Micromechanical Representative Volume Element Research Articles

Representative volume element (RVE) based FEA investigation on the plastic flow behaviour of friction-stir processed AA7075/Si3N4composite under constrained deformation conditions

In the present investigation, the Si3N4reinforced (with a weight percentage of 2.5%, 5% and 7.5%) AA7075-based metal matrix composite has been developed by friction-stir processing. Further, a micro-mechanical representative volume element (RVE)-based finite element analysis (FEA) model has been developed for the evaluation of mechanical properties and plastic flow behaviour of developed composite material in uniaxial conditions. Moreover, a macro-mechanical-based static indentation finite element model has been developed for predicting the plastic flow behaviour, Meyer's hardness, constraint factor (CF) and lip height around indentation as a function of average strain under constrained conditions. The results revealed that Meyer's hardness, yield strength, tensile strength and lip height were increased with the increase in Si3N4reinforced weight percentage. Further, the lip height was inversely proportional to the strain hardening exponent. It has been also observed that the CF of all three developed composite material compositions increased with the increase in average strain ( εavg) up to the transition strain ( εtr) only, after that its value was constant with further increase in average strain ( εavg).

Microscale modelling of lightning damage in fibre-reinforced composites

In this work, three-dimensional (3D) finite element simulations were undertaken to study the effects of lightning strikes on the microscale behaviour of continuous fibre-reinforced composite materials and to predict and understand complex lightning damage mechanisms. This approach is different from the conventional mesoscale or macroscale level of analysis, that predicts the overall lightning damage in composite laminates, thus providing better understanding of lightning-induced thermo-mechanical damage at a fundamental level. Micromechanical representative volume element (RVE) models of a UD composite laminate were created with circular carbon fibres randomly distributed in an epoxy matrix. The effects of various grounding conditions (one-, two-, and four-side grounding), fibre volume fractions ( V f = 55, 60%, and 65%), and peak current amplitudes (10, 20, and 40 kA) on microscopic damage in RVE models were characterised to understand fibre, epoxy matrix, and fibre-matrix interfacial damage associated with a lightning strike. Thermal damage, estimated based on epoxy matrix decomposition temperature, was largely constant up to 20 kA before increasing significantly at 40 kA. Severe thermal damage steadily decreased with increasing V f. Thermo-mechanical damage was predicted using a ductile plasticity model with Drucker–Prager yield criterion for epoxy matrix failure, and cohesive surfaces for fibre-matrix interface debonding. Thermal strain had the largest contribution to thermo-mechanical damage, while dynamic pressure loading was negligible in all RVE models. The RVE model proposed in this work, to the best of the authors’ knowledge, is the first model predicting lightning-induced fibre-matrix interfacial damage.

Growth of random polyhedral void in structural steel based on micromechanical RVE simulations

This paper investigates growth of random polyhedral voids (RPVs) in structural steel, which is a critical stage for ductile fracture of steel. An in-situ high-resolution μXCT experiment shows that most micro-voids in structural steels can be characterized by RPVs. In this study, a micromechanical representative volume element (RVE) model containing an RPV was established with periodic boundary conditions. Comparison of RPV growths with spherical and elliptical void growths was conducted for model validation. On this basis, effects of geometric parameters of the RPV on void growth were analyzed through Python-based parametric modeling in ABAQUS with respect to the aspect ratio, orientation, sphericity, initial void volume fraction, respectively. The results found that growth of the RPV decreases with an increasing initial aspect ratio of the RPV. Growth of the RPV increases as the initial sphericity of RPV decreases. When the initial orientation of RPV tends to be perpendicular to the main tensile direction, a greater void growth will be obtained. The initial volume fraction of RPV has a minor effect on void growth compared with the other geometric parameters. For engineering application, accurate and simplified formulae were proposed to evaluate growth of microscopic RPVs, respectively.

