Crush Analysis of Compression Modeled Chopped Fiber Tubes

Transcription

1 Crush Analysis of Compression Modeled Chopped Fiber Tubes 1 S. DORMOHAMMADI, 1 D. HUANG, 1 M. REPUPILLI, * 1 F. ABDI, 2 Y. SONG and 2 U. GANDHI ABSTRACT Chopped fiber reinforced thermoplastic composites can be very useful in developing lightweight high strength recyclable components for automobiles. Such parts can be produced using injection or compression molding process. In general compression molding is preferred as it can help retain the fiber length compared to injection molding process. The longer fiber results in improved structural properties. A computational method is introduced for the virtual simulation of performance of chopped fibers in polymer composites. This new approach did lead to the development of a specialized Multi-Scale Material Characterization of composite system comprising of: a) chopped fiber material modeling based on nano-mechanics failure theory considering fibers as inclusion, b) micro-macro mechanics, and damage failure theory, c) tensor stiffness averaging technique; and d) structural durability and damage tolerance (D&DT) analysis under crush service loading. The material model established in MCQ-Chopped is integrated/coupled with FEA with GENOA platform software to perform Multi Scale Progressive Failure Analysis (MS-PFA). The crush modeling of composite crushed tube was test validated using GENOA software in 3 distinct integrated steps using, such as follows: a) Characterizing Material Properties - of composite materials composed of chopped fibers using MCQ-Chopped and validating against Toyota coupon test data; b) Mapping and Transformation - of statistical average tensor orientation from unstructured Moldex3D detailed model to LS-DYNA FE solver. In this regard GENOA platform software algorithm was used to perform 3D models data management and visualize the mapping error between two dissimilar meshes. And c) De-Homogenized Multi-Scale Progressive Failure Dynamic Analysis (MS- PFDA) was employed to capture the damage and failure at multi scale levels, namely micro (constituents fiber/matrix) and macro through-the-thickness. The simulation results are compared with test provided load vs. displacement and acceleration vs. time curve. In addition the software prediction provided the damage and fracture evolution and the contributing failure mechanism. Keywords: Compression Molding, Chopped Fiber, crushed tube, De-homogenized modeling, Tensor orientation stiffness, Effect of defects, Strain Rate Effect. 1 AlphaSTAR Corporation, 5150 E. Pacific Coast Hwy, Ste 650, Long Beach, CA Toyota Corporation Technical Center, Ann Arbor Michigan, USA *Corresponding Author: fabdi@alphastarcorp.com

2 1.0 INTRODUCTION Commonly used structural design software s have difficulties predicting manufacturing parameters and constituent properties of short or long fiber reinforced polymer composites to meet mandated design requirements. Certainly, the use of short fiber-reinforced polymer composite materials in aerospace, land, and sea applications has seen a sustained upsurge over the past three decades. Their superior strength and stiffness can be used to full advantage in structural applications only when their behavior under complex loading and different environmental conditions is well understood. Toward that end, the use of damage and failure criteria is essential for carrying out virtual testing and design optimization, without having to resort to time consuming and often too expensive experimental activities, especially under the competitive cost and ambitious time constraints imposed on product development by the marketplace. The objective of the present work is two-fold; implementing a computational methodology able to predict both the effective stiffness and strength of randomly oriented short fiber composites from injection and compression molding, and casting those properties into a useful model for applications on devices undergoing crushing, thus, allowing the prediction of their performance under different service loadings. In addition to being lightweight and economical, materials used for applications to aerospace and automotive structures should also meet the requirements of safety and the ability to absorb impact energy, referred to as crashworthiness. Polymer composites have been replacing metal components thanks to their reduced weight (which lowers fuel consumption), their durability, and their crashworthiness. In particular, carbon reinforced composite tubes, thanks to their high specific energy absorption, are considered as exceptionally efficient energy absorbing devices. Over the years, a large number of experimental studies have been conducted to explain the damage mechanisms of composite tubes. Test results indicate that the mechanisms to dissipate energy in composites is far more complex than those observed in conventional materials, due to matrix cracking, fiber matrix debonding, delamination, fiber pullout, and fiber breakage, among others. Through carefully designed software architecture, advanced materials and structures can be rapidly qualified to meet safety, reliability, and certification requirements. Virtual testing is used to try new materials in structures earlier in an applications timeline. Conducting progressive failure analyses and combining those results predict structure/component safety and integrity based on the physics and micro/macro mechanics of materials, manufacturing processes, available test data, and service environments. The approach takes progressive damage and fracture processes into account and accurately assesses reliability and durability by predicting failure initiation and progression based on constituent material properties. 1.1 Short Fiber Reinforced Polymer Short fiber reinforced polymer (SFRP) composites usually consist of particles that are slender, relatively short compared to the overall dimensions of the part, and imperfectly distributed in a continuous phase matrix. Their applications have been rapidly growing, particularly in the automotive industry, thanks to their versatility

