Micromechanical analysis of yielding of metal matrix composites

A recently proposed micromechanics model is employed to generate initial yield surfaces of unidirectional and cross-ply metal matrix composites under a variety of loading conditions. The yield surfaces are calculated using two different methodologies: on the basis of local matrix stresses and average stresses in the entire matrix phase. It is shown that the results obtained on the basis of local matrix stresses correlate very well with finite-element predictions for most loading directions considered in the present investigation. A critical direction or cone of directions is found that should be avoided with the outlined micromechanics model. This direction corresponds to a particular combination of longitudinal tension (compression) and equal biaxial transverse tension (compression) whose ratio is a function of the constituent properties.It is also illustrated that the results generated on the basis of average matrix stresses generally underestimate initial yielding (i.e., predict higher yield stresses), the extent of which may be significant depending on the direction of loading. Thus, the use of average matrix stresses in analyzing elastoplastic response of composites should be approached with caution.     

Numerical characterization of effective fully coupled thermo-electro-magneto-viscoelastic-plastic response of smart composites

The focus of the present paper is to construct a general purpose micromechanics model to predict the effective fully coupled time-dependent and non-linear multiphysics responses of smart composites. The present model is established on the basis of the variational asymptotic method and implemented using the finite element method. In light of the time-dependent and non-linear characteristics of composites, an incremental procedure in conjunction with an instantaneous tangential electromagnetomechanical matrix of composites was established. The accuracy of the proposed model was verified through the comparison with ABAQUS results. Finally, a numerical example was employed to demonstrate the capability of the proposed model.     

Local effective thermoelastic properties of graded random structure matrix composites

Summary  We consider a linearly thermoelastic composite medium, which consists of a homogeneous matrix containing a statistically inhomogeneous random set of ellipsoidal uncoated or coated inclusions, where the concentration of the inclusions is a function of the coordinates (functionally graded material). Effective properties, such as compliance and thermal expansion coefficient, as well as first statistical moments of stresses in the components are estimated for the general case of inhomogeneity of the thermoelastic inclusion properties. The micromechanical approach is based on the Green function technique as well as on the generalization of the multiparticle effective field method (MEFM), previously proposed for the research of statistically homogeneous random structure composites. The hypothesis of effective field homogeneity near the inclusions is used; nonlocal effects of overall constitutive relations are not considered. Nonlocal dependences of local effective thermoelastic properties as well as those of conditional averages of the stresses in the components on the concentration of the inclusions are demonstrated. Received 11 November 1999; accepted for publication 4 May 2000     

Incremental analysis for nonlinear rubber-like materials by hybrid stress finite element

In this paper, on the basis of the incremental Reissner variational principle, a nonlinear finite element analysis has been accomplished and a formulation of hybrid stress element has been presented for incompressible Mooney rubber-like materials. The corrected terms of the non-equilibrium force and the incompressibility deviation are considered in the formulation. The computed values of numerical example agree very closely with the exact solution.     

STATISTIC MODELING OF THE CREEP BEHAVIOR OF METAL MATRIX COMPOSITES BASED ON FINITE ELEMENT ANALYSIS

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Homogenization of elasto-plastic composites coupled with a nonlinear finite element analysis of the equivalent inclusion problem

This paper deals with the micromechanical modeling of particle reinforced elasto-plastic composites under general non-monotonic loading histories. Incremental mean-field (MF) homogenization models offer an excellent cost-effective solution, however there are cases where their predictions are inaccurate. Here, we assess the applicability of the equivalent inclusion representation, which sustains many homogenization schemes. To this end, MF models are fully coupled with a finite element (FE) solution of the equivalent inclusion problem (EIP). Consequently, Eshelby’s tensor is not used and most (but not all) approximations involved in the generalization of MF models from linear elasticity to the nonlinear regime are avoided. The proposal is implemented for Mori-Tanaka (M-T) and dilute inclusion models and applied to several composite systems with elasto-plastic matrix and spherical or ellipsoidal particles, subjected to various loadings (tension, plane strain, cyclic tension/compression). The predictions are verified against reference full-field FE simulations of multiparticle cells. Results show that the M-T model coupled with the nonlinear FE solution of the EIP is very accurate at the macro level up to 25% volume fraction of reinforcement, while the phase averages remain accurate as long as the volume fraction does not exceed 15%. The strain concentration tensor computed almost exactly from single inclusion FE analysis is compared against approximate expressions assumed by classical MF models. Implications for the development of advanced MF homogenization models are discussed.     

Two-dimensional fractal-like finite element method for thermoelastic crack analysis

The fractal-like finite element method has been proved to be very efficient and accurate in two-dimensional static and dynamic crack problems. In this paper, we extend our previous study to include the thermal effect for two-dimensional isotropic thermal crack problems. Both the temperature intensity factor and thermal stress intensity factor can be calculated directly. The temperature distribution is first found, which is imposed thereafter as a thermal load in the elastic problem. The transformation function used in the study has been found analytically. The effects of different thermal loading on the thermal stress intensity factor are presented. The numerical examples are compared with the results from other methods and find to be in good agreement.     

