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This study investigates the effects of process conditions on the inherent variabilities in fused filament fabrication (FFF) of short carbon-fiber-reinforced Nylon-6 composites, where the sources of uncertainty and their adverse effects on microstructures and Young’s modulus are quantified. Microstructural characteristics such as fiber volume fraction, void volume fraction, and their spatial distributions are first extracted via image-based data analytics, and then their uncertainties are quantified by the analysis of variance. A Monte Carlo sampling method is introduced to enrich the datasets for analyzing uncertainty propagation from micro-level (microstructures) to macro-level (mechanical property). A modified Halpin-Tsai model with the consideration of fiber and void distributions is developed to quantify the propagated uncertainties on Young’s modulus, which are further validated through quasi-static tensile tests. This study examined the process-structure-property relationship of FFF samples and quantified the underlying variations in both micro- and macro-levels.

The effect of the multiaxiality and proportionality of loading on the cyclic behaviour and early cracking behaviour was studied for closed die forged AZ80 Mg alloy. Several different loading paths were presented, uniaxial and biaxial with varying levels of non-proportionality. In multiaxial loading the effect of proportionality is only present on the shear response of the material and increasing levels of non-proportionality is detrimental to the fatigue life. When compared with proportional loading, a 50% reduction in life was observed under 90° out of phase non-proportional loading. The pure axial cracking behaviour is dominated by transverse cracks along the plane of maximum normal stress, whereas in pure shear the material exhibited longitudinal cracking (shear dominated) behaviour in LCF regime and helical cracking (normal stress dominated) in the HCF regime. The synergistic effects of each individual uniaxial cracking modes contribution towards the combined macroscopic cracking behaviour in multiaxial loading was investigated, and was dominated by transverse cracking when the shear strain energy density (SED) contribution to the total SED was low, and mixed cracking when the shear SED contribution was high.

The quasi-static and cyclic response of as-extruded and closed-die extruded-forged AZ80 Mg alloy forged at 250 °C and 20 mm/sec was investigated. Servo hydraulic, fully reversed, strain controlled uniaxial “push-pull”, pure torsion, and biaxial fatigue testing were also conducted on the closed-die forged alloy. Two uniaxial loading paths (pure axial and pure shear) and three different biaxial loading paths were investigated (proportional loading, and non-proportional loading at phase angles of 45° and 90°). After forging of the as-extruded billet, the yield stress in the axial direction increased by 46%, the failure elongation by 35% and the ultimate strength by 13%. The spatial variation in both the local texture, microstructure and superficial hardness throughout the cross section of the forging was investigated and discussed. The web region in the center of the forged billet exhibited a virtually fully recrystallized and refined microstructure with intense basal texture, whereas the rib regions on each side exhibited a partially recrystallized and coarser microstructure with less intense texture. The fatigue life of the forged material in the axial direction showed dramatic improvement relative to the as-extruded material at strain amplitudes which were less than 0.35%. However, at higher strain amplitudes, there are significantly higher cyclic stresses (and associated fatigue damage) in the forged material (relative to the as-extruded), resulting in a decrease in life under fully reversed strain controlled fatigue loading. For the pure axial strain path, the total amount of strain energy density (SED) observed in the stabilized response was a function of number of cycles only, and was insensitive to material condition (as-extruded or forged). However, for the forged material, of all the strain paths investigated, only the pure shear path demonstrated a significantly different relationship of total SED vs. life. Furthermore, the amount of total SED for a given number of cycles decreases when biaxial loading is introduced, though following the same general relationship as the pure axial strain path. The effect of a decrease in total SED for a given number of cycles occurred in all biaxial strain paths, with proportional being the least prominent, then 45° and 90° out of phase being progressively more pronounced respectively. Both the Smith Watson Topper (SWT) and Jahed-Varvani (JV) models were utilized to predict the fatigue life of the uniaxial and biaxial cyclic tests. Calibration of each models intrinsic parameters were done using both of the uniaxial loading paths individually, then these same parameters were used in combination with one another to predict the life in the biaxial cases. Both the SWT and JV models are capable of giving an acceptable prediction, however the JV model’s prediction is more reliable, especially when the cyclic response has pronounced asymmetry. The biaxial fatigue response is somewhat dominated by the axial component for two significant reasons; firstly, the shape of the hysteresis in the shear direction dramatically changes based on phase angle and axial strain amplitude, whereas the axial hysteresis loop remains somewhat invariant to the presence or modulation of the other loading axis. Secondly, the initial crack propagation mode is predominantly transverse to the axial direction in all strain paths except for pure shear (which exhibits longitudinal cracking). Tensile cracking dominating the biaxial failure mode provides qualitative justification of a modification factor to an existing energy based biaxial fatigue life prediction model, enabling it to predict the life of extruded and forged AZ80 Mg reliably for a variety of different biaxial strain paths.

The material behavior of chopped carbon fiber chip-reinforced Sheet Molding Compound (SMC) composite is investigated under both quasi-static and cyclic fatigue loading conditions in the present study. Quasi-static tensile and compressive strength data is collected, followed by a series of fatigue tests under three different cyclic loading conditions, i.e., Tension-Tension (T-T), Compression-Compression (C-C), and Tension-Compression (T-C). The experimental results show a considerable amount of variation for each loading condition, which is found to be induced by the spatial distribution of fiber orientation within the tested specimens. An analytical approach is developed to correlate the fatigue performance of the SMC material with the local modulus, which is determined by the fiber orientation distribution. Additionally, the similar failure modes are observed under different loading conditions. Based on these findings, a new form of Constant Fatigue Life (CFL) diagram is established in which the impact of fiber orientation tensor to the fatigue behavior of SMC is considered. This developed CFL diagram is examined by comparing the measured fatigue performance with prediction where local fiber orientation distribution is quantified from microscopic images.

