Plasticity of a two-phase composite with partially debonded inclusions

The effective elastoplastic behavior of a two-phase composite consisting of partially debonded elastic inclusions and a ductile matrix is investigated by a homogenization method. The method drew information from a recent study by the authors on the effective elastic moduli of the said composite and from an energy approach suggested by Qui and Weng, J. Appl. Mech., 59, 261 [1992] to address the homogenized plastic state of the heterogeneously deformed ductile matrix. Two types of partial debonding configuration are considered; the first is on the top and bottom of the aligned oblate inclusions and the other is on the lateral surface of the prolate ones, with special reference to spherical inclusions for both types of debonding. The transversely isotropic elastoplastic properties of the partially debonded composite are found to be highly dependent upon the debonding mode and the volume concentration and shape of inclusions. A damage mechanics based on Weibull's statistical function is also proposed to study the progressive partial debonding of the initially bonded composite under pure tension and under biaxial tension, respectively, for these two types of partial debonding. It is found that the interfacial strength, particle concentration, inclusion shape and debonding mode all play significant role in the overall response of the heterogeneous system during the progressive debonding process.     

弹塑性复合材料力学性能的细观研究

应用细观力学的Eshelby等效夹杂理论研究了复合材料的弹塑性问题。以铝基复合材料为例,建立了多轴载荷下复合材料弹塑性应力-应变关系,并且理论预报与实验结果符合较好,分析了夹杂形状、体积分数及加载路径对材料宏观性能的影响。同时,还研究了热塑性复合材料热膨胀系数与工艺温度之间的变化规律,分析了热残余应变对材料设计的影响。     

On micromechanical modeling of particulate composites with inclusions of various shapes

The effective elastic properties of statistically homogeneous two-phase particulate composites are considered. Several first-order micromechanical models are re-written in terms of the inclusion compliance contribution tensor (H-tensor). This tensor is a convenient tool to evaluate contribution of arbitrarily shaped inclusions and cavities to the overall composite properties.For any inclusion shape, the procedure starts with calculation of the H-tensor for a single inclusion. The non-interaction approximation is obtained by direct summation. More advanced micromechanical schemes are derived by substituting the non-interaction inclusion compliance contribution tensor into the formulae provided in the paper. The proposed procedure is illustrated by considering several two-dimensional and three-dimensional examples.     

Explicit cross-property correlations for anisotropic two-phase composite materials

Explicit correlations between two groups of anisotropic effective properties—conductivity and elasticity—are established for two-phase composite materials with anisotropic microstructures (non-randomly oriented inclusions of non-spherical shapes). The correlations are derived in the framework of the non-interaction approximation. The elasticity tensor is expressed in terms of the conductivity tensor in closed form. Applications to realistic microstructures, containing mixtures of diverse inclusion shapes are given. Compliance/stiffness contribution tensors of an inclusion, that characterize the inclusion's contribution to the overall elastic response, are derived in the course of analysis; these results are of interest on their own.     

A micromechanical model of elastoplastic and damage behavior of a cohesive geomaterial

The present study is devoted to the development and validation of a nonlinear homogenization approach of the mechanical behavior of Callovo-Oxfordian argillites. The material is modeled as an heterogeneous composite composed of an elastoplastic clay matrix and of linear elastic or elastic damage inclusions. The macroscopic constitutive law is obtained by adapting the incremental method proposed by Hill [Hill, R., 1965. Continuum micro-mechanics of elastoplastic polycrystals. J. Mech. Phys. Solids 13, 89–101]. The approach consists in formulating the macroscopic tangent operator of the material by considering the nonlinear local behavior of each phase. Due to the matrix/inclusion morphology of the microstructure of the argillite, a Mori–Tanaka scheme is considered for the localization step. The developed model is first compared to Finite Element calculations and then validated and applied for the prediction of the macroscopic stress–strain responses of argillites.     

Mean Green operators and Eshelby tensors for hemispherical inclusions and hemisphere interactions in spheres. Application to bi-material spherical inclusions in isotropic spaces

This paper mainly presents an exact expression for the mean shape function of a hemispherical inclusion, from which are obtained analytical forms for the mean Green operator (GO) and Eshelby tensor of this hemi-sphere as well as for the related mean pair interaction Green operator (IGO) between the two hemi-spheres of a sphere, in media with isotropic (elastic or dielectric) properties. We secondly address the problem of bi-material inclusions, in the sense of a two-phase compact set of two or a few elementary domains, a particular inclusion pattern case for which we give an estimate of the mean stress and strain in each phase accounting for interactions. This estimate results from knowing the mean GO (or Eshelby tensor) for each pattern element plus the mean IGO between element pairs, what is rarely fulfilled analytically. The here solved case for bi-material spherical inclusions made of two different hemispherical elements adds to the recently made available solution for bi-material cylindrical inclusions made of piled coaxial finite cylinders. The obtained mean stress estimates are exemplified able to satisfactorily match with FEM calculations up to highly contrasted bi-material inclusions. Other types of bi-material spherical inclusions are mentioned for which the mean GOs for the sub-domains and their pair IGO can be obtained without calculation, owing to particular symmetries of the phase arrangement. Mean GOs and IGOs are also useful in certain homogenization frameworks yielding overall property estimates for inclusion-reinforced matrices. Further discussions and specific applications will be presented in forthcoming papers.     