Effective thermoelastic properties of graded doublyperiodic particulate matrix composites in varying externalstress fields

We consider a linear elastic composite medium, which consists of a homogeneousmatrix containing aligned ellipsoidal uncoated or coated inclusions arranged in a doubly periodicarray and subjected to inhomogeneous boundary conditions. The hypothesis of effective fieldhomogeneity near the inclusions is used. The general integral equation obtained reduces theanalysis of infinite number of inclusion problems to the analysis of a finite number of inclusions insome representative volume element (RVE) . The integral equation is solved by a modifiedversion of the Neumann series; the fast convergence of this method is demonstrated for concreteexamples. The nonlocal macroscopic constitutive equation relating the cell averages of stress andstrain is derived in explicit iterative form of an integral equation. A doubly periodic inclusion fieldin a finite ply subjected to a stress gradient along the functionally graded direction is considered.The stresses averaged over the cell are explicitly represented as functions of the boundaryconditions. Finally, the employed of proposed explicit relations for numerical simulations oftensors describing the local and nonlocal effective elastic properties of finite inclusion pliescontaining a simple cubic lattice of rigid inclusions and voids are considered. The local andnonlocal parts of average strains are estimated for inclusion plies of different thickness. Theboundary layers and scale effects for effective local and nonlocal effective properties as well as foraverage stresses will be revealed.     

Micromechanical analysis of fibrous piezoelectric composites with imperfectly bonded adherence

In this work, two-phase parallel fiber-reinforced periodic piezoelectric composites are considered wherein the constituents exhibit transverse isotropy and the cells have different configurations. Mechanical imperfect contact at the interface of the piezoelectric composites is studied via linear spring model. The statement of the problem for two-phase piezoelectric composites with mechanical imperfect contact is given. The local problems are formulated by means of the asymptotic homogenization method, and their solutions are found using complex variable theory. Analytical formulae are obtained for the effective properties of the composites with spring imperfect type of contact and different rhombic cells. Using the concept of a representative volume element (RVE), a finite element model is created, which combines the angular distribution of fibers and imperfect contact conditions (spring type) between the phases. Periodic boundary conditions are applied to the RVE, so that effective material properties can be derived. The fibers are distributed in such a way that the microstructure is characterized by a rhombic cell. The presented numerical homogenization technique is validated by comparing results with theoretical approach reported in the literature. Some studies of particular cases, numerical examples, and comparisons between the two aforementioned methods with other theoretical results illustrate that the model is efficient for the analysis of composites with presence of rhombic cells and the aforementioned imperfect contact.     

General solutions of coupled thermoelastic problem

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Meso-macro modelling of fibre-reinforced rubber-like composites exhibiting large elastoplastic deformation

Many composites consist of a fabric structure embedded in a matrix material. As an example, in the present paper, the case of pneumatic membranes is considered. Fibres are often made of material which shows noticeable plastic deformation. The stiffness of the fibres determines the overall stiffness of the material such that the correct modelling of the orthotropy of the composite is very important. In addition, the structure experiences large deformations which must be accounted for. Suitable models for this type of materials are therefore derived in the framework of finite anisotropic plasticity. A main problem is, however, the lack of experimental data in the literature. For this reason, a computer model of the composite is set up for numerical experiments. In this way, sufficient data can be generated. The present continuum mechanical model based on these “artificial” test data can be efficiently implemented into a finite element formulation. Using a special integration algorithm, the non-linear equation system consisting initially of 10 equations reduces to two non-linear scalar equations.     

On non-associative anisotropic finite plasticity fully coupled with isotropic ductile damage for metal forming

In this work, non-associative finite strain anisotropic elastoplasticity fully coupled with ductile damage is considered using a thermodynamically consistent framework. First, the kinematics of large strain based on multiplicative decomposition of the total transformation gradient using the rotating frame formulation, is recalled and different objective derivatives defined. By using different anisotropic equivalent stresses (quadratic and non-quadratic) in yield function and in plastic potential, the evolution equations for all the dissipative phenomena are deduced from the generalized normality rule applied to the plastic potential while the consistency condition is still applied to the yield function. The effect of the objective derivatives and the equivalent stresses (quadratic or non-quadratic) on the plastic flow anisotropy and the hardening evolution with damage is considered. Numerical aspects mainly related to the time integration of the fully coupled constitutive equations are discussed. Applications are made to the AISI 304 sheet metal by considering different loading paths as tensile, shear, plane tensile and bulge tests. For each loading path the effect of the rotating frame, the equivalent stress (quadratic or non-quadratic) and the normality rule (with respect to yield function or to the plastic potential) are discussed on the light of some available experimental results.     

