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The properties of unidirectional (UD) composites has been investigated by analyzing their elastic and strength characteristics under shear loading. The UD fiber‐reinforced polymer (FRP) composites usually consist of fibers randomly dispersed throughout the cross‐section in the transverse direction which is generally not accounted for. A micromechanical model based on finite element analysis (FEA) approach is utilized here to examine these properties. The study begins by identifying micro scale unit cells or repetitive unit cells (RUCs) at the micro scale, as well as representative volume elements (RVEs). The distribution of fiber volume fraction (Vf) varies among various micro scale unit cells positioned in the transverse cross‐section. The elastic properties and strength are estimated by considering the properties of the matrix and fibers, and the configuration of micro scale unit cells, which feature a fiber arrangement which is categorized as hexagonal and varying Vf at different locations (from 0.35 to 0.75). However, the overall Vf for the UD composite remains constant at 0.65. Studies are also carried out with the random distribution of fibers at micro scale unit cells. The findings reveal that the random distribution of fibers significantly impacts the shear behavior of the composite. This investigation provides valuable insights into how the mechanical properties of the UD composite are subjective by the distribution of fiber, thereby contributing to the design and development of this light weight high‐performance material. Highlights: Elastic and strength analysis of UD composites is presented.Emphasis is on fiber dispersion in transverse plane.Microscale unit cells, RUCs and RVE are identified.Studies are carried out based on micromechanical model.Influence of fiber distribution on shear behavior is investigated. [ABSTRACT FROM AUTHOR]

In the article, we propose a new method to generate representative volume element (RVE) of random spatial distributions with cylindrical fibers and spherical particles based on the Improved Artificial Bee Colony (IABC) algorithm. In this employed bee phase of IABC, the proposed algorithm adopts a new search strategy, which improves the computational efficiency. To analyze the differences between the fiber distribution generated by this algorithm and the actual fiber distribution, we conducted statistical analysis on the distribution of the generated RVE. The statistical analysis results of the nearest neighbor distance (NND), Second-order intensity function, and pair correlation function were in good agreement with the experiment and complete spatial randomness (CSR) patterns. In addition, the predicted elastic properties were compared with experimental measurements and theoretical prediction methods. The results demonstrate the accuracy and efficiency of the proposed algorithm. This algorithm can quickly generate the RVE of cylindrical fibers and spherical particles with volume fractions of 80% and 62%, and the calculation time for generating the RVE of cylindrical fibers is about 17s. [ABSTRACT FROM AUTHOR]

Inter-fibre failure analysis of carbon fibre-reinforced polymer (CFRP) composites, under biaxial loading conditions, has been a longstanding challenge and is addressed in this study. Biaxial failure analysis of IM7/8552 CFRP unidirectional (UD) composites is conducted under various stress states. Two widely accepted failure criteria, the interactive Tsai-Wu and non-interactive Hashin failure criteria, are comprehensively assessed with finite element-based micromechanical analysis. High-fidelity three-dimensional representative volume elements (RVEs) are subjected to biaxial loadings with imposed periodic boundary conditions. Carbon fibres are assumed to be transversely isotropic and linearly elastic. The Drucker-Prager plastic damage constitutive model and cohesive zone model are utilised to simulate the mechanical response of the matrix and fibre-matrix interface, respectively. Coulomb friction is assumed between the fibres and matrix after interface failure. Two sets of biaxial loading scenarios (i.e. transverse stress dominated and shear stress dominated) with the associated failure modes are selected for the failure analysis and assessment of these failure criteria. A data-driven failure envelope for the composites under biaxial loadings is developed using a univariate cubic spline function. Failure mode transition points are determined under biaxial loadings. It is found that the micromechanics-based numerical model is effective in assessing these two existing criteria. [ABSTRACT FROM AUTHOR]

Due to the versatility of its implementation, additive manufacturing has become the enabling technology in the research and development of innovative engineering components. However, many experimental studies have shown inconsistent results and have highlighted multiple defects in the materials' structure thus bringing the adoption of the additive manufacturing method in practical engineering applications into question, yet limited work has been carried out in the material modelling of such cases. In order to account for the effects of the accumulated defects, a micromechanical analysis based on the representative volume element has been considered, and phase-field modelling has been adopted to model the effects of inter-fiber cracking. The 3D models of representative volume elements were developed in the Abaqus environment based on the fiber dimensions and content acquired using machine learning algorithms, while fulfilling both geometric and material periodicity. Furthermore, the periodic boundary conditions were assumed for each of the representative volume elements in transversal and in-plane shear test cases,. The analysis was conducted by adopting an open-source UMAT subroutine, where the phase-field balance equation was related to the readily available heat transfer equation from Abaqus, avoiding the necessity for a dedicated user-defined element thus enabling the adoption of the standard elements and features available in the Abaqus CAE environment. The model was tested on three representative volume element sizes and the interface properties were calibrated according to the experimentally acquired results for continuous carbon-fiber-reinforced composites subjected to transverse tensile and shear loads. This investigation confirmed the consistency between the experimental results and the numerical solutions acquired using a phase-field fracture approach for the transverse tensile and shear behavior of additively manufactured continuous-fiber-reinforced composites, while showing dependence on the representative volume element type for distinctive load cases. [ABSTRACT FROM AUTHOR]