3 in mechanical properties over corresponding parent polymers. They were originally developed to fill the mechanical performance gap between the unreinforced polymers, used in non-load-bearing applications, and the continuous-fiber laminates, used as primary structures in the aerospace industry. Although not as stiff or as strong as their continuous counterpart, they have several attractive characteristics. In fact, their capability of being manufactured in complex geometries to conform to the desired shape without being damaged or distorted, their isotropic behavior, and their low fabrication costs are desirable enough assets to make short fiber reinforced composites the material of choice. 1.2 De-homogenization and Homogenization Modeling Although composite material models should be based on their actual microstructure, the central idea in material characterization of fiber composites resorts to the existence of macroscopically averaged mechanical properties. In this simplification approach, homogenization, the effective properties that govern the macroscopic behavior of the composite are determined in terms of the mechanical properties and geometrical nature of the individual constituents: the degree of such an approximation depends on the desired engineering accuracy. Composite homogenization is a mechanics based modeling scheme that transforms a heterogeneous structural material into a constitutively equivalent homogeneous continuum, for which a set of effective properties is obtained though established analytical methods. This means that under a given state of deformation, both the composite and the equivalent homogeneous material possess the same amount of stored energy (i.e., under a given set of boundary conditions, the two equivalent materials have the same average stress and average strain field) [1]. Nonetheless, composite de-homogenization is the reverse scheme, through which the microstructure is locally restored back in the homogenized composite and the micro-stress and micro-strain fields are recovered, providing useful damage/failure information as to how a certain failure occurs. These two complementary procedures (forward and backward analyses) form the basis of the multi-scale approach implemented in this work to predict composites behavior. 2.0 METHODOLOGY Computational multi-scale modeling techniques currently practiced by the industry are based on test duplication, but not test prediction, considering uncertainties and defects. Limitations are addressed as: (a) Homogenized transfer of data from one scale to the next causes the loss of accuracy, specifically in FEM solution, where load re-distribution and damage evolution between chopped fibers and resin is not calculated. In addition, failure at the laminate level relies on the homogenization of constituent properties. Yet, in reality, failure is initiated at a much lower level (i.e., fiber, matrix, and interphase levels). (b) The FE numerical based unit cell (fiber/matrix) is time consuming, and utilizes constitutive modeling with little or no-failure mechanisms (e.g., crack at the tip of long fiber) under consideration. (c) The FE unit cell, using numerical approaches, is limited to low amounts of chopped fiber volume ratio. (d) No effects of defects are considered,