Injection molded plastics are widely used for mass production in auto industry. However, it is challenge to produce parts that do not warp. It is helpful to have an accurate way to measure the warpage when investigating and solving warpage issues. In this paper, a new technology is introduced to measure the part warpage quickly and accurately with the help of digital image correlation (DIC) method. The polypropylene plaque were fabricated by injection molding based on An L9 (3ˆ4) Taguchi design of experiments. The warpage of plaque are characterized for all the conditions and at different time after being ejected. Different kinds of warpage results are obtained by DIC method, such as maximum deflection, deflection distribution along desired path, warpage contour on the surface. The plaque warpage increases with the time. The maximum difference can reach as high as 64.9%. The cooling time has the largest influence on the warpage, while the packing pressure has the minor effect. Nevertheless, the warpage difference due to time varying depends on melt temperature, mold temperature, cooling time and packing pressure, in which mold temperature has the highest effects.

Failure analysis is a critical process for the lifetime evaluation of high density polyethylene (HDPE) under cyclic loading since HDPE may encounter different failure modes under different service environments. However, there are only a few investigations on the failure mechanism and failure mode of HDPE in cyclic-loading tests. The objective of this paper is to understand the failure mechanism and propose an approach to predict the failure mode of HDPE under cyclic loading. On the mechanism analysis, our results demonstrated that there could be three failure modes including necking, buckling and fatigue cracking for HDPE under cyclic loading. Both necking and buckling were strongly dependent on the increase of the specimen temperature, which led to the reduction of both yield stress defining necking and tangent modulus governing buckling. On the mode prediction, the yield stress and the tangent modulus could be computed as the functions of specimen temperature which was calculated by FEM heat transfer analysis considering heat generated by inelastic deformation energy and heat transferred with surroundings. Then, necking was predicted by comparing the decreased yield stress with the applied peak stress, and buckling was predicted by comparing the declined buckling stress proportional to tangent modulus with the absolute of the applied valley stress. The proposed methodology was validated as the predicted results were well matched with the experimental data for the tests of HDPE under different cyclic loadings.

This study investigates the failure mechanisms of cross-ply laminates subjected to longitudinal compressive loading. A sequence of failure initiation and propagation process is observed based on optical microscopy images of failed specimens. Specifically, the failure process in the cross-ply laminates involves a combination of four failure mechanisms: fiber kinking, delamination, matrix cracking, and fiber/matrix splitting. We find that the kink-bands in the middle 0° plies of the cross-ply laminates most often show a wedge shape and the angle of matrix cracks in the 90° plies is slightly larger than that of pure 90° plies. The reason has been attributed to the constraining effects by the adjacent plies. The next focus of this study is to propose hybrid micro-macro models to more systematically study the failure mechanisms of the cross-ply laminates. We show that these models accurately predict the combined failure modes of the cross-ply laminates and enable us to closely investigate the interactions of different failure mechanisms. More importantly, the hybrid models achieve great computational efficiency compared to full-scale microstructural models. The combined experimental and computational analyses presented here provide a new level of understanding of the kink-band morphology and damage mechanisms in the cross-ply laminates.

In present study, the fatigue damage behavior of chopped carbon fiber chip-reinforced composite has been experimentally and numerically investigated. A large scatter is exhibited in the S-N diagram due to the random distribution of carbon fiber chips, and therefore a new analysis procedure is proposed to link the local microstructure to the fatigue behavior of the bulk material. Interrupted fatigue tests are also performed so that microstructure characterization can be conducted on the tested samples to analyze the crack initiation and propagation. Inspired from the experimental findings, a multi-scale progressive damage fatigue model is proposed to predict the fatigue behavior. The model incorporates a new stochastic chip-packing algorithm for microstructure reconstruction along with continuum damage models into the representative volume element (RVE) model in ABAQUS/Explicit. The simulation results based on the proposed model are in good agreement with the experimental data in terms of cracking modes and predicted life.

This paper presents a computational framework to predict the tensile failure of chopped carbon fiber SMC composites based on the Representative Volume Element (RVE) model. In the framework, a conforming mesh-based reconstruction algorithm is developed to generate mesostructure RVE models of SMC based on the statistical characteristics. Moreover, constitutive models are proposed for the three phases in SMC composites: fiber chip, matrix, and interface. The model predictions are validated by coupon-level experimental tests on SMC samples of various chip orientation distributions. The meso-scale failure mechanism and failure strength predicted by the RVE models are in good agreement with the experimental results. The presented study demonstrates the capability of the present modeling framework in the design of composites materials with complex micro- and meso- structure.

Failure prediction for carbon fiber reinforced polymer (CFRP) composites has been a longstanding challenge. In this study, we address this challenge by first applying a well-established computational micromechanics model based on representative volume element to predict the failure envelopes of unidirectional (UD) CFRP composites. Then, these failure envelopes are compared with the classical failure criteria. We have evaluated the performances of these failure criteria and identified the aspects for further improvement in their accuracies for the UD CFRP composites studied herein. Based on the failure mechanisms from computational analyses and the comparisons between predicted failure envelopes and classical failure criteria, a new set of homogenized failure criteria is proposed. The newly proposed failure criteria show significant improvement according to our computational and experimental results. Furthermore, we have compared the proposed failure criteria with existing experimental data and computational results available in the literature for different types of composites. Good agreements are generally observed.

Fatigue tests for unidirectional (UD) CFRP composite specimens of various sizes are conducted under different stress ratios. The results show that the specimen size has considerable influence on the transverse tension-tension fatigue performance of UD laminates. The underlying fatigue mechanisms are also investigated through SEM observations. Moreover, a fatigue life prediction method considering size effects is presented, and a good correlation is observed between the prediction and the test data. Finally, to allow for an evaluation of the effects of mean stress, constant fatigue life diagrams for 0°, 10°, and 90° UD composites are established based on four-segment anisomorphic model.

The role of the process deformation history on the mechanical performance of self-pierce riveted (SPR) joints is examined in detail. The SPR process was simulated using a non-linear finite element model coupled with a damage criterion sensitive to the stress state. Results of the FE simulation compared closely to cross-sectional images of experimental SPR joints. The FE simulation results suggest that the strain hardening due to the piercing process is the main mechanism for joint strength under quasi-static condition. Aspects of fatigue damage were modeled including crack initiation, propagation, fretting and number of cycle to failure, and compared to experimental results. Results from the study indicate that residual stresses and plastic strain may alter the crack initiation location and crack propagation plane, leading to more accurate results when included in finite element analysis of SPR joints. Including these residual stresses and plastic strains also changed the predicted fretting locations leading to better agreement with experimental results. Lastly, linear elastic fracture mechanics were performed to estimate fatigue lives based on initial crack location and angle of crack plane. The estimation of the number of cycles to failure that included residual stresses and plastic strains resulted in a better correlation to experimental data when compared to the calculations that excluded residual stresses and plastic strains.