Micromechanics models of composite materials are preferred in the analysis and design of composites for their high computational efficiency. However, the accuracy of the micromechanics models varies widely, depending on the volume fraction of inclusions and the contrast of phase properties, which have not been thoroughly studied, primarily due to the lack of complete and representative experimental data. The recently developed microstructure-free finite element modeling (MF-FEM) is based on the fact that, for a particulate-reinforced composite, if the characteristic size of the inclusions is much smaller than the composite representative volume element (RVE), the elastic properties of the RVE are independent of inclusion shape and size. MF-FEM has a number of advantages over the conventional microstructure-based finite element modeling. MF-FEM predictions have good to excellent agreement with the reported experiment results. In this study, predictions produced by MF-FEM are used in replace of experimental data to compare the accuracy of selected micromechanics models of particulate composites. The results indicate that, only if both the contrasts in phase Young's moduli and phase Poisson's ratios are small, the micromechanics models are able to produce accurate predictions. In other cases, they are more or less inaccurate. This study may serve as a guide for the appropriate use of the micromechanics models. [ABSTRACT FROM AUTHOR]

Due to the versatility of its implementation, additive manufacturing has become the enabling technology in the research and development of innovative engineering components. However, many experimental studies have shown inconsistent results and have highlighted multiple defects in the materials’ structure thus bringing the adoption of the additive manufacturing method in practical engineering applications into question, yet limited work has been carried out in the material modelling of such cases. In order to account for the effects of the accumulated defects, a micromechanical analysis based on the representative volume element has been considered, and phase-field modelling has been adopted to model the effects of inter-fiber cracking. The 3D models of representative volume elements were developed in the Abaqus environment based on the fiber dimensions and content acquired using machine learning algorithms, while fulfilling both geometric and material periodicity. Furthermore, the periodic boundary conditions were assumed for each of the representative volume elements in transversal and in-plane shear test cases,. The analysis was conducted by adopting an open-source UMAT subroutine, where the phase-field balance equation was related to the readily available heat transfer equation from Abaqus, avoiding the necessity for a dedicated user-defined element thus enabling the adoption of the standard elements and features available in the Abaqus CAE environment. The model was tested on three representative volume element sizes and the interface properties were calibrated according to the experimentally acquired results for continuous carbon-fiber-reinforced composites subjected to transverse tensile and shear loads. This investigation confirmed the consistency between the experimental results and the numerical solutions acquired using a phase-field fracture approach for the transverse tensile and shear behavior of additively manufactured continuous-fiber-reinforced composites, while showing dependence on the representative volume element type for distinctive load cases.

• An algorithm to generate microstructures with randomly wavy fibers is proposed. • The algorithm can generate fibers ranging from straight to complex wavy shapes. • Fibers are geometrically characterized by their tortuosity, spread and orientation. • Embedded elements of finite element analysis are used to perform homogenization. • A framework for micromechanics of composites with wavy fibers is presented. During multiscale modeling and analysis of composite materials, accurately capturing the distinctive microstructural features of the material is essential. This is achieved by generating a representative volume element (RVE). Fiber reinforcements in composites can exhibit various shapes, including straight, slightly wavy, or complex shapes, depending on the inherent properties or the manufacturing process. Fibers are characterized based on their tortuosity, spread, and orientation distribution. It is crucial to account for these geometrical attributes during the microstructure generation and subsequent micromechanics modelling as they significantly influence the effective properties of the composite. The present work describes a novel algorithm capable of modeling a broad range of 3D periodic microstructures with fibers having random waviness. The effects of various parameters in the algorithm are studied to understand their influence on fiber shapes. This is followed by finite element analysis of the generated RVEs using the embedded element technique to quantify the microstructure- mechanical properties relationships. Finally, guidelines on the usage of the proposed model to generate fibers with desired microstructure is elucidated. A comprehensive framework for modeling and analyzing microstructures with complex fiber geometry is outlined. [ABSTRACT FROM AUTHOR]

This study presents numerical investigations into the progressive damages in unidirectional carbon fiber reinforced plastics using computational micromechanics with an image-based periodic representative volume element (RVE). This RVE modeling approach combines the methodologies of image-based RVE and artificial periodic RVE to reflect the actual fiber packing while retaining geometrical periodicity. For high-fidelity modeling, the RVE model is prepared with more than 200 carbon fibers extracted from X-ray computed tomography images. Both homogenization simulation for elastic properties and unidirectional loading simulations for plastic and fracture properties are carried out. The constitutive model parameters are identified and verified by comparing the experimental and predicted effective (spatially averaged) elastic and plastic properties, and ultimate strength. Then, with the identified parameters, the local damage initiation and propagation mechanism, and their influence on the macroscopic nonlinear stress–strain behaviors are discussed. Finally, the influences of fiber packing on the prediction accuracy of computational micromechanics are discussed by comparing the results between the proposed image-based RVE and simple RVEs with the square and hexagonal arrays. [ABSTRACT FROM AUTHOR]

The paper is devoted to finite element method based study of stress field heterogeneity at microstructure level of two-phase cemented carbides. Special attention is put on investigation of influence of the microstructure model type on the stress field distributions. Two- and three-dimensional models of the microstructures have been generated. Moreover, two different representations of the microstructure have been considered. The first one assumes uniformly distributed cobalt phase forming continuous boundaries between tungsten carbide particles. The second one assumes that the cobalt phase shape and distribution are created in a way that allows for no differentiation of continuous boundaries between tungsten carbide grains. Finite element analyses have been carried out with different microstructure models. The results of the simulations are stress distributions in each phase of the material. Furthermore, a numerical homogenization has been conducted to investigate the phase properties’ influence on the effective elastic constants of the cemented carbide.