4 such as fiber waviness, fiber agglomeration, fiber/matrix interphase, and void shape, size and distribution. Finally, (e) Computational tools using solid elements are computationally expensive. 2.1 Simulation Process and Verification and Validation Durability and Damage Tolerance (D&DT), life, and reliability predictions were analyzed by means of multi-scale progressive failure analysis (damage and fracture evolution). The proposed methodology for chopped fiber composite material systems consists of utilizing the closed-form solution to the Mori-Tanaka, Classical Laminate Theory (CLT), and Multi-Scale Multi-Physics Progressive Failure Analysis of a unit cell or representative volume element (RVE). The entire process, summarized in Figure 1, consists of 5 steps, each with a distinct objective and validation. Figure 1. Overview of the Integrated Simulation Process. This algorithm/approach is an augmentation to commercial FE software, aimed to provide engineers with the computational predictive technology essential to characterize and qualify advanced composite materials and structures, taking into account manufacturing anomalies (i.e., matrix distortion, residual stress), effects of defects, and scatter of as-built/as-is states within the composite material. 1. Material Chopped Characterization and Qualification (MCQ) calibration utilizes the short fiber size and fabrication variables (e.g., fiber waviness, uniform or non-uniform dispersion, and interphase) to predict the material coupon performance of as-built/as-is. 2. Material Composite Characterization and Qualification (MCQ) calibration contains the reverse engineering process to couple the following disciplines: composite micro- and macro-mechanics, damage progression, fracture, and optimization. Given the stress-strain curve of a single (or multiple) coupon test, the MCQ code will reverse engineer the coupon material by predicting the material constituent properties and fabrication parameters, reproducing the test nonlinear stress-strain curves. 3. The De-Homogenized MS-PFA integrates numerical based FE analyses with multi-scale analyses, which includes: a) nano-scale modeling, to consider the

5 effect of defects (i.e., fiber waviness, void); b) micro-mechanics fiber/matrix/interface; c) macro-scale composite laminate and layups (including hybrid construction of continuous, chopped, multi-functional, and sandwich systems); d) modeling of fictitious reversed engineered fiber orientation, load redistribution between fiber and resin failure types of long fiber, and crack at the tip; and e) layered solid and shell, in order to improve CPU speed, especially for systems employing several chopped fiber layers and/or sub-layers within a FE model. The proposed multi-scale modeling methodology at the material and the structural levels combines the Mori-Tanaka effective far-field method, micromechanics, CLT, and MS-PFA, in order to predict the desired material properties of thermoplastic/thermoset chopped fiber composites, considering the manufacturing processes, without the need for time consuming and expensive testing or detailed finite element models. The effect of interface has been presented earlier by the authors on multi-scale carbon fiber reinforced composite material system on interlaminar shear strength, using a short beam shear specimen from ASTM-D-2344 [2]. 2.2 Progressive Failure Analysis (PFA) PFA is the preferred approach for failure analysis in composite materials. In this approach, a representative volume element, independent of FE failure analysis in each ply constituting the laminate under investigation, is assessed based on the ply limit strength/strain properties. Some of the failure criteria employed is maximum stress - or maximum strain-based and some others are interactive. The damaged plies are then either removed from the unit cell model, or given a negligible Solver UMAT + VCCT/CCZM GENOA Solid (MS-PFA or MS-PFA + *VCCT/DCZM) GENOA Shell (layered) MS-PFA MCQ (Material Characterization and Qualification) All Levels Integrated *GENOA VCCT/DCZM UNNOTCHED SOLUTION TIME 10 hours 2 days 1-2 hour 1-20 Minutes Figure 2. Modeling Complexity Approach Conforms to Building-Block Validation Strategy. stiffness, in order to simulate a failed ply and study its effect on the overall laminate. Only once all the plies in the unit cell are damaged, it is assumed to be completely broken. The stresses in individual plies, obtained using the classical laminate theory, are then compared against the limit stress or strain parameters, using default failure criteria. It is important to note that there is a hierarchy, not only with the complexity of the structure being modeled, but with the modeling approach, namely, low-fidelity models feeding into higher-fidelity models (Figure 2). Modeling at the lower levels allows to quickly predicting results that consider uncertainties and defects. According to the needs and requirements, however, the user may still build Sec

