Meso-scale Representative Volume Element Research Articles

Multiscale image-based modeling for failure prediction of sheet molding compound composite under uniaxial tension

Carbon fiber reinforced polymer (CFRP) composites are extensively utilized as primary load-bearing components in various engineering applications due to their superior strength-to-weight ratio and excellent mechanical properties. However, their intricate microstructural interactions within composite present a significant challenge for failure analysis of CFRP. Although finite element (FE) simulations have been proven feasible to conduct the failure analysis, the classical FE models are developed based on homogeneous fiber characteristics, ignoring the influence of internal structures on the damage evolution process. This paper presents a multiscale image-based modeling approach to predict the tensile failure procedure of chopped carbon fiber sheet molding compound (SMC) composite. To accurately reconstruct the representative volume element (RVE) model of the SMC composite, synchrotron micro-X-ray computed tomography (μXCT) was adapted to explore the SMC internal microstructure. Then microscale RVE models with different fiber volume fractions were constructed to predict the corresponding microcosmic mechanical properties, which were used as the inputs for mesoscale RVE models to determine the constitutive parameters of fiber chips having varied fiber volume and orientations. Finally, the YOLOv5_Seg algorithm was employed to extract the geometric feature parameters of the fiber chips for mesoscale RVE modeling and then the failure location and sequence under uniaxial tension were predicted. It is found that the final simulated failure behaviors were consistent with the experimental observations, confirming the feasibility of this approach for understanding the failure mechanisms of CFRP composites. Thus, once the internal microstructure is determined using experimental techniques or predicted by simulating the composite manufacturing process, this approach can also be utilized for design optimization and performance evaluation for CFRP composites.

Fabrication and multiscale heat transfer modeling of high thermal conductivity Cf/HfB2-SiC composites

With the increasing Mach numbers of hypersonic vehicles, extreme aerothermal environments impose substantial challenges on vehicle materials. High thermal conductivity materials facilitate rapid heat redistribution to diminish localized thermal accumulation and reduce material thermal damage, providing a viable route for further enhancing the operational temperature of materials. Here, we successfully fabricate high thermal conductivity Cf/HfB2-SiC composites through the solid–liquid combination process, achieving an x-direction thermal conductivity of 161.11 W/(m·K), which represents an order of magnitude improvement over traditional carbon fiber-reinforced ultra-high temperature ceramic composites. 3D X-ray computed tomography (CT) is employed to analyze the structural composition of the high thermal conductivity Cf/HfB2-SiC composites, and the Gaussian Mixture Model is applied to segment the CT images, thus establishing a mesoscale representative volume element (RVE) model based on CT. Combining theoretical models and finite element analysis, we propose a multiscale heat transfer model for high thermal conductivity Cf/HfB2-SiC composites, which effectively investigates the heat transfer mechanisms of the composites. The fabrication and multiscale heat transfer modeling of high thermal conductivity Cf/HfB2-SiC composites provide a theoretical basis and guidance for enhancing material performance and design optimization.

Unveiling the mechanisms behind texture formation and its impact on the torsional performance of cold-drawn pearlitic steel wires

High carbon pearlitic steel wires are widely used in the industry, such as for producing tyre cords and steel cables due to its excellent mechanical properties. Cold drawing is a crucial step in steel wire production. Due to the loading state during the cold drawing process, pearlitic wires tend to exhibit a <110> fiber texture. The non-uniform texture distribution on the cross-section of steel wires has been observed experimentally. The mechanisms yielding this non-uniformly distributed texture are carefully investigated in this study using a multi-scale computational approach. Firstly, a macroscale finite element model is established to simulate the deformation behaviour of pearlitic steel wires during cold drawing, with the aim of thoroughly investigating the inhomogeneous elastic-plastic deformation behaviours. Secondly, the macro mechanical responses are incorporated into the mesoscale representative volume element model as boundary conditions to comprehensively study the effect of inhomogeneous deformation characteristics on texture formation. The results present a significant advancement by revealing that the non-uniform texture distribution in a steel wire can primarily be attributed to the multiaxial stress state on the cross-section. Notably, at the center of the steel wire, the maximum principal stress aligns with the drawing axis, resulting in a dominant <110> fiber texture. Conversely, at the subsurface, the maximum principal stress progressively shifts towards the circumferential direction, yielding an evolving texture characterized by a {110}<110> circumferential texture. Furthermore, the research uncovers a crucial finding that it is the {110}<110> circumferential texture that significantly weakens the torsion ability of the wires. This is due to the limited activation of slip systems, marking a key advancement in understanding the mechanical properties of steel wires.

