4, 8, 12, 15; 6, 10, 14, 16 for which h monotonically increases, while W1 and W2 are fixed. The effect of hat stiffener width (W1 and W2) is greater when the height is smaller, but diminishes for stiffeners with greater height. Other parameters, such as space and manufacturing constraints, are likely to take the design close to the configuration described in group ID 1. Figure 8. Maximum deflection and stress of the 32 groups of hat stiffener models (hat only and single-hat- stiffened panel). 111 Figure 9. Strain energy density distribution of 16 groups of single-hat-stiffened panel models. The determination of structural efficiency can be approached either by obtaining maximum deflection and flexural stress, or by calculating and comparing the strain energy in the structure. The analysis of structural strain energy [8] can be a useful method to explore how geometrical parameters affect the load-carrying capability of stiffened panels. For the 16 sets of single-hat-stiffened panel models, the strain energy distribution is shown in Figure 9. For set ID 1, 96% of the strain energy is in the hat stiffener, while the remaining 4% is in the skin plate. The distribution is attributed to the efficient internal load transfer to the stiffener, which results in maximum utilization of stiffener material. Strain energy stored in the plate increases as the parametric group ID increases from 1 to 16. Ideally, one would like to achieve equal energy density in basic structural elements for anticipated loading and boundary conditions. For multi-hat-stiffened panels, the trend in Figure 9 represents the energy density distribution for a panel with closely placed stiffeners bonded. As the distance between stiffeners increases, the strain energy density in the plate portion (referred as the bay area) between sparse stiffeners will increase, while that in the stiffeners will decrease accordingly. 112 Figure 10. Parametric design sensitivity analysis for single-hat-stiffened panel: (a). Maximum structural stress vs. relative material usage. (b). Maximum structural deflection vs. relative material usage. Figure 10 shows the variable sensitivity analysis illustrating the relation between material usage and structural maximum flexural stress and maximum transverse deflection at the mid-point of a hat stiffener bonded to a laminated plate. These parametric variations encompass the design space and trends for a hat stiffener basic element. The material usage data for hat-stiffeners, which is directly related to cross sectional area, varies with design parameters. Geometric configurations with various material usages are chosen to illustrate parametric effects on bending. These configurations have the same 12.7 mm (0.5 inch) bottom flange length, 0.127 mm (0.005 inch) single layer thickness and [90/-45/+45/0]s layup, and (W1)1 < (W1)2 < (W1)3 < (W1)4 and h1<h2<h3<h4. The stacking sequence and therefore the corresponding laminate thickness is held constant. The carpet plots show the variation of deflection and flexural longitudinal stress with hat height, width, and bottom flange length. These trends can be used to reduce design parameters and can be coded to automatically select near-optimum combinations without need for further exploration of the design space. 113 6.2. Analytical solution To validate the analytical solution, the midpoint deflections of the four-hat-stiffened panels under near-uniform loading were measured for loads of 667.23 N (150 lb), 1023.09 N (230 lb), 1356.71 N (305 lb), and 1757.05 N (395 lb). As shown in Figure 11, these deflections were 0.60 mm (0.023 in), 1.00 mm (0.039 in), 1.50 mm (0.059 in), and 1.75 mm (0.069 in), respectively. The corresponding FEA predicted displacements were 0.54 mm (0.021 in), 0.83 mm (0.033 in), 1.10 mm (0.043 in), and 1.42 mm (0.056 in), respectively. The first load increment of 667.23 N (150 lb) was applied using bags filled with lead balls (~2mm diameter), providing near-uniform loading. The remaining increments were obtained using barbells. As the results in Figure 11 show, the midpoint deflection was 1.75 mm (0.069 in) for 6.675 kPa (0.97 psi) near-uniform loading, while FEA simulation gave a deflection value of 1.42 mm (0.056 in). Figure 11. Comparison of LVDT measurements, FEA prediction and analytical solution approximation of midpoint deflections of stiffened panel under different loads. 114 The upper and lower bounds for stiffened panels were obtained from the analytical solution. The midpoint deflection from the homogenized orthotropic panel provides the lower bound, while a simply supported idealized plate between the stiffeners provides the upper bound. The lower bound provides a better approximation for plates with closely spaced stiffeners. The real deformation begins to approach the upper bound as the spacing between stiffeners increases. For a four-hat-stiffened panel, the lower bound for midpoint deflection under 6.675 kPa (0.97 psi) was 0.129 mm (0.005 in), and the upper bound was 2.76 mm (0.109 in), while the measured deflection was 1.75 mm (0.069 in), well within the bounded range. The work performed here establishes a basis for future work to further develop a set of parametric models. The process envisioned for designing structural components of advanced composite aircraft from these parametric modeling constructs will be refined, matured, implemented, and validated to demonstrate the benefits of starting the design with validated parametric design elements. 