6 more complex and advanced solid models (high-fidelity), generating additional extensive damage evolution information. 2.3 Multi-Scale Modeling At the macro-scale, the material is assumed to be anisotropic and homogeneous as a laminate, experiencing a uniform displacement in the loading direction. At the meso-scale, the laminate is then modeled as an assembly of multiple homogeneous and orthotropic lamina through its thickness. The meso-scale is then linked to a micro-scale through the use of a representative volume element, which captures the local heterogeneity of the fiber/matrix constituents and allows the analysis of the influence of local imperfections on the global behavior of the material. In this way, the fiber and polymer properties can be utilized to predict the effective orthotropic properties of the building block of the multi-axial laminate, i.e. the unidirectional fiber lamina. Therefore, multi-scale modeling and simulation of such composite materials have the potential to provide predictive capabilities for correlating mechanical, thermal, and electrical properties to their manufacturing processes, as well as to their structural performance. 2.4 Dehomogenization Approach In some more details, every unidirectional ply within a laminate is modeled by its constituents, fiber and matrix. The laminate, originally treated as a layered structure, is homogenized next, and a set of effective laminate properties is obtained from the laminate geometry (plies orientations and stacking sequence) and fiber/matrix properties, using the classical laminate theory. The effective laminate properties then serve as a material input for finite element analyses of complex composite structural elements, providing the relationship between the applied thermo-mechanical loads and the structural deformation on each finite element. Upon loading of a laminate, failure may occur on one or more plies and/or at the interface between two adjacent plies. However, in most FE codes, deformation of the structure is typically linked to stresses and strains within the homogenized system, and not to those of the composite constituents. Conversely, the guiding concept behind much of our approach has always been that material failure in composites initiates at the constituents level (i.e., fiber/matrix micro-scale), even though the phenomenon is observed at the lamina level (macro-scale). Therefore, in a laminate under global loads, the traditional approach of homogenizing the lamina first and of computing the macro-fields of the lamina next is deemed suitable. Then, macro-mechanics failure theories are employed to identify the lamina where failure is suspected to have occurred, and the actual micro-fields in such lamina are recovered through the de-homogenization process, which restores the actual composite microstructure back in the lamina. A rigorous micromechanics analysis of the composite structure can finally link the deformation of the structure directly to the state of stress and strain of both fiber and matrix phases. In this regard, a novel methodology has been implemented in this work: it is capable of obtaining accurate effective composite properties, as well as recovering the actual stress and strain micro-fields in a loaded laminate through the process of de-homogenization.

7 Figure 3 shows the schematic view of the de-homogenized vs. homogenized multi-scale modeling approaches currently available. As shown, homogenization is based on a numerically (FE based) generated RVE unit cell, considering the smeared fiber orientation and length without the effect of defects. Conversely, de-homogenization is based on an analytical generated RVE unit cell, considering the through-thickness fiber orientation and length and including the effect of defects, allowing fiber, matrix, and interphase stress re-distribution and damage evolution. Multi-scale modeling, unlike all other structural analysis computer codes, goes down to the nano-/micro-level, where failure originates. This methodology was augmented with a new capability dedicated to the prediction of the performance of chopped fiber composites. The new capability, known as MCQ-Chopped (Material Characterization and Qualification), predicts composite randomly oriented fiber orientation, strength, stiffness, through the material thickness, by reverse engineering the material constituents properties (fiber and matrix). By the replication of measured performance from the ASTM coupon tests, the Figure 3. Schematic View of De-Homogenized vs. Homogenized Multi-Scale Modeling computational analytical capability also considers the effect of defects including: (a) Void shape size/distribution, (b) Fiber waviness, (c) Agglomeration, and (d) Interphase. Next, a multi-scale progressive failure analysis (MS-PFA) is performed to evaluate the structural durability and damage tolerance of two SFRP composite tubes, to track the damage and fracture evolution and to determine When, Where, and Why the failure occurs, and What can be done to resolve it. The paper physics approach (originally proposed by Cox [3], then adopted and improved by Fukuda and Kawata [4], and finally revised by Jayaraman and Kortschot [5]) asserts that the elastic modulus of SFRP composites (ESFRP) is only dependent on the angle θ that fibers make with the direction (say, the 1-direction) in which the composite elastic modulus is to be evaluated (Figure 4). The equivalent laminate is idealized as the combination of unidirectional plies, each consisting of fibers having uniform length and orientation, such that it can overall replicate the same orientation distribution as that of the original short fiber composite (captured by the second order orientation distribution tensor).