Recent researches show that the embedment of hollow spheres in the matrix phase of composite materials improves the strength of these structures against crack propagations. Rare studies are reported for calculating equivalent elastic constants of fiber reinforced composites containing hollow spheres. In this paper, the effects of hollow spheres on mechanical characteristics of fiber reinforced composite are studied for the first time. To achieve this aim, a micromechanics based finite element method is employed. Representative volume elements (RVEs) including hollow spheres with different radius, thickness and volume fraction of hollow spheres, are modeled by using 3D finite elements. The equivalent elastic constants are calculated through homogenization technique. The results are compared with available experimental works. Good agreements find between two sets of results. Also, the volume fraction, number and thickness of hollow spheres as effective parameters on mechanical properties of composite were investigated. The results show the equivalent elastic properties increase with increasing the volume fraction and number of hollow spheres and decrease with increasing the number of hollow spheres. Furthermore, the equivalent Young's modulus in transverse directions to the fiber direction and shear modulus of the composite increase with increasing the thickness of hollow spheres. As a final result, the presence of hollow spheres in the matrix phase generally increases the equivalent elastic constants without significant changes in the weight of structures. [ABSTRACT FROM AUTHOR]

This paper presents a micromechanics-based 3D finite element model for predicting the damage initiation, propagation, and failure strength of TC33/Epoxy carbon fiber reinforced polymer (CFRP) unidirectional lamina under biaxial loadings. The finite element model is generated by introducing representative volume element (RVE) with a random distribution of fibers and a non-zero thickness, numerically identified interface phase via cohesive elements. In the finite element model, the carbon fibers are considered as elastic, while the elasto-plastic behavior and damage of the matrix are governed by extended Drucker–Prager plastic yielding model and ductile damage criterion. By imposing periodic boundary conditions to the RVEs, various cases subjected to uniaxial and biaxial loading conditions are carried out. During the combined transverse and in-plane shear stress states, a failure transition from compression- or tension-dominated to shear-dominated is captured, and the effects of the interfacial strength on the transition damage mechanisms are discussed. The corresponding failure locus is compared with the upper bound and lower bound predictions of three phenomenological failure criteria (Hashin, Tasi–Wu, and Puck failure criteria) for composites. It was found that in the interface-dominated failure of a CFRP lamina with a weak interface, the Hashin failure criterion performs best among the currently popular failure criteria. However, in the matrix-dominated failure with a strong interface, the Puck failure criterion performs best. Comparing these three criteria, it can be seen the Tsai–Wu may be generally better than both of others as it presents more neutral predictions in both of the examined cases. [ABSTRACT FROM AUTHOR]

A main problem for the development of comprehensive continuum mechanical models is the lack of experimental data. To overcome this problem, a non-associative viscoelastic-viscoplastic constitutive model which takes into account combined isotropic-kinematic hardening effects for epoxy matrix as well as a three dimensional non-associative anisotropic nonlinear elastic/plastic constitutive model for flax fibre is developed. The constitutive models are assigned to a representative volume element (RVE) of a unidirectional flax fibre/epoxy composite. Upon application of periodic boundary conditions (PBCs), different loading scenarios are subjected to the RVE and the mechanical response of the composite is studied. Based on the performed micromechanical analyses, a continuum model is developed for the unidirectional flax fibre/epoxy composite in Part II of this paper. [ABSTRACT FROM AUTHOR]

Abstract 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. [ABSTRACT FROM AUTHOR]

The purposes of this paper are sixfold. First, any micromechanics model for predicting elastic property (stiffness) of a composite is applicable to a reasonable prediction of a composite strength, provided that the homogenized internal stresses in the matrix are converted into true values. The conversion for all of the stress components free of biaxially transverse loads is presented in the paper. Second, the predictability of 12 well-known micromechanics models for stiffness and strength of a unidirectional composite is assessed against the measured data of all of the nine unidirectional composites used in three world-wide failure exercises. An accuracy ranking is made accordingly. Third, it is demonstrated that the smallest fiber volume in a representative volume element for a finite element approach plays a more dominant role than other issues such as a random fiber array to achieve the highest simulation accuracy. This feature has been largely ignored in the current literature. Fourth, a consistency of a micromechanics model in calculating the internal stresses in the fiber and matrix of the composite is an issue that should be taken into account. Among the 12 models considered, only Bridging Model is consistent. A non-consistency implies that a full three-dimensional approach should be used to predict an effective property of the composite even though it is subjected to a uniaxial load. Fifth, an effective method to detect an interface debonding between the fiber and matrix subjected to an arbitrary load is presented in the paper. Only a transverse tensile strength of the composite, in addition to the original fiber and matrix properties, is needed. Whereas essentially any load can cause the interface to debond earlier before a composite failure, only a transverse tensile load carrying capacity of the composite is influenced significantly by the debonding. Specifically, an interface debonding has insignificant effect on a shear strength of the composite. Sixth, a fiber misalignment-induced kink band failure is analyzed by virtue of the original fiber and matrix properties, and a longitudinal compressive strength is predicted micromechanically. [ABSTRACT FROM AUTHOR]