Meso-scale Finite Element (FE) modelling of biaxial carbon fibre non-crimp-fabric (NCF) based composites under uniaxial tension and in-plane shear

Non-crimp-fabrics (NCF) are promising materials in aerospace applications. The complex internal structure of NCF composites could influence the in-plane performances, which needs to be comprehensively studied. The novel three-dimensional (3D) meso-scale repeated unit cell (RUC) models were proposed for biaxial NCF composites based on the Finite Element (FE) method to conduct a systematic parameter study, including layup sequence, out-of-plane tow waviness, resin-rich areas, transverse tow placements and delamination. The meso RUC model could effectively predict the homogenised uniaxial tensile and in-plane shear properties of biaxial NCF composites based on their meso-scale constituent and material properties. A multiscale framework was also developed for biaxial NCF composites. A micromechanical representative volume element (RVE) model provided homogenised mechanical properties for tows, and a macroscopical FE model validated the test results using the homogenised results obtained from meso RUC models. The numerical results were in good agreement with the experiment results. Therefore, the multiscale framework provides an insight into the critical parameters influencing the in-plane properties of NCF composites and an analysis tool for NCF material design.

The Elastic Properties of Unidirectional Bamboo Fibre Reinforced Epoxy Composites

Natural fibres such as kenaf, jute, bamboo, flax and wood have been the subject of intensive researches in the area of fibre reinforced composite due to their environmental advantages of being renewable, biodegradable and sustainable. Bamboo fibre can be a good choice of natural fibre reinforcement for structural applications due to its excellent strength to weight ratio that is comparable to that of mild steel. In this study, mechanical properties of both continuous and short bamboo fibre reinforced composites are predicted using micromechanical approaches. The finite element method was used where three-dimensional micromechanical representative volume element with square and hexagonal packing geometry was implemented. The results were then compared with the findings from analytical approach that includes the rule of mixture and the Halpin-Tsai model. It was found that for all properties, the FEM and analytical methods give comparable trends of property on volume fraction plots. Furthermore, the longitudinal modulus given by all models are in excellent agreement as it increases linearly with the increase in bamboo fibre volume fraction.

Combining FEM and MD to simulate C60/PA-12 nanocomposites

PurposeThe purpose of this paper is the computation of the elastic mechanical behaviour of the fullerene C60 reinforced polyamide-12 (PA-12) via a two-stage numerical technique which combines the molecular dynamics (MD) method and the finite element method (FEM).Design/methodology/approachAt the first stage, the proposed numerical scheme utilizes MD to characterize the pure PA-12 as well as a very small cubic unit cell containing a C60 molecule, centrally positioned and surrounded by PA-12 molecular chains. At the second stage, a classical continuum mechanics (CM) analysis based on the FEM is adopted to approximate the elastic mechanical performance of the nanocomposite with significantly lower C60 mass concentrations. According to the computed elastic properties arisen by the MD simulations, an equivalent solid element with the same size as the unit cell is developed. Then, a CM micromechanical representative volume element (RVE) of the C60 reinforced PA-12 is modelled via FEM. The matrix phase of the RVE is discretized by using solid finite elements which represent the PA-12 mechanical behaviour predicted by MD, while the C60 neighbouring location is meshed with the equivalent solid element.FindingsSeveral multiscale simulations are performed to study the effect of the nanofiller mass fraction on the mechanical properties of the C60 reinforced PA-12 composite. Comparisons with other corresponding experimental results are attempted, where possible, to test the performance of the proposed method.Originality/valueThe proposed numerical scheme allows accurate representation of atomistic interfacial effects between C60 and PA-12 and simultaneously offers a significantly lower computational cost compared with the MD-only method.