It is important to investigate the constitutive behavior of high density polyethylene (HDPE) under cyclic loading since it is widely used for industrial applications. However, there are only a few preliminary investigations on the constitutive behavior of HDPE under cyclic loading. This work aims at investigating the deformation mechanism, developing the constitutive model especially for the cyclic-loading behavior, and proposing an efficient approach for model calibration. Firstly, the deformation mechanism was successfully explored by conducting a special designed relaxation-unloading test by which the time-independent elastic-plastic behavior was decoupled from the time-dependent overall deformation behavior. Then, a nonlinear elastic-viscoplastic constitutive model was developed based on the parallel rheological framework (PRF) composed of an elastic-plastic network in parallel with multiple nonlinear viscoelastic networks. Finally, an approach was proposed to calibrate the constitutive model by means of relaxation-unloading tests and material parameter optimizations. The agreement between the prediction and the test data successfully demonstrated that the model could be used to precisely simulate the constitutive behavior of HDPE under static, quasi-static and dynamic cyclic loading. The developed constitutive model is beneficial to the long-term durability evaluation of HDPE. The methodology for exploring the deformation mechanism and calibrating the constitutive model may also be applicable to other polymers.

Fatigue life prediction is crucial to the long-term durability evaluation of high density polyethylene (HDPE) which may experience stress-controlled fatigue or strain-controlled fatigue depending on the external loading conditions. Although abundant studies have been carried out on stress-controlled fatigue, investigations on strain-controlled fatigue are insufficient, and the relationship between these two types of fatigues is unclear. In addition, approaches for strain-controlled fatigue life prediction of HDPE are scarce. The present paper aims at revealing the relationship between strain-controlled fatigue and stress-controlled fatigue and proposing a method for fatigue life prediction. Firstly, the stress-controlled fatigue tests were performed to study the influence of stress ratio on fatigue life, and the strain-controlled fatigue tests were successfully conducted thanks to the application of anti-buckling devices. Furthermore, our results showed that the stress level (i.e. stress amplitude and stress ratio) determined the fatigue life for both stress-controlled test and strain-controlled test. More importantly, a stress-based numerical model was established to predict the fatigue life under complicated loading conditions. The numerical model was built based on the constitutive relation for the computation of the stress response, the Walker method for the evaluation of the stress ratio influence, and the damage accumulation for the calculation of the fatigue life. The proposed numerical method was validated by comparing the predicted fatigue lives with the experimental data of the strain-controlled tests.

Stress-controlled uniaxial “push-pull” fatigue testing was conducted on as-received (cast and extruded) and closed-die cast-forged and extruded-forged AZ80 Mg alloy. The as-cast material possessed random texture and somewhat symmetric cyclic responses. The extruded and forged materials possessed sharp basal texture and asymmetric cyclic responses. All materials exhibited tension/compression asymmetry in their cyclic response to varying degrees, depending on the thermomechanical processing conditions. It was discovered that the style of closed-die forging being investigated had spatially varying properties with texture orientations which varied based on the local forging directions and intensities which were dependent on the starting texture as well as the thermomechanical history. Under fatigue testing, the materials all developed some form of mean strain, with the nature and magnitude of this mean strain being dependent on primarily its texture intensity and propensity to twin in either tension or compression reversals. The type of mean strain (tensile or compressive) depends upon both the orientation and intensity of the starting texture of material. The texture induced ratcheting and resulting mean strain evolution was most pronounced in the as-cast material and had a significant impact on the fatigue life. Following forging, the material exhibited an increase in fatigue life of anywhere from 2 to 15 times for the cast then forged material and more modest yet still significant 8 times longer at stress amplitudes around 140 MPa for the extruded then forged material. The extruded forged material exhibited similar fatigue lives to that of the base material at stress amplitudes which approached the yield strength. The nature of the mean stress development and degree of fatigue life improvement depended on the processing conditions and the type of base material (cast or extruded) utilized to create the forging. Two energy based models were utilized to predict the life of the forged material, and gave a reliable life prediction for a variety of material conditions that were investigated.

This study proposed a spatiotemporal algorithm to quantitatively characterize the in-situ 3D fracture behavior of carbon-fiber-reinforced polymer (CFRP) composites at microscale . In-situ micro X-ray computed tomography (µXCT) integrated with a tensile stage was applied to capture the 3D fracture evolution of the CFRP composites, where the initiation and propagation of fracture features (e.g., fiber tip-end crack and fiber/matrix debonding) were identified. After the reconstruction of the 3D material microstructure , the proposed spatiotemporal algorithm thereafter extracted the fracture features by employing multiple image processing techniques for quantitative analysis. A similar distribution of the 3D strain obtained from the volumetric digital image correlation demonstrated the feasibility of the developed spatiotemporal algorithm. Moreover, this algorithm provided in-depth and quantitative analysis of fracture features, which provided insights into the microscale failure mechanism and thus shed light on the improvement of failure criteria for CFRP composites with complex microstructures .

This study investigates the failure mechanisms of notched unidirectional (UD) carbon fiber reinforced polymer (CFRP) laminates subjected to longitudinal compressive loading . A sequence of failure initiation and propagation is observed based on optical microscopy images of specimens during failure. The micrographs reveal that the main failure mechanism in UD laminates is fiber kinking failure. The influence of manufacturing defects and voids on fiber kinking mechanisms is also analyzed. The results show that the voids in the resin-rich area lead to kink-band splitting, while in some cases the voids cause the kink-band to deflect in a new direction depending on the location of the voids. The next focus of this study is to propose a computational micromechanics model considering local fiber waviness to study the fiber kinking failure mechanism. The computational results on kink-band formation and stress-strain response show good consistency with our experimental analysis. Finally, the failure envelopes of σ11-σ22 and σ11-τ12 subjected to combined loading conditions are obtained from the computational model, which provide essential inputs for future theoretical failure criteria.