This study aims to quantify the three-dimensional (3D) micro-voids for damage prediction in warm forging through non-destructive X-ray computed tomography (CT) and RVE approach. Typical biocompatible alloys, i.e., stainless steel 316 L (SS316L) and titanium alloy Ti-6Al-4V, were used as specimen materials in warm-forging a medical implant, i.e., a basal thumb implant. X-ray CT scanning was performed for both the preforms and forged components. Volumetric CT images were then reconstructed and the 3D micro-void distribution and evolution inside the materials were detected and analysed quantitatively. Furthermore, three typical local strain regions, i.e., the small tensile strain region (STSR), small compressive strain region (SCSR) and large compressive strain region (LCSR), were established as the 3D representative volume element (RVE) models for both SS316L and Ti-6Al-4V preforms. The spatial location, size and volume of each micro-void were obtained from defect analysis of the 3D CT images and considered explicitly for subsequent damage prediction. An improved thermo-mechanical coupled micromechanics-based damage (micro-damage) model, which considered the variation of volume fraction of micro-voids (VFMVs), was implemented into finite element (FE) package ABAQUS for localized damage prediction of the RVE models. The damage distributions of the RVE models at different strain levels were visualized and identified. Finally, the localized damage evolutions at both compressive and tensile deformations were predicted and found to match quite well with the findings acquired from CT scanning. Thus, the application of non-destructive X-ray CT measurement of micro-voids, incorporating the RVE approach, was able to play a significant role leading to a more reliable damage prediction in the warm forging process. [ABSTRACT FROM AUTHOR]

A new method to generate the random distribution of fibers in the transverse cross-section of fiber reinforced composites with high fiber volume fraction is presented in this paper. Based on the microscopy observation of the transverse cross-sections of unidirectional composite laminates, hexagon arrangement is set as the initial arrangement status, and the initial velocity of each fiber is arbitrary at an arbitrary direction, the micro-scale representative volume element (RVE) is established by simulating perfectly elastic collision. Combined with the proposed periodic boundary conditions which are suitable for multi-axial loading, the effective elastic properties of composite materials can be predicted. The predicted properties show reasonable agreement with experimental results. By comparing the stress field of RVE with fibers distributed randomly and RVE with fibers distributed periodically, the predicted elastic modulus of RVE with fibers distributed randomly is greater than RVE with fibers distributed periodically. [ABSTRACT FROM AUTHOR]

Determination of effective composite properties for a real distribution of piezoelectric particles in cement matrix is considered using a representative volume element. The scaled boundary finite element method is proposed to analyse cement-based piezoelectric ceramic composites. Quadtree hierarchical meshing structure is utilized to provide a mesh that captures the material variation in the representative volume element effectively based on the colour of the piezoelectric composite’s image. Analyses with carefully selected boundary conditions are performed to obtain the effective material properties of various samples. [ABSTRACT FROM AUTHOR]

This paper presents an adaption of periodic boundary conditions (BC), which is termed tessellation BC. While periodic BC restrict strain localization zones to obey the periodicity of the microstructure, the proposed tessellation BC adjust the periodicity frame to meet the localization zone. Thereby, arbitrary developing localization zones are permitted. Still the formulation is intrinsically unsusceptible against spurious localization. Additionally, a modification of the Hough transformation is derived, which constitutes an unbiased criterion for the detection of the localization zone. The behavior of the derived formulation is demonstrated by various examples and compared with other BC. It is thereby shown that tessellation BC lead to a reasonable dependence of the effective stress on the localization direction. Furthermore, good convergence of stiffness values with increasing size of the representative volume element is shown as well as beneficial characteristics in use with strain softening material. [ABSTRACT FROM AUTHOR]

Deep drawing is one of the most commonly used sheet metal forming processes, which can produce metal parts at a high rate. One of the major problems in deep drawing is springback, which is mainly elastic deformation occurring when the tool is removed. The focus of this work is the prediction of springback in deep drawing for DC04 steel using a micromechanical modeling scheme. A novel method is used for the characterization of material that leads to cyclic stress-strain curve. Simulations are performed with the Yoshida Uemori (YU) model for the prediction of springback for a U draw-bend geometry. The maximum deviation between the geometries of experiment and the springback simulation for hat geometry is 2.2 mm. It is shown that this micromechanical modeling scheme allows us to relate the influence of the microstructure to the springback prediction. [ABSTRACT FROM AUTHOR]

The present work aims to study the bake-hardening behaviour in dual-phase (DP) steels. The mechanical properties and BH-values in dependency of the BH-parameters were determined and related to specific microstructural features in order to characterize the age- and strain-hardening behaviour. Micromechanical modeling by means of representative volume element (RVE) approach was used to describe the effect of BH on the mechanical behaviour of DP steel numerically taking into account microstructural features. 2D RVEs were created based on real microstructures. The flow behaviour of single phases was modelled using a Taylor-type dislocation-based work-hardening approach. The volume change during austenite-to-martensite transformation was also modelled and the resulting prestrained areas in ferrite were considered to be the storage place of GNDs. Afterwards, prestraining of 2% and 5% were imposed on the RVEs through numerical uniaxial tensile test. Then, the BH annealing was implemented on the prestrained RVEs in order to investigate the strain partitioning during annealing. Subsequently, numerical tensile tests were implemented on the bake hardened RVEs in order to study the stress-strain distribution on the microstructures. Finally, the flow curves of simulations on BH-treated and conventional DP steels were compared with experimental results showing a good correlation between experiments and simulations. [ABSTRACT FROM AUTHOR]