A scale-span method to characterize the mechanical property of BCF/PEEK considering uncertain structural characteristics

The focus of this study is exploring a scale-span characterization method to predict the mechanical properties of Braided Carbon Fiber Reinforced Poly Ether Ether Ketone (BCF/PEEK) considering structural uncertainty. Firstly, a complicated micro-scale Representative Volume Element (RVE) model that considers the random position and size of fiber was established via the developed Python script. Analogously, a mathematical expression adopted by the trust region algorithm was proposed to accurately describe the detailed cross-sectional shapes and fluctuation amplitude characteristics of BCF/PEEK for the sake of establishing the precision meso-scale RVE model. Then, the corresponding elastic properties that consider fiber volume fraction and fiber distribution location were characterized via the span-scale characterization method. Meanwhile, the influence of fiber bundle fluctuation amplitude and fiber volume fraction on the mechanical properties was investigated as well. In addition, the mechanical properties of BCF/PEEK with the change of the braid angle between warp and weft yarn were predicted via the established meso-scale RVE model. Finally, a series of experiments have been carried out. The maximum and minimum absolute prediction deviation of all elastic property parameters were only 4.07 % and 1.41 %, respectively, which verified the proposed scale-span characterization method can predict the mechanical properties of composites well.

A material-structure coupled design method to study the impact response of CFRP apron board for railway vehicle

It is of great significance to improve the design efficiency and guide material selection for carbon fiber reinforced polymer (CFRP) vehicle structures, thereby, contributing to lightweight high-speed trains. This study proposes a material-structure integrated design approach that bridges the computational relationship between design variables across multiple scales and the impact responses of CFRP vehicle structures. Computational models are constructed at the micro-scale, meso-scale, and macro-scale to capture the multi-scale characteristics of the CFRP structures. At micro-scale, finite element simulations are used to determine the effective properties of fiber bundles using a representative volume element (RVE) model. This information is then transferred to the meso-scale RVE model to calculate the homogenized mechanical properties of the lamina. Finally, a macro-scale model is established to investigate the damage mechanisms and impact resistance of the CFRP apron board against the projectile impact. The influences of design variables, such as fiber type and volume fraction, are analyzed to provide further insights into the design of CFRP apron boards.

Multiscale damage and low-velocity impact study of three-dimensional woven composites

Three-dimensional woven composites address the limitation of weak interlaminar strength found in traditional laminated composites and offer superior resistance to out-of-plane impact. However, the complex material composition and structural intricacies necessitate investigation into their damage mechanisms. This study introduces novel and reliable microscale and mesoscale Representative Volume Element (RVE) models for three-dimensional woven composites, developed through advanced CT scanning and comprehensive multi-directional tensile and shear experiments. The research explores the impact of fiber volume fraction on yarn mechanical properties using the microscale RVE model, yielding precise macroscale homogenization parameters through the mesoscale RVE model. Furthermore, a macro-meso model tailored for low-velocity impact scenarios is established, significantly enhancing computational efficiency without compromising accuracy, thus providing support for further research on the impact properties of three-dimensional woven composites.