In the present study, the quasi-static and fatigue behavior of chopped glass fiber reinforced sheet molding compound composite was investigated. Considering the stochastic meso-structure induced by processing, fiber orientation within specimens was analyzed based on the sectional images obtained by X-ray Computerized Tomography (XCT). Quasi-static tensile and compressive tests were conducted, in which the strain distribution was recorded by Digital Image Correlation (DIC) system. The fatigue behavior of material was evaluated under tension–tension (R = 0.1) and tension–compression (R = -1) loading. Interrupted fatigue test was conducted to investigate the damage evolution on the side surface of specimen using optical microscopy. A modeling method based on Representative Volume Element (RVE) was modified and applied to predict the fatigue behavior of glass fiber SMC. The simulation result showed a good consistency with experimental results on both prediction of the fatigue life and the damage mechanisms under cyclic loading.

Woven fiber composites have been increasingly employed as light-weight materials in aerospace, construction, and transportation industries due to their superior properties. These materials possess a hierarchical structure that necessitates the use of multiscale simulations in their modeling. To account for the inherent uncertainty in materials, such simulations must be integrated with statistical uncertainty quantification (UQ) and propagation (UP) methods. However, limited advancement has been made in this regard due to the significant computational costs and complexities in modeling spatially correlated structural variations coupled at different scales. In this work, a non-intrusive approach is proposed for multiscale UQ and UP to address these limitations. We introduce the top-down sampling method that allows to model non-stationary and continuous (but not differentiable) spatial variations of uncertainty sources by creating nested random fields (RFs) where the hyperparameters of an ensemble of RFs is characterized by yet another RF. We employ multi-response Gaussian RFs in top-down sampling and leverage statistical techniques (such as metamodeling and dimensionality reduction) to address the considerable computational costs of multiscale simulations. We apply our approach to quantify the uncertainty in a cured woven composite due to spatial variations of yarn angle, fiber volume fraction, and fiber misalignment angle. Our results indicate that, even in linear analysis, the effect of uncertainty sources on the material’s response could be significant.

A multi-scale computational analysis based on representative volume element (RVE) modeling and molecular dynamics (MD) simulations is developed to investigate the microscopic failure mechanisms of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The average properties of the 200-nm thickness interphase region between fiber and matrix are characterized through MD simulations and an analytical gradient model. The results demonstrate that the interphase region has higher Young’s modulus and strength, compared to the bulk matrix. This stiffened interphase region influences the composite response significantly. Specifically, the traditional two-phase model with zero-thickness interface fails to capture the stress-strain behavior compared to the experimental data. However, by adding the interphase region to a modified RVE model, the accuracy of simulation results will be improved significantly. Furthermore, a coupled experimental-computational micromechanics approach is adopted to calibrate and validate the cohesive parameters of the interface. By including the cohesive interface, our modified RVE model accurately captures the failure strength of the composites. Finally, different failure mechanisms for specimens are investigated using our multi-scale computational framework. The results show that the failure modes of UD CFRP composites are very complex and multiple failure mechanisms co-exist depending on the loading conditions, agreeing well with our experimental analyses.

Predicting the mechanical behavior of the chopped carbon fiber Sheet Molding Compound (SMC) due to spatial variations in local material properties is critical for the structural performance analysis but is computationally challenging. Such spatial variations are induced by the material flow in the compression molding process. In this work, a new multiscale SMC modeling framework and the associated computational techniques are developed to provide accurate and efficient predictions of SMC mechanical performance. The proposed multiscale modeling framework contains three modules. First, a stochastic algorithm for 3D chip-packing reconstruction is developed to efficiently generate the SMC mesoscale Representative Volume Element (RVE) model for Finite Element Analysis (FEA). A new fiber orientation tensor recovery function is embedded in the reconstruction algorithm to match reconstructions with the target characteristics of fiber orientation distribution. Second, a metamodeling module is established to improve the computational efficiency by creating the surrogates of mesoscale analyses. Third, the macroscale behaviors are predicted by an efficient multiscale model, in which the spatially varying material properties are obtained based on the local fiber orientation tensors. Our approach is validated through experiments at both meso- and macro-scales, such as tensile tests assisted by Digital Image Correlation (DIC) and mesostructure imaging.

Mixed-mode fatigue crack growth behavior of an automotive adhesive bonding system (AA5754O- A951-BM4601) has been investigated using a compound compact mixed-mode specimen. The test was performed under load control with 0.1 R ratio and 3Hz frequency. A long-distance moving microscope was employed to record the real-time length of the fatigue crack in the adhesive layer during testing. The strain energy release rate components of the crack were analyzed by finite element method. The pure-mode fatigue crack growth test results show that a given value of G I results in a fatigue crack growth rate over an order of magnitude higher than for an equal value of G II. The mixed- mode tests results indicate that under a given loading angle, the fatigue crack growth behavior is also influenced by the test load due to the changing shear mode ratio when the crack grows. The fatigue crack growth data were then processed by a generalized Paris relation formula and employed in the direct fatigue life prediction of single lap shear joints with the same bonding system. The life prediction shows good results in the low-cycle region but slightly conservative results in the high- cycle region when compared to coupon fatigue tests.

With a better balance among good mechanical performance, high freedom of design, and low material and manufacturing cost, chopped carbon fiber chip reinforced sheet molding compound (SMC) composites show great potential in different engineering applications. In this paper, bending fatigue behaviors of SMC composites considering the heterogeneous fiber orientation distributions have been thoroughly investigated utilizing both experimental and computational methods. First, four-point bending fatigue tests are performed with designed SMC composites, and the local modulus is adopted as a metric to represent the local fiber orientation of two opposing sides. Interestingly, SMC composites with and without large discrepancy in local modulus of opposing sides show different fatigue behaviors. Interrupted tests are conducted to explore the bending fatigue failure mechanism, and the damage processes of valid specimens are also closely examined. We find that the fatigue failure of SMC composites under four-point bending is governed by crack propagation instead of crack initiation . Because of this, the heterogeneous local fiber orientations of both sides of the specimen influence fatigue life . The microstructure of the lower side shows a direct influence while that of the upper side also exhibiting influence which becomes more prominent for high cycle fatigue cases. Furthermore, a hybrid micro–macro computational model is proposed to efficiently study the cyclic bending behavior of SMC composites. The region of interest is reconstructed with a modified random sequential absorption algorithm to conserve all the microstructural details including the heterogeneous fiber orientation, while the rest of the regions are modeled as homogenized macro-scale continua. Combined with a framework to capture the progressive fatigue damage under cyclic bending, the bending fatigue behaviors of SMC composites are accurately captured by the hybrid computational model comparing with our experimental analysis.