8 Figure 4. Orientation Tensor Determination (OTD). Figure 5. Strain-Rate Effect Experimental Data of PP. Figure 6. Compression Molded: Tubes Halves Manufactured by Compression Molding Processes The prediction of the elastic moduli of a composite where the short fibers exhibit in-plane random orientation are based on the classical laminate analogy [6], which bridges the macromechanics of short fiber composites with that of laminated composites. The laminate analogy approach has been compared by Fu and Lauke [7] with other theories (namely, the paper physics approach, the rule-of-thumb expression, and the aggregate model), and also with existing experimental results, showing a satisfactory agreement.

9 2.5 Strain-Rate Effects Fiber-reinforced polymers are known to have a strain rate dependent deformation response. Therefore, in order to properly simulate a high velocity impact of a crush tube problem using MS-PFDA, it is more accurate to account for the strain-rate dependence of the modulus and strength. To quantify the strain-rate dependence, Toyota carried out multiple tests on the same class of material at four strain-rates, 0.1, 1, 10, and 100 (1/s) (Figure 5). The strain-rate dependence was employed in our material modeling to determine the effective modulus and strength. The strain-rate was calculated on every element at each iteration, and material properties were updated accordingly. However, in the absence of experimental data, the effective strain-rate dependent modulus could also be calculated using Goldberg s approach [8]. 3.0 EXPERIMENTAL DYNAMIC TESTS All the experimental dynamic tests reported in this paper were performed using Polypropylene with 40%wt fiber content (PP-SGF40). The tubes components were manufactured using compression molding techniques (Figure 6). The impact crush test set-up included tube crushed with a mass of Kg at a speed of 7.2 m/s. where the part is placed longitudinally in the test chamber and all random chopped fibers the continuous fibers of composite are aligned in the direction of the impactor to fully exploit the intrinsic strength of the fiber reinforced composite. Figure 7 shows the two tubes fragments after the impact test has taken place. 4.0 MATERIAL CHARACTERIZATION AND VALIDATION Figure 7. Final Impact Test To obtain appropriate input data for the simulation of Crushed Tube Part. of the composite components and for the validation of the numerical material model, static coupon tests were performed. The material characterization tests were performed in tension, according to the ASTM Standard D3039, along two principal directions: one, by aligning the injection direction (flow) along the tensile-test direction; the other, by aligning the direction transverse to the injection (cross-flow) along the tensile-test direction. Coupon tests were performed up to material failure: the Young s modulus, Poisson s ratio, yield stress and strain were obtained from these two tests. The flat specimens, used to measure these properties, were made from one ply of injection or compression molding, and composite end tabs were bonded at each end. Two strain gages were bonded onto one side of the specimen, in order to acquire longitudinal and transverse strains. The judicious combination of composite micro- and macro-mechanics, damage progression, and a robust optimization method enabled the reliable simulation of the chopped fibers performance. The effectiveness of the methodology is illustrated by replicating stress-strain curves from compression molding (Figure 8). The material system employed in this work was PP-SGF40: a 40%wt fraction of glass short fiber with an average length of 9.0 mm was employed, along with polypropelene (PP) matrix. The effective fiber and matrix

10 constituent properties are determined using MCQ knowing the fabrication parameters such as fiber orientation and fiber volume fractions. The constituent properties were then used to calculate the orthotropic aligned layer properties, in which all short fibers are assumed to be aligned with the 0 -direction. a) Flow Stress-Strain Curve b) Cross flow Stress-Strain Curves Figure 8. Aligned Layer Nonlinearity: Comparison between Test Data and MCQ Predictions. The results of the calibration using flow and cross flow data for compression molded specimens are shown in Figure 8. MCQ determines the effective fiber and matrix properties aligned layer properties and its nonlinearity (Figure 9), and the fictitious lay-up (i.e., layer orientation and thickness) for the CM test specimens (Figure 10). (a) Laminate Flow Stress-Strain Curve: Comparison between Test and MCQ-Chopped Prediction (b) Aligned Ply Stress-Strain Curve: Reverse Engineered (MCQ-Chopped) Figure 9. Compression Molding Aligned Ply Nonlinearity Table 1. Particle and Compression Molding Manufacturing Properties Shape Fiber Type Straight Void Volume 2.00E-2 Fraction Fiber Weight 4.00E-1 Fraction Length [mm] 9.00E+0 Width [mm] 1.30E-2 Height [mm] 1.30E-2 Dispersion Uniform