A novel multiscale prediction strategy for simulating the progressive damage behavior of plain-woven bamboo fabrics reinforced epoxy resin composites

This study proposed a novel multiscale prediction strategy, including mesoscale and macroscale damage evolution modeling, to investigate the effective properties and progressive damage failure behavior of plain-woven reinforced composites (PWRCs) under various external loads (tension, compression). A high-precision mesoscale representative volume element (RVE) that could accurately describe the local mechanical behavior of PWRCs was developed by combining experimental characterization (scanning electron microscope and X-ray computed tomography) and numerical simulation. To solve the problem of inaccurate prediction results caused by multiscale characteristics and complex stress changes in the damaged area of PWRCs, the strain-based 3D Hashin failure criterion and the multiscale damage models were used to predict the damage initiation and evolution of mesoscale reinforcement (bamboo fiber yarn bundle) and macroscale composites, respectively. Considering the damage evolution law of isotropic materials, a damage model based on the Von Mises criterion was used to characterize the damage initiation and evolution of mesoscale matrix epoxy resin (EP) under external loading. The effective properties and mechanical behavior of the PWRCs were transferred from mesoscale to macroscale through the progressive homogenization method. The bilinear constitutive relationship of the mixed-mode cohesive element was used to characterize the interlaminar failure of the PWRCs. Finally, the corresponding mechanical characterization (tension, compression) of the PWRCs was carried out. Moreover, the experimental results were highly consistent with the simulation results, verifying the reliability of the novel multiscale prediction strategy in investigating the mechanical response of the PWRCs at multiple scales and revealing the damage mechanism of the PWRCs.

A mesoscale computational approach to predict ABD matrix of thin woven composites

The ABD matrix is a fundamental method to characterize the overall stiffness behavior of laminated composite structures. Although classical laminate theory has been widely used, it has limitations in predicting the ABD matrix for woven composites. To address this issue, this paper presents a mesoscale homogenization approach aimed at computing the ABD matrix for thin woven composites accurately. The mesoscale representative volume element (RVE) of the woven composite is generated using TexGen and imposed with periodic boundary conditions to enforce the Kirchhoff thin plate assumption. The ABD matrix is computed by conducting six separate finite element simulations, each representing one simple in-plane or out-of-plane deformation in a specified direction. Moreover, to facilitate the implementation of the method, an open-source plugin tool was developed within ABAQUS CAE, automating the ABD matrix calculation for various types of woven composites including 2D weave, 3D weave, and multiaxial. The accuracy of the proposed method was validated through benchmark calculations against existing literature results.

Effect of void defects on mechanical behavior and failure features of C/C honeycomb structure

The combination of honeycomb structure and carbon/carbon (C/C) composites offers unique high load-bearing and light-weight advantages in satellite-bearing platforms. However, the defects generated by the imperfect preparation process are inevitable. This paper employs the chemical vapor infiltration (CVI) technique to fabricate novel C/C honeycomb structures and considers the presence of internal void defects. Based on micro-computerized tomography (μ-CT) images, the void distribution and porosity as well as the micro-structure characteristics are acquired. Meso-scale representative volume element (RVE) models is established to predict the performance of honeycomb wall material. A secondary development of ABAQUS is performed to establish a model of honeycomb structure containing void defects. Multi-scale models are developed for investigating the mechanical performance of the C/C honeycomb structure. Experimental methods and finite element simulations are utilized to examine the effects of porosity and different weave structures on the compression and shear properties, as well as damage modes of C/C honeycomb structures in detail. The results demonstrate that the presence of low porosity ρ = 1 % severely diminishes the load-bearing capacity of the honeycomb and affects its damage pattern. Twill-2 weave C/C honeycomb inherits the advanced performance of the composites and exhibits superior comprehensive properties compared to plain weave and twill-1 weave honeycomb structures.

Mechanical Characterization of Multifunctional Metal-Coated Polymer Lattice Structures.