Analysis of elastoplastic deformation in metal-matrix composites with particulate reinforcements

In this paper, elastoplastic stress-strain behavior during tensile deformation of an aluminum alloy matrix composite containing alumina circular and non-circular particles is analyzed. In terms of cell models in conjunction with continuum plasticity theory, various periodic arrays of particles are assumed in a three-dimensional finite element simulation. The geometrical effects of particle volume fraction, shape, aspect ratio, array and distribution, as well as non-circular particle orientation on the overall elastoplastic stress-strain behavior are examined in view to design optimum microstructures of the composites. The project supported by the National Natural Science Foundation of China and the State Education Commission of China     

Stress-resultant plasticity theories for composite laminated plates

Constitutive laws are presented for the inelastic analysis of laminated composite plates. The implications of using an elastoplastic theory, applied in a stress-resultant formulation, are discussed and investigated. Two different stress-resultant plasticity theories are proposed, both of which overlook the matrix and fiber inelastic behavior and describe the inelastic response of the laminate as a function of overall laminate properties. Results from numerical experiments with the proposed models are compared with results obtained using a micromechanical elastoplastic composite constitutive model.     

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.     

压电复合材料中的Eshelby夹杂问题

通过采用解析延拓和共形映射技术，获得了压电复合材料中有关Eshelby夹杂几个典型问题的精确弹性解答，即横观各向同性压电介质中任意形状的Eshelby夹杂与圆柱异相夹杂间相互作用；一般各向异性压电介质中任意形状的Eshelby夹杂与双压电材料所形成界面的相互作用．成功求解这些问题的关健在于构造一个辅助函数．与Ru所采用的方法不同，所引入的辅助函数在无穷远点不存在极点，从而使得所展开的分析更加自然合理．分析结果清楚地揭示出Eshelby夹杂的存在对压电复合材料机电耦合响应将产生不容被忽视的影响．很典型的一个例于是当一个Eshelby椭圆夹杂与圆柱异相夹杂相互作用时，每个夹杂体内部的应力场和电场都将是不均匀的；另一个例于是位于界面附近的Eshelby夹杂有可能是界面发生损伤的一个重要原因．     

A two-level micromechanical theory for a shape-memory alloy reinforced composite

A two-level micromechanical theory is developed to study the influence of the shape and volume concentration of shape-memory alloy (SMA) inclusions on the overall stress–strain behavior of a SMA-reinforced composite. The first level exists on the smaller SMA level, in which, under the action of stress, parent austenite may transform into martensite. The second level is on the larger scale consisting of the metastable SMA inclusions and an inactive polymer matrix. The evolution of martensite microstructure is evaluated from the irreversible thermodynamics, in conjunction with the micromechanics and physics of martensitic transformation. By taking martensite to exist in the form of thin plates on the micro scale and assuming SMA inclusions to be homogeneously aligned spheroids on the macro scale, the overall stress–strain behaviors of a NiTi-reinforced composite are calculated for various SMA shapes and concentrations. The results indicate that, under a tensile axial loading, martensitic transformation is easier to take place when SMA inclusions exist in the form of long fibers, but most difficult to occur when they are in the form of flat discs. In general the levels of the applied stress at which martensite transformation commences, finishes, and austenitic transformation starts, and finishes, are found to decrease with increasing aspect ratio of the SMA inclusions while the damping capacity increases with it; these properties point to the advantage of using fibrous composites for actuators or sensors under a tensile loading.     

Stress concentrations in the particulate composite with transversely isotropic phases

The accurate series solution have been obtained of the elasticity theory problem for a transversely isotropic solid containing a finite or infinite periodic array of anisotropic spherical inclusions. The method of solution has been developed based on the multipole expansion technique. The basic idea of method consists in expansion the displacement vector into a series over the set of vectorial functions satisfying the governing equations of elastic equilibrium. The re-expansion formulae derived for these functions provide exact satisfaction of the interfacial boundary conditions. As a result, the primary spatial boundary-value problem is reduced to an infinite set of linear algebraic equations. The method has been applied systematically to solve for three models of composite, namely a single inclusion, a finite array of inclusions and an infinite periodic array of inclusions, respectively, embedded in a transversely isotropic solid. The numerical results are presented demonstrating that elastic properties mismatch, anisotropy degree, orientation of the anisotropy axes and interactions between the inclusions can produce significant local stress concentration and, thus, affect greatly the overall elastic behavior of composite.     