Micromechanical-based finite element simulations were carried out to investigate the transient plastic strain rate evolutions of ferrite and martensite dual-phase steel during strain path changes. A representative volume element (RVE) was generated through a three-dimensional (3D) reconstruction of microstructure images which were acquired from sequential polishing of a small material volume. The 10 × 10 × 10 μm 3 3D RVEs consisted of martensite islands embedded in a ferrite base matrix. Each phase was assumed to exhibit distinct mechanical properties but the grain and phase boundary effects were ignored in this work. The effective mechanical properties for the constituent phases were assumed to be well defined by the von Mises or Hill 1948 yield criteria, the associated flow rule, and an empirical isotropic hardening equation based on chemical composition. This model was applied to investigate the transient behavior of the r-value (Lankford coefficient) in uniaxial tension when the loading direction changed. In addition to monotonic tension, compression-tension, and tension-orthogonal tension, sequences were considered. The simulation results captured well in a qualitative manner the experimental r-value evolutions in terms of a temporary transition and asymptotic limit. The evolutions of stress states in ferrite and martensite were analyzed to explain the r-value behavior that resulted from three factors: (1) r-value differences between ferrite and martensite, (2) martensite configuration-induced stress state in phases, and (3) stress partitioning and its evolution during non-proportional loading. Finally, an analytical relationship between the stress evolution in the constituent phases and the relevant r-value changes is suggested. [ABSTRACT FROM AUTHOR]

A “bottom-up” representative volume element (RVE) for a dual phase steel was constructed based on measured microstructural properties (“microproperties”). This differs from the common procedure of inferring hypothetical microproperties by fitting to macroscopic behavior using an assumed micro-to-macrolaw. The bottom-up approach allows the assessment of the law itself by comparing RVE-predicted mechanical behavior with independent macroscopic measurements, thus revealing the nature of the controlling micromechanisms. An RVE for DP980 steel was constructed using actual microproperties. Finite element (FE) simulations of elastic-plastic transitions were compared with independent loading-unloading-loading and compression-tension experiments. Constitutive models of three types were utilized: 1) a standard continuum model, 2) a standard Crystal Plasticity (CP) model, and 3) a SuperDislocation (SD) model similar to CP but including the elastic interactions of discrete dislocations. These comparisons led to following conclusions: 1) While a constitutive model that ignores elastic interaction of defects can be fit to macroscopic or microscopic behavior, it cannot represent both accurately, 2) Elastic interactions among dislocations are the predominant source of nonlinearity in the nominally-elastic region (i.e. at stresses below the standard yield stress), and 3) Continuum stress inhomogeneity arising from the hard martensite / soft ferrite microstructure has a minor role in the observed transitional nonlinearity in the absence of discrete dislocation interactions. [ABSTRACT FROM AUTHOR]

For large-scale engineering applications, macroscopic phenomenological damage mechanics models with less complexity are usually applied due to their high computational efficiency and simple implementation procedures in finite element simulations. Compared with micromechanical models, however, they also have a significant disadvantage, namely the lack of microstructure sensitivity. This work aims to develop a method to integrate the influence of microstructural features into the parameter calibration of a stress-state-dependent damage mechanics model (the modified Bai-Wierzbicki model) for a C45E + N steel. For this purpose, virtual experiments are performed on an artificial microstructure model to derive the plasticity and damage initiation behaviour for the investigated material. A crystal plasticity model for ferrite along with an empirical strain hardening law for pearlite are assigned to the corresponding constituents in the artificial microstructure model to define their material properties. Nanoindentation tests and numerical analysis are used to calibrate the parameters of the crystal plasticity model. By applying different boundary conditions to the artificial microstructure model, both the plasticity and the damage initiation behaviour under different stress states are calibrated by the virtual experiments. In addition, this approach is also applied to investigating the influence of microstructure on plasticity and damage initiation. [ABSTRACT FROM AUTHOR]

The purpose of this study was to develop a micromechanics-based damage (micro-damage) model that was concerned with the evolution of micro-voids for failure prediction in cold forming. Typical stainless steel SS316L was selected as the specimen material, and the nonlinear isotropic hardening rule was extended to describe the large deformation of the specimen undergoing cold forming. A micro-focus high-resolution X-ray computed tomography (CT) system was employed to trace and measure the micro-voids inside the specimen directly. Three-dimensional (3D) representative volume element (RVE) models with different sizes and spatial locations were reconstructed from the processed CT images of the specimen, and the average size and volume fraction of micro-voids (VFMV) for the specimen were determined via statistical analysis. Subsequently, the micro-damage model was compiled as a user-defined material subroutine into the finite element (FE) package ABAQUS. The stress-strain responses and damage evolutions of SS316L specimens under tensile and compressive deformations at different strain rates were predicted and further verified experimentally. It was concluded that the proposed micro-damage model is convincing for failure prediction in cold forming of the SS316L material. [ABSTRACT FROM AUTHOR]

The effect of martensitic phase fraction on the cyclic stress-strain behavior of two DP steels is investigated via a micromechanical model based on a representative volume element (RVE). A dislocation density based model and a Chaboche hardening model are used to identify the isotropic and kinematic hardening behavior of constituent phases, respectively. The Chaboche parameters obtained by fitting flow curves computed from a dislocation density based model for both ferrite and martensite phases of each steel are incorporated into a Finite Element code ABAQUS to simulate the low cycle fatigue with a combined hardening behavior. Based on experimental observations reported in the literature, fatigue crack initiates in ferrite phase. A ductile damage model, therefore, is used to simulate damage initiation in ferrite. The results show that the martensite fraction has a significant influence on cyclic plastic strain accumulation during the cyclic deformation. It is also concluded that with an increase in the martensite volume fraction in DP steel, the elastic component of the total strain amplitude increases and higher fatigue strength is, subsequently, observed. [ABSTRACT FROM AUTHOR]