Metal-coated lattice structures hold significant promise for customizing mechanical properties in diverse industrial applications, including the mechanical arms of unmanned aerial vehicles. However, their intricate geometries pose computational challenges, resulting in time-intensive and costly numerical evaluations. This study introduces a parameterization-based multiscale method to analyze body-centered cubic lattice structures with metal coatings. We establish the validity and precision of our proposed method with a comparative analysis of numerical results at the Representative Volume Element (RVE) scale and experimental findings, specifically addressing both elastic tensile and bending stiffness. Furthermore, we showcase the method's accuracy in interpreting the bending stiffness of coated lattice structures using a homogenized material-based solid model, underscoring its effectiveness in predicting the elastic properties of such structures. In exploring the mechanical characterization of coated lattice structures, we unveil positive correlations between elastic tensile stiffness and both coating thickness and strut diameter. Additionally, the metal coating significantly enhances the structural elastic bending stiffness multiple times over. The diverse failure patterns observed in coated lattices under tensile and bending loads primarily stem from varied loading-induced stress states rather than external factors. This work not only mitigates computational challenges but also successfully bridges the gap between mesoscale RVE mechanical properties and those at the global structural scale.

Prediction and adjustment of elastic properties in three‐dimensional orthogonal woven composites through dual‐scale modeling

AbstractThree‐dimensional (3D) orthogonal woven composites can overcome the drawback of weak interlaminar strengths in traditional laminated composites and exhibit excellent resistance to out‐of‐plane impact, however, the significant difference in properties in the in‐plane orthogonal direction will limit the potential range of application thereof. Predicting elastic properties and exploring methods of adjustment are therefore of paramount importance. Using computed tomography (CT) scanning to obtain detailed parameter models, a corresponding dual‐scale model of microscopic representative volume element (RVE) and mesoscopic RVE was established, and the accuracy of the model was experimentally validated, which can predict the elastic properties of materials. In addition, the influences of the yarn fiber volume fraction and weaving distance on elastic properties were evaluated using the elastic modulus visualization method, and a formula integrating these two factors is provided for adjustment of the in‐plane orthogonal Young's modulus.Highlights Experimentally validated microscale and mesoscale RVE models were established. The influences of factors on elastic properties were visualized. The relationship between Young's modulus and influencing factors was derived. A reliable strategy for adjusting the in‐plane Young's modulus was proposed.

Mesoscale analysis of aging mechanical behaviors of 3D woven composites

3D orthogonal woven composites (3DOWCs) are inevitably subjected to the severe cyclic hygrothermal aging environment in the application of supersonic aircraft structures and their durability should be proven. However, most current works relating to the hygrothermal aging of 3DOWCs rely on the experimental methods which are of high cost. To address this issue, a matrix-yarn mesoscale model of 3DOWCs was established to investigate the cyclic hygrothermal aging mechanical behaviors in this paper. High-fidelity mesoscale representative volume element (RVE) was constructed with realistic geometric configuration of the reinforcement. Only the aging properties of pure resin were needed in the mesoscale model. The aging properties of fiber yarns were calculated with Chamis formulas accounting for resin aging. Tension-compression asymmetry behavior of resin matrix was accounted in the constitutive model. The damage initiation and propagation of resin matrix, yarn and cohesive interface were modeled by the progressive 3D damage model. The mechanical properties of 3DOWCs before and after aging were predicted by the mesoscale model and validated with experiment. This work can provide effective tool for the design of 3DOWCs applied in harsh environments.

Experimental and numerical investigation on tension–tension fatigue behavior of three-dimensional five-directional hybrid braided composites

This paper presents an experimental and numerical investigation on tension–tension fatigue behavior of hybrid carbon/glass three-dimensional five-directional (3D5D) braided composites. Fatigue tests were carried out under the stress ratio of 0.1. The experimental results show that the fatigue strength significantly decreases as the fatigue life increases and the stiffness gradually decreases as the loading cycles increase. The fatigue life at the stress level within 35 %–50 % ultimate tensile strength (UTS) is within 4 × 103–6 × 105 cycles. The stiffness degradation before failure increases from 39 % to 58 % as the fatigue stress decreases from 50 % UTS to 35 % UTS. Under tension–tension fatigue loading, matrix cracking inside the yarns and interfacial debonding between the yarns and the matrix firstly occur and propagate, then matrix cracking appears in the resin-rich regions and numerous fiber breakage happens until final failure. The fatigue performance and damage mechanisms of braided composites are affected by fiber hybrid mode and braiding methods. Additionally, a mesoscale representative volume element (RVE) model with periodic boundary conditions and a progressive fatigue damage model was developed for the 3D5D hybrid braided composites. The numerical simulation results of fatigue life, stiffness degradation and damage progression have good agreement with experiments, demonstrating the validity of the developed model.