Three-dimensional thermoelastic analysis of finite length laminated cylindrical panels with functionally graded layers

Based on the 3D thermoelasticity theory, the thermoelastic analysis of laminated cylindrical panels with finite length and functionally graded (FG) layers subjected to three-dimensional (3D) thermal loading are presented. The material properties are assumed to be temperature-dependent and graded in the thickness direction. The variations of the field variables across the panel thickness are accurately modeled by using a layerwise differential quadrature (DQ) approach. After validating the approach, as an important application, two common types of FG sandwich cylindrical panels, namely, the sandwich panels with FG face sheets and homogeneous core and the sandwich panels with homogeneous face sheets and FG core are analyzed. The effect of micromechanical modeling of the material properties on the thermoelastic behavior of the panels is studied by comparing the results obtained using the rule of mixture and Mori–Tanaka scheme. The comparison studies reveal that the difference between the results of the two micromechanical models is very small and can be neglected. Then, the effects of different geometrical parameters, material graded index and also the temperature dependence of the material properties on the thermoelastic behavior of the FG sandwich cylindrical panels are carried out.     

Mixed-mode stress intensity factors of 3D interface crack in fully coupled electromagnetothermoelastic multiphase composites

This contribution presents an extended hypersingular intergro-differential equation (E-HIDE) method for modeling the 3D interface crack problem in fully coupled electromagnetothermoelastic anisotropic multiphase composites under extended electro-magneto-thermo-elastic coupled loads through theoretical analysis and numerical simulations. First, based on the extended boundary element method, the 3D interface crack problem is reduced to solving a set of E-HIDEs coupled with extended boundary integral equations, in which the unknown functions are the extended displacement discontinuities. Then, the behavior of the extended singular stress indices around the interface crack front terminating at the interface is analyzed by the extended main-part analysis. The extended stress intensity factors near the crack front are defined. In addition, a numerical method for a 3D interface crack problem subjected to extended loads is proposed, in which the extended displacement discontinuities are approximated by the product of basic density functions and polynomials. Finally, the radiation distribution of extended stress intensity factors at the interface crack surface are calculated, and the results are presented toward demonstrating the applicability of the proposed method.     

Elastoplastic modeling of circular fiber-reinforced ductile matrix composites considering a finite RVE

A micromechanical elastoplastic damage model considering a finite RVE is proposed to predict the overall elastoplastic damage behavior of circular fiber-reinforced ductile (matrix) composites. The constitutive damage model proposed in our preceding work (Kim and Lee, 2009) considering a finite Eshelby’s tensor (Li et al., 2005, Wang et al., 2005) is extended to accommodate the elastoplastic behavior of the composites. On the basis of the exterior-point Eshelby’s tensor for circular inclusions and the ensemble-averaged effective yield criterion, a micromechanical framework for predicting the effective elastoplastic damage behavior of ductile composites is derived. A series of numerical simulations are carried out to illustrate stress–strain response of the proposed micromechanical framework and to examine the influence of a Weibull parameter on the elastoplastic behavior of the composites. Furthermore, comparisons between the present predictions and experimental data available in the literature are made to further assess the predictive capability of the proposed model.     

Influence of fiber architecture on the inelastic response of metal matrix composites

This three-part paper focuses on the effect of fiber architecture (i.e. shape and distribution) on the elastic and inelastic response of unidirectionally reinforced metal matrix composites (MMCs). The first part provides an annotated survey of the literature; it is presented as an historical perspective dealing with the effects of fiber shape and distribution on the response of advanced polymeric matrix composites and MMCs. A summary of the state of teh art will assist in defining new directions in this quickly reviving area of research. The second part outlines a recently developed analytical micromechanics model that is particularly well suited for studying the influence of these effects on the response of MMCs. This micromechanics model, referred to as the generalized method of cells (GMC), can predict the overall inelastic behavior of unidirectional, multiphase composites, given the properties of the constituents. The model is also general enough to predict the response of unidirectional composites that are reinforced by either continuous or discontinuous fibers, with different inclusion shapes and spatial arrangements, in the presence of either perfect or imperfect interfaces and/or interfacial layers. Recent developments on this promising model, as well as directions for future enhancements of the model's predictive capability, are included. Finally, the third part provides qualitative results generated by using GMC for a representative titanium matrix composite system, SCS-6/TIMETAL 21S. The results presented correctly demonstrate the relative effects of fiber arrangement and shape on the longitudinal and transverse stress-strain and creep behavior of MMCs, with both strong and weak fiber/matrix interfacial bonds. Fiber arrangements included square, square-diagonal, hexagonal and rectangular periodic arrays, as well as a random array. The fiber shapes were circular, square, and cross-shaped cross-sections. The effect of fiber volume fraction on the stress-strain response is also discussed, as is the thus-far poorly documented strain rate sensitivity effect. In addition to the well-documented features of the architecture-dependent behavior of continuously reinforced two-phase MMCs, new results are presented about continuous multiphase internal architectures. Specifically, the stress-strain and creep responses of composites with different size fibers and different internal arrangements and bond strengths are investigated; the aim was to determine the feasibility of using this approach to enhance the transverse toughness and creep resistance of titanium matrix composites (TMCs).     

On the finite torsion and radial heating of thermoelastic cylinders

The non-linear response to finite torsion accompanied by arbitrary radial heating of a cylinder of incompressible thermoelastic material with temperature-independent heat flux response is shown to be characterized completely by constitutive data collected from a block of the same material in a state of simple shear with uniform heating normal to the plane of shear.