Multiscale simulation of fullerene reinforced composite structures: From molecular dynamics to finite element continuum mechanics

The aim of the present study is to propose a multiscale computational technique for the prediction of the elastic mechanical properties of nanoreinforced composites. The proposed method utilizes a molecular dynamics (MD) based numerical scheme to capture the mechanical behaviour of the nanocomposite at nanoscale and then a classical continuum mechanics (CM) analysis based on the finite element method (FEM) to characterise the microscopic performance of the nanofilled composite material. The material under investigation is polyamide 12 (PA 12) randomly reinforced with fullerenes C60. At the first stage of the analysis, in order to capture the atomistic interfacial effects between C60 and PA 12, a very small cubic unit cell containing a C60 molecule, centrally positioned and surrounded by PA 12 molecular chains, is simulated via MD. Inter- and intra-molecular atomic interactions are described by using the Condensed Phase Optimized Molecular Potential for Atomistic Simulation Studies (COMPASS). According to the elastic properties data arisen by the MD simulations, an equivalent finite element volume with the same size as the unit cell is developed. At the second stage, a CM micromechanical representative volume element (RVE) of the C60 reinforced PA 12 is developed via FEM. The matrix phase of the RVE is discretised by using solid finite elements which represent the PA 12 mechanical behaviour while each C60 location is meshed with equivalent solid finite elements. Several multiscale simulations are performed to study the effect of the nanofiller volume fraction on the mechanical properties of the C60 reinforced PA 12 composite. Comparisons with other corresponding experimental results are attempted, where possible, to test the performance of the proposed method.

The electro-mechanical behavior of conductive filler reinforced polymer composite undergone large deformation: A combined numerical-analytical study

Abstract The electro-mechanical performance of flexible strain sensors under large deformation is of great concern due to their applications in measuring large strain. In this paper, we develop a combined numerical-analytical approach to study the electro-mechanical behavior of conductive filler reinforced polymer composite under uniaxial tensile load. This developed approach couples the displacement field of the microstructure and the evolution of the micro circuit. A 2D micromechanical representative volume element model is used to simulate the deformation and strain field in the composite, taking into consideration the random distribution of conductive aggregates and the hyperelastic mechanical properties of the polymer matrix. We then predict the evolution of electrical resistance using the tunneling conduction theory and transfer-matrix approach, based on the strain distribution of the material under various tensile deformations. The numerical results agree well with experimental results in terms of different material parameters and tensile conditions. This suggests the developed model is capable of predicting the nonlinear electro-mechanical response of the studied material under large deformation and revealing the effect of particle mass fraction on the electro-mechanical performance. The present approach can be served as a useful tool in the design and improvement of conductive filler-polymer composites for flexible strain sensor application.

Constructing micro-mechanical representative volume element of medium Mn steel from EBSD data

Medium Mn advanced high strength steel (AHSS) with significant combination of strength and ductility is one of candidates of the Third Generation AHSS. However, the specific plastic instability behavior of medium Mn steels is different from traditional steels and physical mechanism behind it is unclear. Representative volume element (RVE) has been proved to be applicable of describing microstructural deformation and revealing the micro-deformation mechanism. In this paper, a two dimensional micro-mechanical RVE of medium Mn steel, 7MnCA, is constructed from its electron back scatter diffraction (EBSD) data. The deformation behavior under uniaxial tension is investigated based on the constructed RVE models incorporating with phases morphology and distribution. The results show that the present RVEs constructed from EBSD data through image-processing algorithm with different filling strategies are capable to predict the macroscopic mechanical behavior of medium Mn steel with finite element analysis.

Virtual characterization and macroscopic material modeling of a carbon fiber-reinforced PA6 UD composite

Despite the increasing use of continuously fiber-reinforced composites with thermoplastic matrices in load-bearing structural applications, published research on their deformation behavior in general and their long-term behavior in particular is very limited. As a result, adequate material models to describe their time- and direction-dependent behavior on a macroscopic scale are lagging. The present study uses micromechanical representative volume element models and numerical homogenization techniques to analyze the material behavior of a carbon fiber-reinforced PA6 material as a function of load direction and time. The matrix is modeled as viscoelastic–viscoplastic. Based on the results of the representative volume element model, a homogenized macroscopic modeling approach is proposed. It is shown that the time dependency of the unidirectional composite is highly anisotropic. Plastic deformation occurs in the matrix, but may be neglected in the homogenized composite at laminate-relevant strain levels. The proposed homogenized orthotropic, nonlinear viscoelastic material model adequately captures the behavior of the heterogeneous unidirectional composite.