Research into the thermal expansion behavior of spread tow woven pierced carbon/carbon composites at high temperature

Textile-reinforced carbon/carbon composites are frequently used for thermal safety due to their superb thermophysical properties. The coefficient of thermal expansion (CTE) is a fundamental performance metric of spread tow woven pierced carbon/carbon composites (STWPs). The multiscale representative volume element (RVE) models constructed as part of this work were used for investigating the CTEs of STWPs at high temperature. The temperature displacement coupling analysis step was established to predict the CTEs of STWPs considering the high-temperature environment. In addition, periodic displacement boundary conditions were adopted as node constraints with the spatial periodicity of RVE models. The influences of pore positions and configurations on the CTEs of the matrix were considered through two different matrix RVE model. The CTEs of the spread tow (ST) and fiber rod were computed using two microscale RVE models with an unequal fiber volume fraction. A novel modeling strategy for the mesoscale RVE model was put forth in order to calculate the CTEs of the STWPs due to the remarkable lightness and thinness of the ST. Only 9.64% and 7.92% errors in the in-plane and out-of-plane directions were found when the experimental findings were compared to those predicted by numerical models, demonstrating the accuracy and effectiveness of the multiscale RVE models. Moreover, the impacts of areal density of ST woven fabric on the CTEs of STWPs were discussed. The fundings demonstrated that the in-plane and out-of-plane CTEs both decreased as the areal density increased.

Statistical field theory for nonlinear elasticity of polymer networks with excluded volume interactions.

Polymer networks formed by cross linking flexible polymer chains are ubiquitous in many natural and synthetic soft-matter systems. Current micromechanics models generally do not account for excluded volume interactions except, for instance, through imposing a phenomenological incompressibility constraint at the continuum scale. This work aims to examine the role of excluded volume interactions on the mechanical response. The approach is based on the framework of the self-consistent statistical field theory of polymers, which provides an efficient mesoscale approach that enables the accounting of excluded volume effects without the expense of large-scale molecular modeling. A mesoscale representative volume element is populated with multiple interacting chains, and the macroscale nonlinear elastic deformation is imposed by mapping the end-to-end vectors of the chains by this deformation. In the absence of excluded volume interactions, it recovers the closed-form results of the classical theory of rubber elasticity. With excluded volume interactions, the model is solved numerically in three dimensions using a finite element method to obtain the energy, stresses, and linearized moduli under imposed macroscale deformation. Highlights of the numerical study include: (i) the linearized Poisson's ratio is very close to the incompressible limit without a phenomenological imposition of incompressibility; (ii) despite the harmonic Gaussian chain as a starting point, there is an emergent strain-softening and strain-stiffening response that is characteristic of real polymer networks, driven by the interplay between the entropy and the excluded volume interactions; and (iii) the emergence of a deformation-sensitive localization instability at large excluded volumes.

Study on impact resistance and parameter optimization of patch‐repaired plain woven composite based on multi‐scale analysis

AbstractPatch‐repaired plain woven composite structures were exposed to internal damage caused by impact during service, which reduced mechanical properties. A multi‐scale modeling strategy was proposed to study the impact resistance characteristics of patch‐repaired plain woven carbon‐fiber‐reinforced‐polymer (CFRP) laminates. The micro representative volume element (RVE) was extracted from the yarn; a local homogenization method was used to obtain the equivalent cross‐ply laminate (ECPL) cells corresponding to the mesoscale RVE. The finite element model (FEM) of patch‐repaired plain woven laminate was established by extending the ECPL cells. The FEM was checked by the low‐velocity impact (LVI) tests, and the impact parameter errors were within 10%. Furthermore, impact resistance of repaired specimens under different impact conditions (e.g., the impact energy was 3 ~ 20 J) was studied. Finally, patch parameters (patch thickness, patch size, off‐axis angle) of the repaired specimen were optimized by multi‐objective optimization based on the surrogate model and response surface method (RSM). After multi‐objective function optimization, the optimal patch parameter configuration (the thickness of the patch was 0.87 mm, the diameter was 66 mm, and the off‐axis angle was 44.2°) reduced the absorbed energy value of the repaired specimen from 4.9089 to 4.1640 J, and the delamination area of the repaired specimen from 605 to 280 mm2. All the results provide a reference for patch repair of plain woven composites.