Discrepancy in reported elastic properties for nanocomposites is argued to be most likely a result of either variations in the size of reinforcement or lack of control of the composite microstructure. In general, there will be a size variation in nanotubes in a given composite, contribution from each nanotube diameter and the volume percentage that tubes of a definite diameter occupy within the composite toward the overall elastic modulus is modeled. In this work, Digimat-FE is used to generate a realistic three dimensional microstructure for the current carbon nanotube/ epoxy composite. A system of aligned carbon nanotubes embedded in epoxy matrix is modeled. In the system of aligned multi walled carbon nanotubes, the entire volume of the model has been divided into finite individual sub-composites, each one containing a specific nanotube diameter with a local volume fraction. A second model showed a single representative volume element for the current nano-composite, in which the carbon nanotubes were simulated as a randomly (fully) dispersed, where all particles have been separated from each other. Moreover, a micromechanical approach for modeling short fiber composites was developed to account for the structure of the multi-walled carbon nanotube reinforcement and predict the elastic modulus of the nanocomposite as a function of the constituent properties, reinforcement geometry and nanotube structure. Finite element results show increase in elastic modulus with increasing aspect ratio for composites with high filler loading (3 vol%). Micromechanical predictions highlight the structure or size influence of the nanotube reinforcement on the properties of the nanocomposite. The nanocomposite elastic properties were found to particularly be sensitive to the nanotube diameter, since larger diameter nanotubes showed a lower effective modulus and occupied a greater volume fraction in the composite relative to smaller-diameter nanotubes. [ABSTRACT FROM AUTHOR]

The axial compressive strength of continuous fibre composites is often the key design parameter used by mechanical engineers. The complex interactions between the fibres and the matrix requires the use of sophisticated numerical models to estimate this property. A preliminary design step is conventionally used for the dimensioning of composite structures. This step requires quick tools such as analytical criteria. In this work, we discuss such a criterion and its input parameters related to the nonlinear shear behaviour of the unidirectional ply. These parameters are usually measured using experimental techniques. We show that a simple micro-mechanical numerical model (representative hexagonal volume element with periodic boundary conditions), easily usable by engineers, makes it possible to estimate this nonlinear shear behaviour, thus reducing the number of tests required. This also makes it possible, on the one hand, to accelerate the preliminary design test, and, on the other hand, to select the constituents and thus tailor the material response. [ABSTRACT FROM AUTHOR]

The present article deals with micromechanical composite modeling. Both analytical and computational micromechanics approaches are described as well as micromechanical modeling of damage. Based on micromechanics of failure theory, a user subroutine including a progressive damage algorithm is programmed for finite element analysis. Three theory-experiment correlations of tubes under a three-point bending test have been carried out using the bi-phase material model developed along with this project. These studies include three-ply schedules. [ABSTRACT FROM PUBLISHER]

There is a steady increase in the implementation of dual phase steels in stamped automotive components. Therefore, steel suppliers who develop dual phase steels are interested in predicting the microstructure-properties relationship for optimization of microstructural design. This goal is achievable by micromechanical modeling. The representative volume element (RVE) method has been a popular technique for micromechanical modeling of dual phase steels. It is generally considered that 2D modeling underestimates the flow curves and that 3D modeling predicts the experimental stress-strain curves more accurately. However, much of the research has focused on 2D modeling. This paper develops 3D micromechanical modeling of DP500 and bainite-aided DP600 steels by including statistical quantitative metallography data in the models. More than 3000 grains were analyzed in each steel. Hence, both volume fraction and morphology of martensite were statistically determined. This model predicted the ultimate tensile strength of these two dual phase steels with less than 0.5% error. [ABSTRACT FROM AUTHOR]

The micromechanical prediction of mechanical properties of composites, using a finite element method, is highly affected by selecting a suitable representative volume element. In the present research, the effects of the representative volume element aspect ratio on the stiffness of aligned short fiber composites have been studied. First, an analytical method is suggested to predict the longitudinal and transverse moduli of composites considering the representative volume element aspect ratio. Then, the optimum aspect ratio of the representative volume element is estimated by comparing the results obtained by the present method with those of a micromechanical method. Comparing the stiffness of the optimized representative volume element with some experimental results available in the literature shows that the result of the present method is also in a good agreement with experiments. [ABSTRACT FROM AUTHOR]

This paper investigates the effective material properties of lightweight concrete containing polymer foam particles through both experiments and numerical modeling. Different volume fractions of foam particles have been added to cement paste to fabricate lightweight concrete samples. To interpret the experimental results, an inclusion method based boundary integral equation has been proposed. The effect of the material mismatch between the foam particles and the cement matrix can be simulated by an eigenstrain, which is a fictitious nonmechanical strain. Due to the interaction between particles and boundary effect, the eigenstrain on a particle is not uniform. An asymptotic analysis shows that a quadratic distribution of the eigenstrain over each particle provides very good accuracy. Since the discretization of particles is not needed due to applying an analytic form of eigenstrain field, a large number of spherical inhomogeneities can be simulated and the local field can be calculated in a lightweight concrete sample. The formulation has been implemented in a software package for the simulation of material samples and has been verified with the finite element method for two top-down particles embedded in a cylinder. The simulation results based on idealized microstructure exhibit a very good agreement with the experimental results of the effective elastic moduli. A simple and empirical study also predicts the strengths of the composites very well. The developed algorithm can be used for virtual mechanical experiments of particulate composites. [ABSTRACT FROM AUTHOR]