Quantitative Assessment of Variation in Poroelastic Properties of Composite Materials Using Micromechanical RVE Models

A poroelastic composite material, containing different material phases and filled with fluids, serves as a model to formulate the overall ablative behaviors of such materials. This article deals with the assessment of variation in nondeterministic poroelastic properties of two-phase composite materials using micromechanical representative volume element (RVE) models. Considering the configuration and arrangement of pores in a matrix phase, various RVEs are modeled and analyzed according to their porosity. In order to quantitatively investigate the effects of microstructure, changes in effective elastic moduli and poroelastic parameters are measured via finite element (FE) analysis. The poroelastic parameters are calculated from the effective elastic moduli and the pore-pressure-induced strains. The reliability of the numerical results is verified through image-based FE models with the actual shape of pores in carbon-phenolic ablative materials. Additionally, the variation of strain energy density is measured, which can possibly be used to evaluate microstress concentrations.

Micromechanical modeling on cyclic plastic behavior of unidirectional fiber reinforced aluminum matrix composites

This work investigates the cyclic plastic behavior of continuous fiber-reinforced aluminum matrix composites (CFAMCs) with different volume fractions of fiber up to a maximum value of 63.61% using micromechanical approach of modeling. Shakedown, ratcheting limit and load-bearing capacity have been studied. The FEM models, based on two dimensional micromechanical representative volume element (RVE) with a square packing geometry, were subjected to constant macro stress under off-axis loading condition and thermal cycling conditions. A number of direct numerical methods, under the Linear Matching Method (LMM) framework, are adopted for the determination of limit load, reverse plasticity limit and ratchet limit of AMCs. The typical micromechanical model adopted in all analysis consists of continuous fibers with circular cross section, embedded in an aluminum matrix. Two most common reinforcing materials alumina and silicon carbide are investigated. Various factors that affect shakedown and ratcheting behaviors of composites are analyzed and discussed, including effects of fiber volume fraction and temperature on the AMC's low cycle fatigue life.

Interfacial Micromechanics Assessment of Classical Rheological Models. I: Single Interface Size and Viscosity

AbstractCreep functions are often represented by “rheological models” consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters ar...

Interfacial Micromechanics Assessment of Classical Rheological Models. II: Multiple Interface Sizes and Viscosities

AbstractCreep functions are often represented by “rheological models” consisting of springs and dashpots, while the actual microscopic origins of creep, such as micro-sliding along interfaces, has only recently been explicitly considered in a continuum mechanics framework. The question arises whether formal analogies between the former and the latter can be derived: This question is answered here for the rheological models of the Kelvin-Voigt and Maxwell type. Thereby, it appears a full analogy between shear stresses and strains acting on the rheological models, and those acting on a micromechanical representative volume element consisting of an elastic solid matrix with embedded viscous interfaces, whereby the respective viscosity arises from layered polar fluids absorbed at these interfaces. The corresponding Kelvin-Voigt parameters are much simpler and more intuitively related to the micromechanical quantities, when compared to the Maxwell parameters. More specifically, rheological spring parameters ar...