11 The same fiber and matrix properties were used for CM processes, except for the average fiber length, which in the CM is longer than that in the IM, due to more fiber breakage in the injection process, as shown in Table 1. The orientation tensor validation was performed to show the applicability of the approach. The second-order orientation tensor was measured on the tube manufactured using compression molding technique and compared with the computed data from Moldex3D. The second-order orientation tensor was also measured for flow direction coupon manufactured using injection molding process. The orientation tensor was used knowing aligned layer properties and the measured second-order orientation tensor to determine the stiffness of the coupon in flow direction and to compare with tensile test of flow direction (Figure 11). Figure 10. Orientations throughout Laminate Thickness by MCQ-Chopped. Figure 11. Stress-Strain Curve: Comparison between Test Data and MCQ-Predictions. The material validation was performed using a 3-Point-Bending test on the CM specimens, although this test was not necessary for the material calibration. Thus, a 3-Point-Bending simulation was run on CM models with the following assumption: (1) A solid element was used, (2) The material card was based on the calibrated material properties, and (3) GENOA running ABAQUS/Standard was employed (rather than ABAQUS using UMAT) in order to avoid convergence issues caused by material degradation (typical of implicit analyses). A comparison of the load vs. displacement curves, between the test and GENOA/ABAQUS simulations, is shown in Figure 12.

12 4.1 Orientation Tensor Mapping Validation To validate the orientation tensor mapping from the donor mesh (Moldex3D) to the structured shell mesh (FE model), a qualitative comparison of the orientation tensor components distribution [9, 10] is shown for tube CM manufactured part (Figure 13). 5.0 NUMERICAL MODELING MS-PFDA-LS-DYNA Crush worthiness analysis was Figure Point Bending Compression Molding Test: Load-Displacement Curves (Flow and Cross-Flow Directions). performed on layered shell element model to predict the damage and fracture evolution process. The case study presented herein illustrates the capabilities of the proposed computational framework embedded in the MCQ/GENOA suite. The user-friendliness coupled with the interactive and fast computational capabilities of the program make it a valuable tool for obtaining preliminary design data and gaining a fundamental understanding of how various parameters (e.g., materials, stacking sequence, geometry, boundary conditions, manufacturing process, and loads) influence the results. (a) Moldex3D (b) GENOA Mapping Figure 13. Orientation Tensor [A] Components Compression Molding Comparison of the Orientation Distribution between the Moldex3D Model (left) and FE Model (right).

13 5.1 Finite Element Analysis There are two ways to run progressive failure analysis using GENOA software: (a) GENOA running commercial FE solver, and (b) Commercial FE software using GENOA in its material subroutine. In this work, option (b) was adopted, for a faster analysis and higher computational efficiency. The crush tube was meshed using quad and 32 tri shell elements, with a total of nodes [9]. IMPACTOR/BASE: The basic geometry of the FE model, generated according to the guidelines, is shown in Figure 14. The impactor was modeled as a rigid plate (mass of Kg), placed at the tube right-end, and was enabled to slide only along the tube longitudinal axis with an initial inward velocity of 7,300 mm/s. Similarly, the base was modeled as a rigid plate, placed at the tube left-end, and completely restrained from motion. SOLVER: In order to simulate the nonlinear axial tube crush, a multi-scale progressive dynamic failure analysis (MS-PFDA) was performed, using the explicit finite element code LS-DYNA (version mpp d R8.0.0) augmented with the GENOA UMAT subroutine. CONTACT: To enforce contact between the two rigid plates and the tube, an AUTOMATIC SINGLE SURFACE contact type was defined, which also includes the tube self-contact while crumpling on itself. A master-surface to slave-node type of interaction was defined between the impactor/base rigid surfaces and the deformable tube nodes. The algorithm, implements a self-contact, based on a penalty formulation, on the tube lateral surface, to prevent selfpenetration and to provide the friction effect to its sliding elements, if any. A Figure 14. Determine Ply Angle Through Thickness friction coefficient of De-Homogenization Approach was employed.