Purpose – The purpose of this paper is to present knowledge in estimating yield surfaces of heterogeneous media by use of homogenization, especially where the macroscopic behaviour is driven by weak interfaces between phase constituents. Design/methodology/approach – A computational homogenization procedure is used to determine the yield surface of a Representative Volume Element (RVE) that contains a fully debonded inclusion embedded within ideally plastic matrix, whereby the interface is modelled by a Coulomb type friction law. Findings – The macroscopic behaviour of the RVE is shown to coincide an RVE with a hole for expanding loads, whereas for compressive loads, it was shown to approach an RVE with a fully bonded inclusion. Originality/value – The present paper builds on Gurson’s work in estimating macroscopic yield surfaces of heterogeneous materials. The work is novel in the sense that there had been no previous publications discussing influence of weak interfaces on yield surfaces. [ABSTRACT FROM AUTHOR]

This study investigates the influence of void microstructure on the effective elastic properties of high fiber volume fraction discontinuous fiber-reinforced composites with randomly oriented fibers. A void microstructure is characterized by using parameters such as the number of voids, void volume fraction, void Aspect Ratio and void size distribution. In order to overcome the difficulties associated with the creation of high fiber volume fraction representative volume element models containing voids, a novel automation program called “ArtiComp” is developed. This program is used to generate representative volume element models of discontinuous fiber-reinforced composites containing randomly oriented straight fibers, curved fibers and spheroidal voids. The effective properties of discontinuous fiber-reinforced composites are computed using a finite element-based micromechanics approach. For comparison, the Mori-Tanaka method is used to compute the effective properties of unidirectional discontinuous fiber-reinforced composites and then orientation averaging is performed on these properties to obtain the effective properties of discontinuous fiber-reinforced composites with randomly oriented fibers. The comparison shows that the finite element predicted properties are stiffer than the analytically predicted properties. The results indicate that the finite element predicted properties are dependent on the number of voids used to represent the void volume. It is seen that the effective properties significantly decrease when void volume fraction is increased. The void Aspect Ratio and void size distribution are found to have a negligible influence on the effective properties. Finally, it is observed that straight fiber composites with voids perform better than the corresponding curved fiber composites with voids. [ABSTRACT FROM AUTHOR]

This paper presents a micromechanical element-free method to study elastic properties of carbon nanotubes (CNTs) reinforced composites. A three-dimensional nanoscale cylindrical representative volume element (RVE) has been considered in the analysis, in which CNT and matrix are both modeled as elastic materials based on continuum mechanics. The proposed model is used to investigate the behaviors of CNT-reinforced composites with respect to their effective mechanical properties. The relevant formulas to extract the effective material constants for three loading cases are derived in detail, based on the elasticity theory. Besides, the meshless method based on the moving least-squares (MLS) approximation and element-free Galerkin (EFG) method is implemented to evaluate the established model. The computed results are compared with the available solutions obtained from other analytical and numerical methods. Moreover, these results show that the presence of CNTs can significantly improve the longitudinal and transverse characteristics of the composite materials. [ABSTRACT FROM AUTHOR]

We are considering the effect of the particle shape on the effective elastic properties and representative volume element of two-phase composites. In this work, microstructures with ellipsoidal and spherical particles are considered. Three dimensional particles are randomly generated for different volume fractions without any contact between neighbouring spheres according to Poisson process. The used analysis is based on numerical homogenization approaches by finite element method and morphological characterization of microstructures by random fields. The effects of various parameters such as particles volume fraction, contrast in phase properties and particles shape were identified. The statistical methods are introduced and then coupled with numerical simulations. The notion of statistically representative volume, named the deterministic representative volume element (RVE), is used. The variation of this RVE as a function of particles volume fraction for heterogeneous materials is presented. These variations suggest us to identify the morphological distribution of particles which is more anisotropic and which needs a large RVE size. [ABSTRACT FROM AUTHOR]

In the present study, the plasticity and creep behaviors of heterogeneous composites containing randomly distributed particles were considered to predict the effect of boundary conditions (BCs) numerically derived solutions. Modeling was performed using two dimensional representative volume elements (RVEs) with different sizes and particle volume fraction. Structural heterogeneity along the model boundaries considerably influenced the overall numerical solutions that developed stress/strain fluctuations, while inner part of the model showed almost the same strain fields. In both plasticity and creep models, the thickness of BC-affected region was larger in plastic or creep strain fields than in elastic strain fields when dividing the total strain of volume elements into elastic, and plastic or creep strain. When the particle volume fraction increased, the thickness of the BC-affected region reached a critical size with the exception of the plasticity model. Comparing the results of the linear and nonlinear problems, the thickness was larger in the nonlinear problem than the linear one. The results suggested that the mechanism proposed for the elasticity model could be applied to nonlinear models to determine the size of the RVE for the specific research purposes or predicting potential errors to estimate the effective properties. [ABSTRACT FROM AUTHOR]