Dynamic Modulus Prediction of Asphalt Concrete Mixtures through Computational Micromechanics

This paper presents a computational micromechanics modeling approach to predict the dynamic modulus of asphalt concrete mixtures. The modeling uses a finite element method combined with the micromechanical representative volume element (RVE) of mixtures and laboratory tests that characterize the properties of individual mixture constituents. The model treats asphalt concrete mixtures as heterogeneous with two primary phases: a linear viscoelastic fine aggregate matrix (FAM) phase and a linear elastic aggregate phase. The mechanical properties of each phase were experimentally obtained by conducting constitutive tests: oscillatory torsion tests for the viscoelastic FAM phase and quasistatic nanoindentation tests for the elastic aggregate particles. Material properties of each mixture phase were then used in the finite element simulation of two-dimensional mixture microstructures obtained from digital image processes of asphalt concrete mixtures. Model simulations were compared with the experimental dynamic moduli of asphalt concrete mixtures. Simulation results indicated that the micromechanical approach based on the mixture microstructure and phase properties could fairly predict the overall mixture properties that are typically obtained from laboratory mixture tests. Furthermore, the RVE dimension of 60 mm might be used to predict the undamaged viscoelastic stiffness characteristics of asphalt concrete mixtures with reduced computing efforts.

Failure behavior of resorcinol–formaldehyde latex coated aramid short‐fiber‐reinforced rubber sealing under transverse tension

ABSTRACTComposites composed of rubber, sepiolite fiber, and resorcinol–formaldehyde latex‐coated aramid short fibers were prepared. Mechanical and morphological characterizations were carried out. To investigate the effect of interfacial debonding on the failure behavior of short‐fiber‐reinforced rubber composites, a micromechanical representative volume element model for the composites was developed. The cohesive zone model was used to analyze the interfacial failure. We found that computational results were in good agreement with the experimental results when the interfacial fracture energy was 1 J/m2 and the interfacial strength was 10 MPa. A parametrical study on the interface and interphase of the composite was conducted. The results indicate that a good interfacial strength and a choice of interphase modulus between 40 and 50 MPa enhanced the ductile behavior and strength of the composite. The ductile properties of the composite also increased with increasing interfacial fracture energy. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41672.

Effect of Fiber Geometry and Representative Volume Element on Elastic and Thermal Properties of Unidirectional Fiber-Reinforced Composites

The aim of present work is focused on the evaluation of elastic and thermal properties of unidirectional fiber-reinforced polymer composites with different volume fractions of fiber up to 0.7 using micromechanical approach. Two ways for calculating the material properties, that is, analytical and numerical approaches, were presented. In numerical approach, finite element analysis was used to evaluate the elastic modulus and thermal conductivity of composite from the constituent material properties. The finite element model based on three-dimensional micromechanical representative volume element (RVE) with a square and hexagonal packing geometry was implemented by using finite element code ANSYS. Circular cross section of fiber and square cross section of fiber were considered to develop RVE. The periodic boundary conditions are applied to the RVE to calculate elastic modulus of composite. The steady state heat transfer simulations were performed in thermal analysis to calculate thermal conductivity of composite. In analytical approach, the elastic modulus is calculated by rule of mixture, Halpin-Tsai model, and periodic microstructure. Thermal conductivity is calculated analytically by using rule of mixture, the Chawla model, and the Hashin model. The material properties obtained using finite element techniques were compared with different analytical methods and good agreement was achieved. The results are affected by a number of parameters such as volume fraction of the fibers, geometry of fiber, and RVE.

Finite element investigations on the microstructure of fibre-reinforced composites

The effect of residual stress due to the curing process on damage evolution in unidirectional (UD) fibre-rein- forced polymer-matrix composites under longitudinal and transverse loading has been investigated using a three-dimen- sional micromechanical representative volume element (RVE) model with a hexagonal packing geometry and the finite element method. Residual stress has been determined by considering two contributions: volume shrinkage of matrix resin from the crosslink polymerization during isothermal curing and thermal contraction of both resin and fibre as a result of cooling from the curing temperature to room temperature. To examine the effect of residual stress on failure, a study based on different failure criteria and a stiffness degradation technique has been used for damage analysis of the RVE subjected to mechanical loading after curing for a range of fibre volume fractions. Predicted damage initiation and evolution are clearly influenced by the presence of residual stress.