14 SECTION: The tube was modeled by 4-node shell elements, according to the Belytschko Tsay formulation (elfrom = 2), which uses one integration point per element and any number of integration points through the thickness. A multi-layered shell, with one ply per integration point through-the-thickness was employed. MATERIAL: In order to implement a composite numerical model, the PART_COMPOSITE card was defined. According to this card, the laminate has a thickness defined by the sum of each individual layer. Due to physics of the problem, fiber orientation varies from point to point; separate lay-up definitions were used for each region of elements. The heart of this analysis was the material definition of composites and damage initiation and progression calculation. In particular, the GENOA material library that implements the strength-, strain-based, and interactive criteria, was used for modeling of composite tubes to give a numerical behavior near to the experimental ones. CONTROL HRG: Zero energy modes resulting from using the reduced integration shell-element formulation are eliminated by hourglass control. Deformation of shell elements in an hourglass mode can result in the negative volume. Hence, we used hourglass control option in LS-DYNA simulations to resolve this problem. For hourglass control, we used in LS-DYNA standard formulation with hourglass coefficient of 0.1 and linear bulk viscosity with default values. MATERIAL/DAMAGE: The material in the FE model is defined as fiber and matrix constituent s properties and damage and failure criteria. Strain-rate effect was also considered due to high velocity crushing condition using the test data provided by TEMA. Progressive damage and fracture evaluations are carried out by imposing failure criteria locally within unit sub-volumes with reference to the local coordinate orientations in the material directions. At each individual load step, stresses in stitching and in-plane sub-volumes that can be obtained Figure 15. Compression Molding Damage through the composite micro-stress and Fracture Criteria Employed in UMAT analysis are assessed according to distinct failure criteria in Figure 15. The GENOA gives the user ability to prevent highly distorted elements by controlling the element removal in MAT USER.

15 6.0 COMPARISON BETWEEN NUMERICAL AND EXPERIMENTAL RESULTS A sequence of the deformed shapes of injection and compression molded tubes, at different simulation times, is shown in Figure 16. The numerical and experimental decelerations vs. displacement of the impactor a) Original Part b) Deformmed Figure 16. Compression Molded Part are compared in Figure 17. Both the experimental data and the numerical results were filtered using SAE 180 in the LS-PrePost. It is evident from the comparison that the GENOA MS-PFDA is able to approximate the initial peak load, residual strength, and energy absorption with good accuracy. The weakness of homogenization approach is mostly due to difficulties in failure theories formulated at the homogenized material which lead to immature failure for tube crushing analysis. A look at the simulation also shows how similar the chopped fiber composite material behavior and crushing pattern, with material breaking off from the specimens, is to the actual experimental collapse sequence. For crush tube, the difference between the GENOA MS-PFDA analysis and the experimental data is lower than 10% for the peak load and 15% for the residual strength. The discrepancy between the numerical results and experimental data is mainly due to the difficulty in accurately modeling the scatter in short fiber orientation and manufacturing process of chopped fiber composite materials. It is concluded that the compression molded part has significant higher energy absorption capacity compared to the injection molded counterpart, mostly resulting from its longer average fiber length. a) Load Vs. Time