6.3. Experimental measurements To build confidence in the parametric study, a hat-stiffened panel was modeled in FEM and experimentally validated using LVDT measurements on an optical table with five different loadings. At each load case, deflections at 75 points on the five panel bays (the flat panel areas between two adjacent stiffeners) and 44 points on four hat stiffeners (Figure 4b) were measured. The measurements were made on equidistant points along centerlines on bays and stiffeners. The y direction was parallel to the stiffener axis, and the x direction was normal to the stiffener axis. The measured panel displacements then were compared to FEA predicted results. 115 Figure 12. Correlation of LVDT measured and FEA predicted multi-point deflections on the four-hat- stiffened composite panel. 116 Figure 13. Correlation of LVDT measured and FEA predicted multi-point deflections, 667 N. linear subtraction. 117 Figure 14. Correlation of LVDT measured and FEA predicted multi-point deflections, 1023 N. linear subtraction. 118 Figure 15. Correlation of LVDT measured and FEA predicted multi-point deflections, 1357 N. linear subtraction. 119 The measured and FEA predicted deflection values for the four incremental load cases (68 kg (150 lbs), 104.3 kg (230 lbs), 138.3 kg (305 lbs) and 179.2 kg (395 lbs) of total load) along the X and Y-axis in five bays are plotted in Figure 12. The LVDT measured data are represented by dots, while the FEA data are represented by squares. For the three middle panel bays (numbered 2, 1, and 4), FEA predictions matched well with measurements. For the two panel bays at far left and right (bays 3 and 5), in both x and y data the differences between LVDT and FEA data were greater than those for bays 2, 1, and 4, although FEA predictions yielded deflection shapes similar to measured values. The differences were attributed to the simply supported boundary condition at the four edges of the panel and the idealized near-uniform loading conditions. At the four edges, there were inevitable deviations from flatness due to the manufacture quality and minor defects in the supporting frame. For all load cases, loads were more evenly distributed in the center area of the structure (that is, middle bays 2, 1, and 4), and end bays (3 and 5) showed slightly asymmetric deflection compared to the middle bays. The asymmetry was expected because end bays were subjected to three simply supported edges and one (stiffener side) partially fixed edge. Other bays had partially fixed support from the hat stiffeners with high torsional rigidity. Because all tests were performed within the linear regime, we were able to eliminate these defects by performing a linear subtraction (Figures 13 to Figure 15). For instance, in Figure 13, linear subtraction was performed using data from the 667.23 N (150 lb) load tests, yielding equivalent load values of (1023.09 N – 667.23 N) = 355.86 N (80 lb), (1356.71 N – 667.23 N) = 689.48 N (155 lb), and (1757.05 N – 667.23 N) = 1089.82 N (245 lb), respectively. This linear-subtraction method reduces the effect of manufacturing-induced variations in material properties present in the 120 stiffened plate. The effect of non-uniform loading because of the loading procedure cannot be eliminated by this procedure. Furthermore, linear subtractions were performed using data from 1023.09 N (230 lb.)’s, and 1356.71 N (305 lb.)’s data, and these are plotted in Figure 14 and Figure 15 respectively. Note that for bays 3 and 5, greater values of the applied loading in the linear subtraction method yield closer correlations of the magnitude the LVDT measurements and FEA predictions. This is because defects such as wrinkles and flatness deviations in the panel were reduced with the lower initial loading. 7. Conclusions We have described the process of developing analytical and parametric FEA models for design and analysis of hat-stiffened composite panels. Numerical and experimental results were compared to demonstrate the predictive capability of the FEM modeling of hat- stiffened composite panels. The ultimate goal of this work was to produce reliable design data for hat-stiffener stiffened panels to enable future designers to design structural parts using higher order abstract elements. At present, these design processes are needlessly repeated over and over by designers. We contend that these processes can be standardized to abbreviate the design process. We have illustrated the processes of creating parametric models for buildup of composite structures using an example of hat-stiffened composite panels, commonly deployed in aircraft structures. From the parametric study of hat stiffeners, we conclude that the height of the hat stiffener is the most influential parameter. The distance between stiffeners influences the local deformation. As a rule-of-thumb, the spacing between stiffeners should not exceed three times the total width of the hat stiffener. Closely spaced stiffener designs efficiently use stiffeners to enhance specific bending stiffness of the panel. The energy stored in the 121 stiffener under uniform pressure loading varies with geometric parameters. The best use of a structural element is when specific strain energy (strain energy per unit mass) is maximized for the internal load resultants it is designed to carry. In the case considered, the hat stiffener should carry the bulk of the flexural strain energy compared to the plate element that is designed to carry shear load. Hat stiffeners carry more than 