Self-consistent modeling of large plastic deformation, texture and morphology evolution in semi-crystalline polymers

A self-consistent model for semi-crystalline polymers is proposed to study their constitutive behavior, texture and morphology evolution during large plastic deformation. The material is considered as an aggregate of composite inclusions, each representing a stack of crystalline lamellae with their adjacent amorphous layers. The deformation within the inclusions is volume-averaged over the phases. The interlamellar shear is modeled as an additional slip system with a slip direction depending on the inclusion's stress. Hardening of the amorphous phase due to molecular orientation and, eventually, coarse slip, is introduced via Arruda-Boyce hardening law for the corresponding plastic resistance. The morphology evolution is accounted for through the change of shape of the inclusions under the applied deformation gradient. The overall behavior is obtained via a viscoplastic tangent self-consistent scheme. The model is applied to high density polyethylene (HDPE). The stress-strain response, texture and morphology changes are simulated under different modes of straining and compared to experimental data as well as to the predictions of other models.     

功能梯度界面相对周期分布纤维增强复合材料反平面剪切的影响

基于复变函数理论和边界配点法,探索了功能梯度界面相在周期均匀分布纤维增强复合材料反平面剪切问题中所起的作用.由于纤维在复合材料基体中的周期分布是均匀的,将其简化成含一功能梯度界面相夹杂的方形单胞.采用分层均匀化方法,将功能梯度界面相离散成K层界面层.当K足够大时,每个界面层可视为匀质材料,同时计算得到的复合材料宏观性能...     

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).     

Micromechanical modeling of the elasto-viscoplastic behavior of semi-crystalline polymers

A micromechanically based constitutive model for the elasto-viscoplastic deformation and texture evolution of semi-crystalline polymers is developed. The model idealizes the microstructure to consist of an aggregate of two-phase layered composite inclusions. A new framework for the composite inclusion model is formulated to facilitate the use of finite deformation elasto-viscoplastic constitutive models for each constituent phase. The crystalline lamellae are modeled as anisotropic elastic with plastic flow occurring via crystallographic slip. The amorphous phase is modeled as isotropic elastic with plastic flow being a rate-dependent process with strain hardening resulting from molecular orientation. The volume-averaged deformation and stress within the inclusions are related to the macroscopic fields by a hybrid interaction model. The uniaxial compression of initially isotropic high density polyethylene (HDPE) is taken as a case study. The ability of the model to capture the elasto-plastic stress-strain behavior of HDPE during monotonic and cyclic loading, the evolution of anisotropy, and the effect of crystallinity on initial modulus, yield stress, post-yield behavior and unloading-reloading cycles are presented.     

Magneto-electro-elastic coated inclusion problem and its application to magnetic-piezoelectric composite materials

In this work, a micromechanical model for the estimate of the magneto-electro-elastic behavior of the magnetic-piezoelectric composites with coated reinforcements is proposed. The coating is considered as a thin layer with properties different from those of the inclusion and the matrix. The micromechanical approach based on the Green’s functions techniques and on the interfacial operators is designed for solving the magneto-electro-elastic inhomogeneous coated inclusion problem. The effective magneto-electro-elastic properties of the composite containing thinly coated inclusions are obtained through the Mori–Tanaka’s model. Numerical investigations into magneto-electro-elastic moduli responsible for the magneto-electric coupling are presented as functions of the volume fraction and characteristics of the coated inclusions. Comparisons with existing models are presented for various shape and orientation of the coated inclusions.     

An elastoplastic multi-level damage model for ductile matrix composites considering evolutionary weakened interface

An elastoplastic multi-level damage model considering evolutionary weakened interface is developed in this work to predict the effective elastoplastic behavior and multi-level damage evolution in particle reinforced ductile matrix composites (PRDMCs). The elastoplastic multi-level damage model is micromechanically derived on the basis of the ensemble-volume averaging procedure and the first-order effects of eigenstrains. The Eshelby’s tensor for an ellipsoidal inclusion with slightly weakened interface [Qu, J., 1993a. Eshelby tensor for an elastic inclusion with slightly weakened interfaces. Journal of Applied Mechanics 60 (4), 1048–1050; Qu, J., 1993b. The effect of slightly weakened interfaces on the overall elastic properties of composite materials. Mechanics of Materials, 14, 269–281] is adopted to model particles having mildly or severely weakened interface, and a multi-level damage model [Lee, H.K., Pyo, S.H., in press. Multi-level modeling of effective elastic behavior and progressive weakened interface in particulate composites. Composites Science and Technology] in accordance with the Weibull’s probabilistic function is employed to describe the sequential, progressive weakened interface in the composites. Numerical examples corresponding to uniaxial, biaxial and triaxial tension loadings are solved to illustrate the potential of the proposed micromechanical framework. A series of parametric analysis are carried out to investigate the influence of model parameters on the progression of weakened interface in the composites. Furthermore, the present prediction is compared with available experimental data in the literature to verify the proposed elastoplastic multi-level damage model.     

Plastic deformation anisotropy and work-hardening of composite materials

An energy-balance method is applied to discuss plastic anisotropy and work-hardening rate of a composite material. It is found that aligned fibers introduce a strongly anisotropic mode of plastic deformation while randomly-oriented inclusions produce isotropic plastic deformation. The hardening rate due to randomly-oriented inclusions is shown to be independent of the inclusion shape, and to be equal to that due to spherical inclusions when the elastic constants of the inclusions are the same as those of the matrix.