The retrieval of the weld tool at the end of the friction stir welding process leaves behind a distinctive physical feature in the welded material which is commonly referred to as the exit-hole or the key-hole. Conventionally, the key-hole is left intact in the weldment due to the complexity involved in the design and manufacturing process, which then becomes an integral part of the weldment. To study the influence of the key-hole on fatigue life, rolled aluminum 6022-T4 sheet was friction stir linear welded to die-cast magnesium AM60 B sheet in lap-shear configuration. The lap-shear weld coupons with the key-hole were fatigue tested at different load levels at load ratio of R = 0.1. A significant reduction in fatigue life was observed as compared to friction stir linear welded lap-shear coupons without the key-hole. Two distinctive failure modes were observed; (a) at maximum fatigue loads at and above 1500 N, the welds failed due to interfacial failure through the weld nugget and, (b) at maximum fatigue loads below 1500 N, the welds failed due to kinked crack growth through the top aluminum sheet. Nevertheless, analysis of the fatigue results suggests that the key-hole had no role in initiating or propagating the fatigue crack. But the reduction in linear weld length due to the presence of the key-hole in the lap-shear test coupons combined with the existence of the brittle inter metallic compounds in the weld nugget contributed to lower fatigue life as compared to lap-shear welds produced without the key-hole. To further confirm the failure analysis in this study, fatigue predictions were made using a structural stress approach for the welds with and without the key-hole. The structural stress calculations show that the experimental fatigue results can be correlated to the reduction in weld length due to the key-hole.

Fatigue life prediction of advanced high strength steels (AHSS) spot welded joints is of great importance for autobody design with AHSS being increasingly used. In the present work, the fatigue failure behaviors of the DP780GI spot welded joints under the tensile shear (TS) and coach peel (CP) loading conditions are experimentally investigated and numerically modelled. Two failure modes, eyebrow failure and weld button pull out occur in the tests of TS joints, while only interfacial fracture exists in CP joints. A fatigue life prediction method based the crack growth approach is proposed. The TS/CP specimens are simplified to the neural line models, by which the reaction forces and moments directly acting on the spot welds are calculated. Then the stress intensity factor is obtained by using the finite element method and analytical equations fitted to the FE results. Finally, the fatigue life of a spot weld is evaluated by applying the Paris law to the crack front and including the plastic zone in crack path update. The calculated fatigue lives show good agreement with experiment results for DP780GI, within five times error band.

Fused filament fabrication (FFF) with continuous carbon fiber filaments has proven to be a promising manufacturing technique in engineering applications. To provide guidance in the design of 3D printed carbon fiber reinforced polymer (CFPR) components, the longitudinal compression failure of continuous CFPR composites using the FFF technique is investigated systematically. First, longitudinal compression tests are performed for 3D printed continuous CFRP composites with and without designed waved filaments. The degradation of the failure strength is remarkable when the waved filaments are introduced. Nevertheless, further degradation is limited when more waved filaments are adopted. Next, the fracture morphologies are analyzed, and in-plane and out-of-plane kink-bands are observed in the microscopic images. For the specimens with waved filaments, fracture occurs at the cross-section with the contact region of the waved and regular filaments, as well as the cross-section with the maximum misalignment angle. Correspondingly, a computational framework for 3D printed continuous CFPR composites is established to explore the longitudinal compression failure mechanisms. The meso-scale computational models are reconstructed according to the geometric features of the deposited continuous CFRP filaments and the actual void volume fraction. The elastic properties of the filament are calculated by a micro-scale representative volume element (RVE) model, which is based on the fiber random distribution algorithm. The plastic deformation and failure is described by a filament constitutive model which is established by the Liu-Huang-Stout yield criterion and a simplified Tsai-Wu failure criterion. The experimental validation demonstrates the feasibility of the computational models to predict the stress-strain curves of 3D printed materials, and also capture the realistic longitudinal compression failure behavior.

In this study, integrated experimental tests and computational modeling are proposed to investigate the failure mechanisms of open-hole cross-ply carbon fiber reinforced polymer (CFRP) laminated composites. In particular, we propose two effective methods, which include width-tapered double cantilever beam (WTDCB) and fixed-ratio mixed-mode end load split (FRMMELS) tests, to obtain the experimental data more reliably. We then calibrate the traction-separation laws of cohesive zone model (CZM) used among laminas of the composites by leveraging these two methods. The experimental results of fracture energy, i.e. GIc and GTc, obtained from WTDCB and FRMMELS tests are generally insensitive to the crack length thus requiring no effort to accurately measure the crack tip. Moreover, FRMMELS sample contains a fixed mixed-mode ratio of GIIc/GTc depending on the width taper ratio. Examining comparisons between experimental results of FRMMELS tests and failure surface of B–K failure criterion predicted from a curve fitting, good agreement between the predictions and experimental data has been found, indicating that FRMMELS tests are an effective method to determine mixed-mode fracture criterion. In addition, a coupled experimental-computational modeling of WTDCB, edge notched flexure, and FRMMELS tests are adopted to calibrate and validate the interfacial strengths. Finally, failure mechanisms of open-hole cross-ply CFRP laminates under flexural loading have been studied systematically using experimental and multi-scale computational analyses based on the developed CZM model. The initiation and propagation of delamination, the failure of laminated layers as well as load-displacement curves predicted from computational analyses are in good agreement with what we have observed experimentally.