In this paper, micromechanical modelling and simulation were performed for unidirectional fibre reinforced composites subjected to transverse and in-plane shear by finite element method. Representative volume element consisting of fibre, matrix and interface was established for the simulation, considering random fibre distribution. The two dominant damage mechanisms of fibre reinforced composites, matrix plastic deformation and interfacial debonding were taken into account in the simulation. Periodic boundary conditions were applied to the representative volume elements. The simulation results indicate that the failure behaviour of the composites under transverse shear is dominated by matrix plastic damage, while the in-plane shear damage is initiated by interfacial debonding and then ultimate failure is caused by matrix damage. Fibre distribution is found to have a more significant effect on the failure behaviour of the composites under transverse shear than in-plane shear. The predicted in-plane shear strength and failure strain show reasonable agreement with the experimental results. [ABSTRACT FROM AUTHOR]

The aim of the work is to predict the onset and the progression of damage in the continuous fiber reinforced composite laminates taking into consideration the different mechanical behavior of the constituents in the composite under different loading conditions. The stresses in the constituents are obtained using a representative volume element (RVE) approach. Finite element analysis is carried out to extract the stresses in the constituents and the overall effective properties of the composite material. To consider the realistic behavior of the matrix of the composite material, a modified Drucker–Prager failure criterion is used. Direct test data on the individual constituents are used in this approach to model the failure of each of the constituents separately using the extracted stresses in the individual constituents. Failure envelope plotted for a unidirectional fiber reinforced composite material using the proposed model clearly shows that the initiation of damage is different in different constituents of the composite material. This is more realistic compared to the popularly used macroscopic criteria such as Tsai–Wu criterion. Propagation of failure in fiber reinforced composite is captured using a simple progressive damage model. It is also found that the hexagonal RVE has more predictive capabilities than the square RVE since the average distance between the fiber may play a major role in the strength prediction of composites. [ABSTRACT FROM AUTHOR]

Aspects of numerical results from computational experiments on representative volume element (RVE) problems using finite element analyses are discussed. Two different boundary conditions (BCs) are examined and compared numerically for volume elements with different sizes, where tests have been performed on the uniaxial tensile deformation of random particle reinforced composites. Structural heterogeneities near model boundaries such as the free-edges of particle/matrix interfaces significantly influenced the overall numerical solutions, producing force and displacement fluctuations along the boundaries. Interestingly, this effect was shown to be limited to surface regions within a certain distance of the boundaries, while the interior of the model showed almost identical strain fields regardless of the applied BCs. Also, the thickness of the BC-affected regions remained constant with varying volume element sizes in the models. When the volume element size was large enough compared to the thickness of the BC-affected regions, the structural response of most of the model was found to be almost independent of the applied BC such that the apparent properties converged to the effective properties. Finally, the mechanism that leads a RVE model for random heterogeneous materials to be representative is discussed in terms of the size of the volume element and the thickness of the BC-affected region. [ABSTRACT FROM AUTHOR]

This paper introduces a multiscale modeling approach to simulate the macromechanical properties of cementitious composites with polyurethane reinforcement. The polyurethane inclusions to hydrated cement paste matrix are represented by continuum 3D elements. Simulations of the real phenomenon that occur at the micro level of the composite have been done by mean-field homogenization technique and finite element analysis. The multiscale model presented in this work enables us to evaluate the stress–strain behavior and other engineering properties. Different configurations of polyurethane cement composite have been studied including variation of loading conditions, weight fraction of polyurethane and the aspect ratios of the polyurethane inclusion. The effect of shape and alignment of polyurethane on the stiffness of the composite has also been evaluated. Strength and stiffness values obtained from the proposed approach are in good agreement with that obtained from open literature. [ABSTRACT FROM AUTHOR]

This paper presents an approach to evaluate the macroscopic properties of ceramic materials based on the homogenisation of the results of micromechanical simulations performed on Representative Volume Elements (RVEs) of polycrystalline microstructures. The RVEs are defined using a bespoke algorithm to generate numerical model geometries statistically representative of the microstructure of polycrystalline ceramics. The material properties of single crystals and grain boundaries, obtained from direct experimental measurements at the relevant scales, are used for the generation of RVEs, which are then subjected to unit load cases. The results of the numerical simulations, performed using the explicit Finite Element Method (FEM), are used to calculate the macroscopic material parameters governing elastic deformation, and brittle failure due to initiation and propagation of cracks at the grain scale. The automated approach adopted to generate and analyse the response of RVEs under a specified set of loading conditions permits a statistically relevant number of simulations to be performed on different combinations of microstructural morphologies, distributions of crystallographic orientations, and defects, thus demonstrating a homogenisation and upscaling methodology that captures several important aspects of the stochastic variability typically exhibited by ceramic materials. The numerical simulations of elastic deformation and brittle failure of polycrystalline alumina (A l 2 O 3) are compared against both experimental measurements and analytical calculations, showing good agreement for both elastic deformation - expressed in terms of homogenised elastic moduli - and failure strength - observed both as changes in the crack pattern at the microscale and when measured as the value of the stress at the onset of failure. [Display omitted] • The use of structured meshes provides robust models for large parametric studies. • A novel cohesive formulation is implemented to model interfaces in a raster model. • Micromechanical models capture the stochastic variability of mechanical properties. • The models show the importance of defects on failure strength mean value and variance. [ABSTRACT FROM AUTHOR]

Highlights: [•] Fiber waviness significantly affects E 11; other properties are moderately affected. [•] E 22 initially decreases and then increases as a function of fiber waviness. [•] Material property mismatch has a strong influence on the effective properties. [•] Fiber spatial distribution has a weak influence on the effective properties. [•] Fiber/matrix interphase has a strong influence on the effective properties. [Copyright &y& Elsevier]