Multiscale Finite-Element Analysis of Damage Behavior of Curved Ramp Bridge Deck Pavement Considering Tire–Bridge Interaction Effect

The present study developed a three-dimensional (3D) multiscale modeling approach to investigate the mesoscale damage behavior of curved ramp bridge deck pavement subjected to tire loading. First, a full-scale tire–bridge interaction finite element (FE) model was established to solve the macroscopic response of deck pavement during vehicle turning. Subsequently, the 3D mesostructure of the asphalt concrete layer was reconstructed from X-ray computer tomography (CT) images through a digital image processing (DIP) technology. Finally, a homogenization method was adopted to link the mechanical properties of deck pavement at two different scales, and a mapping procedure was employed to transfer the boundary displacements from macroscale pavement target element to the mesoscale representative volume element (RVE) model. Also, the bilinear cohesive elements were applied to simulate damage initiation in the RVEs. The results showed that smaller curvature radius and higher travel speed can promote unbalanced stress and local damage of the outer loading zone. From the mesoscale viewpoint, reducing curvature radius or increasing travel speed could result in crack direction shifts and increase the irregularity of microcrack distribution. In addition, transverse microcracks are commonly found in the center of the tire load, while longitudinal microcracks are distributed on the deck pavement surface around the tire edges and the dual-tire clearance center.

A dynamic FEM-DEM multiscale modeling approach for concrete structures

The dynamic behavior of concrete is strain-rate-dependent, which affects the failure modes of structures. In this study, a multiscale modeling approach is developed for concrete structures under dynamic loading, which couples the macroscale finite element method (FEM) and the mesoscale discrete element method (DEM). The dynamic response of structures is analyzed using the macroscale FEM, and a representative volume element (RVE), composed of aggregate, mortar, and interface, is simulated using the mesoscale DEM to capture the strain rate effects of concrete. By fully taking the advantages of macroscale and mesoscale simulations, it is no longer essential to use complex constitutive laws or input rate-dependent parameters for the macroscale FEM modeling because the concrete fracture can be explicitly illustrated through the breaking process of the mesoscale RVE. This approach is applied to concrete beams and the Koyna dam to verify its applicability. These practical comparisons demonstrate that the seismic tensile strength increases with the strain rates under seismic loading and that the actual repeated crack-closure process of concrete is adequately simulated by the proposed method.

Postbuckling response of unitized stiffened textile composite panels: Computational modeling

A computational investigation of unitized stiffened textile composite panels that are manufactured from triaxially braided textile composites and loaded in axial compression into the postbuckling regime is presented. The stiffened panels are unitized because the textile nature of the constituent material, in conjunction with an alternative stiffener design, form a near-net shape one-piece stiffened panel structure where the textile laminae that form the skin section of the panel are also used, without discontinuity of material, to form the stiffener. A multiscale computational model is presented where the architecture-dependent behavior of a discretely modeled mesoscale representative volume element is passed up to the orthotropic homogenized macroscale stiffened panel shell model. The mesoscale model is automatically executed based on input from the macroscale shell model. Progressive damage initiation and propagation is accomplished by implementing a crack band model in the macroscale model to simulate a material softening behavior. The experimental results are compared to the computational multiscale framework analysis results where a mesoscale triaxially braided textile composite architecture-based model serves as the damage initiation criterion for a smeared progressive damage crack band model in the orthotropic homogenized stiffened panel macroscale shell model.

An integrated computational materials engineering framework to analyze the failure behaviors of carbon fiber reinforced polymer composites for lightweight vehicle applications

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.