80% of the strain energy for the practically useful design space defined by independent design variables. Logical extension of the present work should focus on developing design tools, such as a combination of MSC NASTRAN/PATRAN, ABAQUS, MATLAB and C++ platforms, for the automated development of analytical models. A potential outcome of extending the effort would be a library of higher order abstract elements to abbreviate the design process by starting the design process with a set of built-in, composite structural elements. The work performed here establishes the basis for future efforts to develop a set of parametric models. The process envisioned for designing structural components of advanced composite aircraft from these parametric modeling constructs must first be refined, matured, implemented and validated to demonstrate the benefits of starting the design with validated parametric design elements. 8. References 1. Shastry BP, Venkateswararao G, Reddy MN, Stability of stiffened plates using high precision finite elements. Nuclear Eng and Design 1976;36:91-95. 2. Nutt SR, Centea T. Sustainable manufacturing using out-of-autoclave prepregs. CAMX 2014, Orlando, FL, United States, October 13-16, 2014. 3. Kim, GH, Choi, JH, & Kweon, JH. Manufacture and performance evaluation of the composite hat-stiffened panel. Compos Struct 2010;92:2276-2284. 122 4. Sinha G, Mukhopadhyay M, Static and dynamic analysis of stiffened shells—a review, Indian Natl. Sci. Acad. 1995;61:195–219 5. Bhar A, Phoenix S, & Satsangi S. Finite element analysis of laminated composite stiffened plates using FSDT and HSDT: A comparative perspective. Compos Struct 2010;312-321. 6. Prusty B. Gangadhara. Linear static analysis of composite hat-stiffened laminated shells using finite elements. Finite Elements in Analysis and Design 2003;1125-1138. 7. Kumar Y , & Mukhopadhyay, M. Transient response analysis of laminated stiffened plates. Compos Struct 2002;97-107. 8. Kristinsdottir, BP, Zabinsky, ZB, Tuttle, ME, & Neogi, S. Optimal design of large composite panels with varing loads. Compos Struct 2001;51:93-102. 9. Coburn B, Wu Z, Weaver, P. M., Buckling analysis of stiffened variable angle tow panels. Compos Struct 2014;111:259-270. 10. Krueger R, Minguet PJ, O’Brien TK. A method for calculating strain energy release rates in preliminary design of composite skin-stringer debonding under multi-axial loading. NASA TR 1999;888399. 11. Junhou P, & Shenoi R.A. Examination of key aspects defining the performance characteristics of out-of-plane joints in FRP marine structures. Composites: Part A 1996;89-103. 12. Shenoi RA, & Hawkins GL. An investigation into the performance characteristics of top-hat stiffener to shell plating joints. Compos Struct 1995;30:109-121. 13. Langtangen HP. Computational partical differential equations. 2 nd edition. Springer 2003. 14. Kwon YW, Bang H. The finite element method using MATLAB. 2 nd edition. CRC Press. 2000. 15. MSC NASTRAN/PATRAN PCL (PATRAN Command Language) User’s reference manual. 2014. 16. Vinson J, Sierakowski R. The behavior of structures composed of composite materials. 123 Kluwer Academic Publishers. 2002. 17. Cytec CYCOM 5320 epoxy resin product technical data sheets, 2009. 18. Henkel LOCTITE E-120HP Hysol adhesive product technical data sheets, 2013. 124 PART V Future Work 1. During mechanical testing of the COSB material, we found its Mode I fracture toughness is even higher than virgin UNI composite laminates. This is probably due to its internal configuration that strands are superposing each other, and as a result the overall Mode I fracture behavior of strand COSB is similar to woven composites. To determine its fracture toughness, we will: a. Perform TENF (Tabbed End Notched Fracture) test on COSB coupons, b. Determine the residue strength of COSBs damaged from low speed impact. We’ll use INSTRON drop tower and NDT (nondestructive testing) C type ultrasonic scan to perform one of the most promising methods in determining fracture toughness of material: CAI (Compression After Impact). Figure 1: TENF of Mode I Fracture of COSB Material. 125 2. When receiving re-used material from factory for possible future massive production, materials won’t be as fresh as virgin material and they will probably have been aged for week or even months. A DSC (Differential Scanning Calorimetry) can determine the cured degree of composites and by performing tests on very small amount of material samples, we will find out at which degree of cure, these prepreg strands are at the easiest stage to be manipulated during manufacturing in order to achieve optimized layup and mechanical properties. Figure 2: DSC measurement of Degree of Cure for Prepregs aged for fresh material, 0.5 month, and 1 month. 3. Based on the FEA model achieved in the current work, we will model more advanced hybrid COSB with different strand shape, size, and materials (different types of materials, as well as aged materials with downgraded properties). 126 4. The current achieved HOASE (Higher Order Abstract Structural Element) model of hat stiffened panel was used in measuring the flexural bending behavior, because stiffen in bending direction is one of the most important criteria in rating stiffeners behavior. In future, other structural properties such as buckling and postbuckling of hat stiffened panel HOASE with the same fast and accurate prediction will be established. Figure 3: Hat stiffener (Upper: Simply Supported, Lower: Fixed Edges) in Buckling Mode.