In this work, multi-scale finite element analyses based on three-dimensional (3D) hybrid macro/micro-scale computational models subjected to various loading conditions are carried out to examine the in-situ effect imposed by the neighboring plies on the failure initiation and propagation of cross-ply laminates. A detailed comparative study on crack suppression mechanisms due to the effect of embedded laminar thickness and adjacent ply orientation is presented. Furthermore, we compare the results of in-situ transverse failure strain and strength between the computational models and analytical predictions. Good agreements are generally observed, indicating the constructed computational models are highly accurate to quantify the in-situ effect. Subsequently, empirical formulas for calculating the in-situ strengths as a function of embedded ply thickness and different ply angle between embedded and adjacent plies are developed, during which several material parameters are obtained using a reverse fitting method. Finally, a new set of failure criteria for σ(22)-τ(12), σ(22)-τ(23), and σ(11)-τ(12) accounting for the in-situ strengths are proposed to predict laminated composites failure under multi-axial stress states. This study demonstrates an effective and efficient computational technique towards the accurate prediction of the failure behaviors and strengths of cross-ply laminates by including the in-situ effects.

In current work, the crashworthiness of woven carbon fiber reinforced plastic (CFRP) hat section component is investigated under two types of loading experimentally and numerically, i.e., axial crushing and dynamic three-point bending. The crushing characteristics of woven CFRP hat section sample are evaluated at various impact velocities and layup orientations which exhibit different effects under two types of loading. With impact velocity/energy increasing, the bending behaviors illustrate different evolutions with distinct stages which are affected by the damage development. Layup orientation shows a little effect on the bending behaviors, while it exerts remarkable effects on the axial crushing which leads to different crushing modes and thus different energy absorption capabilities. The finite element model with multiple layers of thick shell element and cohesive element is shown to capture the crushing behaviors reasonably well in both axial crushing and dynamic bending. The corresponding damage evolutions are also analyzed with simulations to explain the crushing behaviors.

The fatigue behavior of self-piercing riveted (SPR) joints of aluminum alloy 6111-T4 has been experimentally and numerically investigated in current study. The dominant fatigue failure mode under tensile-shear (TS) loading is the corner crack at riveted hole with approximate quarter-elliptical crack front, and interrupted tests revealed that the crack growth life was much shorter than crack initiation life. A fatigue parameter, Smith-Watson-Topper (SWT) was proposed for crack initiation prediction in the 3D finite element analysis, while a structural load based crack growth approach was introduced for crack growth life estimation. Good agreement was found between predictions and experimental results.

In this work, we investigate the effect of sheet stacking orientation on fatigue behavior in friction stir linear welding of AZ31 Mg alloy. It is well known that during friction stir welding, the advancing and retreating flow of the material generated by the tool creates asymmetrical weld features resulting is anisotropic mechanical behavior. As such, friction stir welding of overlap joints was carried out on 2 mm thick sheets, where the orientation of the pull direction of the coupon was varied with respect to the tool rotation direction. Subsequently experimental fatigue tests were performed to evaluate this effect of the sheet stacking orientation on cyclic behavior. The fatigue results showed that the overlap joints loaded on the retreating side exhibited superior performance compared to the advancing side. Post-mortem analysis coupled with finite element results suggest that the geometrical shape of the faying surface produced by the advancing and retreating material flow largely determines the number of cycles to failure in these friction stir linear welded overlap joints.

Woven composites are considered as a promising material choice for lightweight applications. An improved non-orthogonal material model that can decouple the strong tension and weak shear behavior of the woven composite under large shear deformation is proposed for simulating the preforming of woven composites. The tension, shear and compression moduli in the model are calibrated using the tension, bias-extension and bending experiments, respectively. The interaction between the composite layers is characterized by a sliding test. The newly developed material model is implemented in the commercial finite element software LS-DYNA® and validated by a double dome study.

We present a data-driven nonlinear uncertainty quantification and propagation framework to study the microstructure-induced stochastic performance of unidirectional (UD) carbon fiber reinforced polymer (CFRP) composites. The proposed approach integrates (1) microscopic image characterization, (2) stochastic microstructure reconstruction, and (3) efficient multiscale finite element simulations enabled by self-consistent clustering (SCA) analysis. To model the complex microstructural variability, the proposed UQ methods take the non-Gaussian uncertainty sources into account through a distribution-free sampling approach leveraging nonparametric and asymptotic statistical tools. A hierarchical conditional sampling strategy enables the simultaneous sampling of multiple sources of uncertainties. Our approach provides insights into the impact of microstructural variabilities, which are shown to have an increasing impact on the nonlinear responses of UD CFRP parts under progressive compression loading and ultimately on the failure rate over time. We discover that before CFRP parts start to fail, a characteristic time period emerges with distinctive uncertainty distributions specific to the microstructure variability and the probability of failure. Identifying the failure time period is crucial to the reliability prediction, which is an essential component of CFRP design.

The mechanical behaviors and damage evolutions of carbon/epoxy woven fabric composites with three different geometries, i.e., one plain weave and two twill weave patterns with different areal densities, are studied under tensile loading. The effects of weave patterns on mechanical properties are investigated by monotonic and cyclic tension tests. Remarkable variations in stress–strain curve, Poisson’s ratio, residual strain and strain map exist in the three composites. Crimp ratio is found to be a critical factor to govern the mechanical properties. With smaller crimp ratio, a quasi-linear stress–strain curve with higher elastic modulus and strength is observed. The stress–strain curves of composites with higher crimp ratio contain transition stages with significant tangent modulus degradation. Elastic modulus, strength and damage initiation are all correlated with the crimp ratio linearly regardless of the fabric pattern. Dramatic nonlinear evolution in Poisson’s ratio occurs in the composite with higher crimp ratio. Cyclic tension results indicate that the residual strain is a more appropriate damage indicator than the unloading elastic modulus. Microstructure examination shows that damage developments are essentially related to the fabric geometry, and result in various mechanical behaviors. This study provides important insights into the geometry-deformation mechanism-mechanical property relationship of the woven composites.

A bottom-up multi-scale modeling approach is used to develop an Integrated Computational Materials Engineering (ICME) framework for carbon fiber reinforced polymer (CFRP) composites, which has the potential to reduce development to deployment lead time for structural applications in lightweight vehicles. In this work, we develop and integrate computational models comprising of four size scales to fully describe and characterize three types of CFRP composites. In detail, the properties of the interphase region are determined by an analytical gradient model and molecular dynamics analysis at the nano-scale, which is then incorporated into micro-scale unidirectional (UD) representative volume element (RVE) models to characterize the failure strengths and envelopes of UD CFRP composites. Then, the results are leveraged to propose an elasto-plastic-damage constitutive law for UD composites to study the fiber tows of woven composites as well as the chips of sheet molding compound (SMC) composites. Subsequently, the failure mechanisms and failure strengths of woven and SMC composites are predicted by the meso-scale RVE models. Finally, building upon the models and results from lower scales, we show that a homogenized macro-scale model can capture the mechanical performance of a hat-section-shaped part under four-point bending. Along with the model integration, we will also demonstrate that the computational results are in good agreement with experiments conducted at different scales. The present study illustrates the potential and significance of integrated multi-scale computational modeling tools that can virtually evaluate the performance of CFRP composites and provide design guidance for CFRP composites used in structural applications.