16 b) Accelration Vs. Time Figure 17. Crushed Tube Compression Molding Prediction Vs. Test 7.0 CONCLUSIONS This work presents a numerical methodology on how to predict the stiffness, strength, and energy absorption of two chopped fiber composite structures, manufactured using injection and compression molding techniques. The material properties, extracted from simple flat test specimens, and the average fiber orientation distribution, predicted by a commercial code, were mapped over the complex 3D geometry of two tubes undergoing axial crushing. Crush tests were performed in conjunction with measurements of the impactor s dynamic motion. Thus deceleration-displacement data was also collected. The modeling of two composite tubes undergoing crush was test-validated using the GENOA MS-PFA software, coupled with the explicit dynamic finite element code LS-DYNA through the following three distinct steps: (1) Material Characterization and Qualification (MCQ) of the mechanical properties (i.e., strength and stiffness) of randomly oriented chopped fibers coupons. Using the flow and cross-flow properties (stress-strain curves) derived from ASTM D638 coupon tensile tests, a micro-mechanics based optimization algorithm is used to calibrate, or reverse-engineer, the fiber orientation, the fiber and matrix constituent properties, and the matrix non-linear behavior. (2) Mapping and transformation of the statistical average tensor orientation, from an unstructured Moldex3D mesh to a structured FE mesh. In this regard, the GENOA mapping algorithm was used to perform 3D models data management and to visualize any mapping inconsistencies between the two dissimilar meshes. (3) De-homogenized MS-PFDA (GENOA-LSDYNA) crashworthiness analysis was performed on the two composite tubes to predict the damage and fracture evolution process. It was shown that the homogenized approach, commonly used in commercial software, does not result in an accurate load-displacement resistance

17 curve. On the contrary, it was evident that the use of the proposed de-homogenized methodology was superior, in that it enabled the analysis of damage and fracture down to the micro-scale, allowing the breakage of fiber and matrix separately, resulting in a more accurate load-displacement curve, well comparable to the real crushing behavior of CM tubes. Despite the complexity of the chopped fiber material characterization and damage/fracture phenomena, a good agreement between numerical results and experimental data has been achieved for fairly complex structures under dynamic loading. The MS-PFDA is able to simulate the chopped fiber composite material behavior with material breaking from the specimens and consequently approximate the initial peak load, residual strength, and absorbed energy and the actual crushing with an accuracy of about 10%. This study demonstrates the capability of the proposed methodology to predict the response of composite structures undergoing crushing. When used in the design of energy absorbing composite devices, it can significantly reduce the dependence on physical testing. 8.0 REFERENCES 1. Christensen RM, Waals FM. Effective Stiffness of Randomly Oriented Fibre Composites. Journal of Composite Materials 1972; 6(3), p Garg M, Abdi F, McHugh S. Analyzing Interlaminar Shear Strength of Multi-Scale Composites via Combined Finite Element and Progressive Failure Analysis Approach. SAMPE 2008, Memphis, TN, USA, September Cox HL. The Elasticity and Strength of Paper and Other fibrous Materials. British Journal of Applied Physics 1952; 3, p Fukuda H, Kawata K. On Young s Modulus of Short Fibre Composites. Fibre Science Technology 1974; 7(3), p Jayaraman K, Kortschot MT. Correction to the Fukuda Kawata Young s Modulus and the Fukuda Chou Strength Theory for Short Fiber-Reinforced Composite Materials. Journal of Materials Science, 1996; 31(8), p Halpin JC, Pagano NJ. The Laminate Approximation for Randomly Oriented Fibre Composites. Journal of Composite Materials 1969; 3, p Fu SY, Lauke B. The Elastic Modulus of Misaligned Short Fiber Reinforced Polymers. Composites Science and Technology 1998; 58, p Goldberg R, Roberts GD, Gilat A. Analytical Studies of the High Strain Rate Tensile Response of a Polymer Matrix Composite. Journal of Advanced Materials, 2004; 36(3), p DorMohammadi S, Abdi F, Mandapati R, Baid HK, Lee MC, Gandhi U. Impact Crush Modeling of Chopped Fiber Reinforced Polymers. Proceedings of the 30 th Annual Technical Conference of the American Society for Composites (ASC) 2015, East Lansing, MI, USA, September Baid HK, Abdi F., Lee MC, Vaidya U. Chopped Fiber Composite Progressive Failure Model Under Service Loading. SAMPE 2015, Baltimore, MD, USA, May 2015.