Abstract (if available)

Abstract Composite Oriented Strand Boards (COSB) are a bulk molding compound type of random fiber composites (RaFC) comprised of pre-impregnated strand tapes. This type of material has numerous applications such as: ❧ 1. In recycling expired composite materials, ❧ 2. In re-use of composite scraps generated from manufacturing work in automotive and aerospace industry. ❧ 3. In making composites tooling, because both the mold and curing part would have the same coefficient of thermal expansion. ❧ 4. When the strand aspect ratio is low, it has good drapability and is idea for compression molding of small complex parts such as brackets and hinges, where varying wall thickness, tight radii and rib feathers are common. It is therefore a good candidate to replace complex metallic parts that are commonly attached to carbon fiber reinforced polymers primary structures in modern aircrafts. ❧ Previous work in the field included exploring the possibility of using COSB to manufacture different structures that can be used in daily life e.g. cell phone case, skateboard, or as a cheaper replacement of some existed composite parts e.g. as the face sheet of the sandwich panels, or to replace hat stiffener made with virgin unidirectional prepreg composites. However, the mechanical properties of this type of material have not been systematically reported. A numerical tool is needed in predicting the behavior of COSB RaFC materials, and to replace years of mechanical testing work. ❧ In this work, there are mainly three goals: ❧ 1. Till present, there’s still no standards in testing or measuring this type of materials’ various mechanical properties including tensile and compression modulus and strength, fracture toughness, strength after impact damage, flexural bending strength, short beam shear strength etc. To conclude a complete report of COSB RaFC’s mechanical properties will take more than decades of mechanical destructive testing work, and numerous of funding and human resources. In this work, we aimed at investigating the possibility of using geometric modeling and Finite Element Method (both fiber level micro-scale and coupon level meso-scale) to predict COSB material’s microstructure and mechanical properties. ❧ 2. The FEA modeling results were experimentally validated via advanced manufacturing of composites and structures. ❧ 3. In order to support future work of making COSB material into 3D contoured structures that can replace some of the existing expensive ones, we aimed at establishing a set of higher order abstract structural elements using parametric finite element analysis (part level macro-scale) to define the design sensitivity of composite hat stiffened panels, a widely used structure in aerospace industry.

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Asset Metadata

Creator Jin, Bo Cheng (author)

Core Title Development of composite oriented strand board and structures

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Mechanical Engineering

Publication Date 12/07/2019

Defense Date 09/26/2017

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag advanced manufacturing,aerospace structures,composite oriented strand board,finite element analysis,high performance composite materials,OAI-PMH Harvest

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Nutt, Steven (committee chair), Nakano, Aiichiro (committee member), Safadi, Oussama (committee member)

Creator Email bochengj@usc.edu,bocjin@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c40-461778

Unique identifier UC11266682

Identifier etd-JinBoCheng-5945.pdf (filename),usctheses-c40-461778 (legacy record id)

Legacy Identifier etd-JinBoCheng-5945.pdf

Dmrecord 461778

Document Type Dissertation

Rights Jin, Bo Cheng

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

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