Fatigue behaviors of hybrid joint, the combination of cold-formed mechanical fastening with adhesive bonding, are yet to be understood comprehensively even though they have been widely used in industries. The lack of understanding is mainly attributed to the complicated load transfer path and possible interactions between the two types of joining techniques, namely mechanical interlocking and adhesive bonding. In the present work, fatigue tests are performed on self-piercing riveted (SPR) joint, adhesive-bonded joint, and the SPR-bonded joint under lap shear and 45° loading conditions. Failure mechanisms are evaluated based on terminated fatigue test and numerical analysis. Periodical and asymmetric failure mode can be identified in SPR-bonded joint. Although both crack pinning and asymmetric failure mode induced by SPR suppress the crack growth in adhesive bonding, the effect of crack pinning is significant only when crack approaches SPR. The asymmetric failure also leads to load transfer path evolution, intensifying damage on SPR joining. A mechanism-based fatigue life evaluation method is proposed by characterizing the interactions with crack growth method and structural stress method. The calculated results are compared with the experimental ones, and good correlations are observed for both lap shear and 45° loading conditions.

Chopped carbon fiber sheet molding compound has a great potential in lightweight automotive, marine, and aerospace applications. One of the most challenging tasks is to predict the failure strength of the material due to its anisotropy and heterogeneity, as well as complex stress states in real-world working conditions. In this paper, a novel constitutive model of carbon fiber chip is proposed to capture the pre- and post-failure behaviors under different loading modes. On this basis, we propose a new computational micromechanics model, which is calibrated and validated by uniaxial tensile, compressive, and in-plane shear experiments. Furthermore, a set of microstructures representative volume element (RVE) models under complex loading conditions are reconstructed to understand the relationship between the microstructure characteristics and the failure envelopes. Finally, several modified versions of classical failure criteria are proposed for anisotropic materials with consideration of the fiber orientation tensor. The modified Tsai-Wu failure criterion, which shows the best accuracy among all failure criteria, is highlighted in the comparative study.

The mechanical properties and damage evolutions of carbon/epoxy woven fabric composites with three different fabric architectures, including one plain weave and two twill weave patterns, are experimentally investigated under multiaxial stress states. In particular, the effects of weave patterns are investigated by monotonic and cyclic off-axis tension tests. Both elastic modulus and strength degrade remarkably with increasing off-axis loading angle, while Poisson's ratio is much higher than that measured from on-axis tests and increases with loading strain gradually. Different fabric architectures show limited effects on the modulus and strength under multiaxial stress states, and they are well predicted by transformation equation and Tsai-Wu failure criteria, respectively. However, significantly different failure behaviors are observed in three fabric composites, and microstructure observation shows that fabric architecture affects the stress concentration and the damage development. Smaller crimp ratio and compacted structure postpone the damage development but result in more abrupt failure under multiaxial stress states.

The fatigue behavior of self-piercing riveted joints of aluminum alloy AA6111-T4 and steel HSLA340 sheets has been experimentally and numerically investigated in present paper. Fatigue results reveal that the mating sheet stiffness and load ratio have significant impact on the fatigue strength, and the dominant failure mode under tensile–shear loading is eyebrow crack with an approximately semi-elliptical crack front. New stress intensity factor equations are derived for a semi-elliptical surface crack in a finite plate near a rigid cylindrical inclusion with axial shear force and bending moment, including the ratio of crack depth to crack length ranged from 0.2 to 1 and the ratio of crack depth to sheet thickness ranged from 0.2 to 0.8. A new structural load fatigue crack growth model is proposed, and predictions of fatigue lives and final crack aspect ratios show good agreement with experimental results.

The fatigue behavior of self-piercing rivet (SPR) joints joining differing thicknesses of AA6111-T4 aluminum and HSLA340 steel sheets in lap shear geometry was investigated in this paper. Crack initiation in the aluminum sheet was the dominant failure mode, while unexpected rivet shank failure tended to occur at high loading levels. Fretting wear was also observed at interface between aluminum and steel sheets as well as between the rivet and sheets under sinusoidal cyclic tension–tension loading. An Energy Dispersive X-ray (EDX) analysis of fretting debris revealed the presence of oxides of aluminum and zinc. Fretting was shown to be critical to crack initiation. For initiations in the aluminum sheet, micro cracks were found to nucleate early in the fatigue life, and crack initiation life was found to be much shorter than crack growth life.

A comprehensive study of fatigue life and damage mechanisms of friction stir linear welded dissimilar aluminum-to-magnesium alloys in lap-shear configuration is presented. The overlap linear welds were created by welding AA6022 aluminum alloy to AM60B magnesium alloy. The test results showed significant scatter in the fatigue life and the corresponding fracture modes. Two distinct modes of failure were observed for the lap-shear specimens. In one of the failure modes observed, fracture occurred when the dominant fatigue crack propagated into either the magnesium or aluminum sheet in a kink-crack formation. In addition, fretting debris was found at locations of crack initiation for this fracture mode. In the other observed mode of failure, fracture occurred by interfacial weld separation, where fractography analysis suggests that the fatigue cracks initiated at weld defects and then propagated through the brittle intermetallic phase formed during welding.

In this paper, the feedback signal of ultrasonic fatigue system was used to in situ deduce the accumulated fatigue damage via ultrasonic nonlinearity parameter. It was observed that compared with the resonant frequency, the ultrasonic nonlinearity parameter shows a greater sensitivity to fatigue damage like crack initiation and crack propagation. Conventional fatigue testing was carried out and the variation of specimen rigidity and plastic strain of the material were obtained which correlated well with the ultrasonic nonlinearity parameter. Also, the ultrasonic fatigue crack initiation was verified by interrupted test.

This study focuses on the notch effect on the fatigue failure of chopped carbon fiber chip-reinforced sheet molding compound (SMC) composites by using both experimental and numerical methods. The S-N diagrams of notched specimens are first obtained experimentally, which exhibit large scatter and are shown to depend on the spatial distribution of local fiber orientations. After considering the effect of this spatial distribution by adopting a new fatigue damage parameter to normalize the results, we achieve a much better correlation in the normalized S-N diagram for all the notched specimens with different hole diameters. Next, compared with the fatigue results of smooth specimens without notches, we find that SMC composites under tension-tension fatigue loading exhibit notch-insensitivity, which renders this type of composites a better candidate in joints or similar applications. Meanwhile, the fatigue failure mechanisms of notched SMC composites are explored through a microstructure characterization procedure. On this basis, a computational micromechanics model considering the notch effect and an improved multi-scale progressive damage fatigue law, calibrated by coupon-level fatigue tests of smooth SMC composites under different loading conditions, are employed to predict the fatigue behavior of notched SMC composites. We show that detailed failure processes and fatigue life of notched SMC composites can be efficiently and adequately predicted by this computational framework.

The dynamic crushing characteristics of unidirectional carbon fiber reinforced plastic composites under two loading types, dynamic three-point bending and axial crushing, are investigated by experiment and finite element simulation. Hat section samples with two different layup orientations are tested at various impact velocities to investigate its effects. The experiment results show that delamination plays a critical role in dynamic bending deformation. Different layup orientations lead to similar crushing bending behaviors, but remarkable variations in delamination pattern evolutions. In contrast, layup orientation exerts more significant effects on failure modes and energy absorption in axial crushing. A finite element model with multiple layers of thick shell element and cohesive element is established, and simulations are performed for both dynamic three-point bending and axial crushing. The model can capture the crushing behaviors in the two loading types reasonably well. The damage evolution and energy absorption through various mechanisms at different loading conditions are discussed.

This paper addresses the challenge of reconstructing nonuniformly orientated fiber-reinforced polymer composites (FRPs) with three-dimensional (3D) geometric complexity, especially for fibers with curvatures, and proposes a framework using micro X-ray computed tomography (μXCT) images to quantify the fiber characteristics in 3D space for elastic modulus prediction. The FRP microstructure is first obtained from the μXCT images. Then, the fiber centerlines are efficiently extracted with the proposed fiber reconstruction algorithm, i.e., iterative template matching, and the 3D coordinates of the fiber centerlines are adopted for quantitative characterization of the fiber morphology. Finally, Young's modulus is predicted using the Halpin-Tsai model and laminate analogy approach, and the fiber configuration averaging method with the consideration of the fiber morphology. The new framework is demonstrated on both injection-molded short and long carbon fiber-reinforced polymer composites, whose fiber morphology and predicted mechanical properties are validated through previous pyrolysis and quasi-static tensile tests, respectively.

This paper presents a predictive multiscale modeling scheme for Unidirectional (UD) Carbon Fiber Reinforced Polymers (CFRP). A bottom-up modeling procedure is discussed for predicting the performance of UD structures. UD material responses are computed from high fidelity Representative Volume Elements (RVEs). A data-driven Reduced Order Modeling approach compresses RVEs into Reduced Order Models so material responses can be computed in a concurrent fashion along with the structural level simulation. The approach presented in this paper is validated against experimental data and is believed to provide design guidance for future fiber reinforced polymers development.

The fiber orientation distribution is one of the important microstructure variables for thermoplastic composites reinforced with discontinuous fibers. In this paper, the long fibers in the injection molded part are measured in detail by micro X-ray CT. A three dimensional (3D) structure of the sample is built and two dimensional images are generated for image analysis. The orientation tensor of fibers is calculated in the flow plane. It shows a symmetric distribution of fibers through the thickness direction, which consists of outer skin, transition zone and the core. The skin layer is so thin that it has only one layer of highly oriented fibers. The core layer also has highly oriented fibers but the direction of fibers is different from that in the skin layer. Nevertheless, the clustering of the fibers is characterized quantitatively in the core. The transition zone can be divided into two subzones by the principal directions of the tensor.

In this paper, thermomechanical fatigue life (TMF) prediction is performed on an automotive exhaust manifold using in-house postprocessor code (Hotlife) with four different constitutive models: elastoplastic model with kinematic hardening, two-layer viscoplastic model, and two unified elasto-viscoplastic models based on the equations proposed by Sehitoglu and Chaboche, respectively. Commercial FEA software Abaqus has been used for the analysis. The first two models are already available in Abaqus; the Chaboche and Sehitoglu models were implemented using a user material subroutine (UMAT, available in Abaqus). The stress and strain histories calculated by these four models are output to Hotlife for post-processing. The results from the prediction are then compared to the experimental TMF life obtained from a component thermal fatigue bench test. Result show the Hotlife calculations based on the two implemented elasto-viscoplastic models yield better correlation with test results.

A numerical model of fatigue crack propagation based on the Theory of Critical Distances has been developed in a previous paper (Zheng et al., 2013 [1]). The present study aims to investigate the capability of the crack propagation model to predict the effects of overloads and underloads. The plastic energy density at the critical distance ahead of crack tip is affected by the changes in the plasticity-induced crack closure levels and has been used as a measure of the fatigue damage. It is concluded that the predicted crack retardation and acceleration after the overload and underload, respectively, are in satisfactory agreement with the experimental observations.

In most current works related to the structure analysis of cured woven composites, the influence of yarn angle variation on the local material properties is neglected. In this paper, its influence was studied, and an integrated preforming-performance simulation model, accounting for the influence of yarn angle variation, was proposed. The multi-scale modeling approach was adopted to predict the material properties of cured woven composites with different yarn angles. The results were compared with experiments to validate its effectiveness. In the integrated preforming-performance simulation model, non-orthogonal constitutive law was used in the preforming simulation to compute yarn orientations and yarn angle distribution. To demonstrate the capabilities of the integrated simulation model, simulations were conducted and compared with experiments. The results show that the proposed simulation model has more accurate prediction than the simulation model without considering the influence of yarn angle, and the impact of yarn angle shouldn’t be neglected.