Effect of elastic–plastic matrix on thermo-mechanical response of continuous anisotropic fiber-reinforced composites

Based on a concentric cylinder model, the analytical elastic–plastic solution of deformations and stresses for the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers subjected to axisymmetric thermo-mechanical loading is developed. How the plasticity, volume fraction, physical and mechanical properties of the matrix affect the elastic–plastic thermo-mechanical response of the composites is investigated. The plasticity of the matrix decreases greatly the axial compressive stress in the matrix, but more noticeably increases the axial compressive stress in the fiber. For the composites reinforced with transversely isotropic, circumferentially orthotropic and radially orthotropic fibers, decreasing the volume fraction, thermal expansion coefficient and Young's modulus, and increasing the yield stress and hardening parameter of the matrix can lower the maximum equivalent stress of the fiber. However, increasing the yield stress and hardening parameter of the matrix raises the maximum equivalent stress of the matrix.     

Elastic–plastic thermomechanical response of composite co-axial cylinders

A new method is developed in this paper to deal with the thermomechanical response of continuous fiber-reinforced composites. Treating the matrix as an elastic-perfectly plastic solid, the analytical formulae of the deformations and stresses of the matrix are obtained from the plasticity theory, axisymmetric equilibrium equation, and stress–strain and strain–displacement relations. The fiber is taken to be an anisotropic, elastic material, and the formulae calculating its deformations and stresses are also presented. The boundary conditions and the consistence of deformations and stresses between the fiber and matrix, and between elastic and plastic regions of the matrix are employed to determine the unknown constants in the analytical formulae. With the developed method, the thermomechanical stress distributions in composites reinforced with circumferentially orthotropic, radially orthotropic and transversely isotropic fibers are investigated, and how the elastic-perfectly plastic property and different materials of the matrix affect the thermomechanical response of the composites is discussed. For the thermomechanical loads and composite systems given in this paper, the elastic-perfectly plastic property of the matrix can reduce the compressive stresses in the fiber, and the tensile circumferential and axial stresses in the matrix. A strong matrix can raise the compressive stresses in the fiber, and the tensile circumferential and axial stresses in the matrix.     

On the local elastic–plastic behaviour of the interface in titanium/silicon carbide composites

The purpose of this study is to conduct a high-resolution nonlinear finite element analysis of the elastic–plastic behaviour of titanium/silicon carbide composites subject to transverse loading. This class of metal matrix composites is designed for the next generation of supersonic jet engines and deserves careful assessment of its behaviour under thermo mechanical loads. Three aspects of the work are accordingly examined. The first is concerned with the development of a representative unit cell capable of accurately describing the local elastic–plastic behaviour of the interface in metal matrix composites under thermal and mechanical loads. The second is concerned with the determination of the influence of mismatch in the mechanical properties between the inhomogeneity and the matrix upon the induced stress fields and the plastic zone development and its growth. The third is concerned with unloading and the role played by the interface upon residual stresses. It is found that the maximum interfacial stress in the matrix appears in the case involving cooling from the relieving temperature with subsequent applied compressive loading. It is also found that the mismatch in mechanical properties between the matrix and the inhomogeneity introduces significant changes in the stress distribution in the matrix. Specifically, it is observed that the maximum radial and tangential stresses in the matrix take place at the interface. The plastic deformation of the matrix leads to a relaxation of these stresses and assists in developing a more uniform interfacial stress distribution. However, the matrix stresses and the resulting equivalent plastic strains still reach their maximum values at that interface. The results show similarities in the patterns of the interfacial stress distribution and plastic zone development for all ranges of fibre volume fractions and loading levels examined. However, they also show marked differences in both the magnitude and patterns of matrix stress distribution between the adjacent inhomogeneities as a result of interaction effects between the fibres.     

Micromechanics of stress transfer through the interphase in fiber-reinforced composites

A micromechanical model to predict the interphasial/interfacial stress transfer in a three-phase fiber-reinforced composite is presented. The axisymmetric system consists of a fiber embedded in a compliant matrix having an interphase between them. Each constituent of the composite is regarded as a linear elastic continuum. The matrix is treated as an isotropic material while the fiber and interphase are considered as a transversely isotropic material. Traction-free boundary conditions are strictly enforced. It is assumed that the interfaces are perfect and strong. A pair of uncoupled governing partial differential equations is obtained in terms of unknown displacements. Furthermore, assuming that the Eigenvalues exist for this system of equations, Eigenfunction expansion method is employed to derive an exact solution in terms of the Bessel functions. Analytical solutions are obtained for free boundary conditions at the external surface of the matrix cylinder to model a single fiber pull-out problem, and for fixed boundary conditions to approximately model a hexagonal array of fibers in the matrix material. This formulation provides an analytical framework for the analysis of interphasial and interfacial stresses as well as displacements in the entire 3D axisymmetric system. Finite element (FE) analysis was also performed to simulate stress transfer from the fiber to the matrix through the interphase. Analytically obtained stress fields are verified with FE results. Shear and radial interphasial stresses provide insight into the design of engineered interfaces/interphases.     

Analytical investigation of thermomechanical stresses in graded interphase between the fiber and the matrix

In this article, the thermomechanical stresses in the graded interphase between the fiber and the matrix in fiber-reinforced composites are investigated. First, the general theoretical analysis of two-dimensional steady-state mechanical and thermal stresses in a graded cylinder along the radial direction with the Power Law and Exponential Law distribution of the material properties is developed. Then the theoretical solution is applied to investigate the mechanical stresses and the thermal stresses of the fiber-matrix interphase, and the effects of material graded constant on the mechanical stresses and thermal stresses are discussed. Finally, the stress transfer mechanisms in the graded interphase are investigated which indicates that the total stresses in the fiber-matrix interphase increased with the increasing of the interphase thickness if the material graded constant varied with the radius in Power Law, but decreased in Exponential Law.     

A continuum elastic–plastic model for woven-fabric/polymer-matrix composite materials under biaxial stresses

In this study a simple continuum model for the macro-mechanical prediction of the elastic–plastic behavior of woven-fabric/polymer-matrix composites has been proposed. This model uses a scalar hardening parameter (which is a function of the current applied stress state) instead of an effective stress-strain relation to determine plastic strain increments. For simplicity, the stresses are expressed as invariants based on the material symmetry. It has been shown, by the use of experimental data for two different woven-fabric/polymer-matrix composite materials, that the newly proposed model accurately describes the non-linear mechanical behavior for different in-plane biaxial stress states ranging from pure shear to pure tension.     

Crack in an imperfect interface in composites

The behavior of cracks at the interface of composites is studied. The geometry of the composite is idealized as two-dimensional, isotropic, linearly “elastic” infinite strips made of two different materials joined by a damaged layer approximated by continuous distributed shear and tension springs. The damage considered in the layer is an interface crack. A general formulation is developed in terms of two simultaneous integral equations. An asymptotic analysis of the integral equations based on Muskhelishvili's techniques reveals logarithmic singularities in the normal (cleavage) stresses and strain functions at the crack tips. The special case of two bonded half-planes is also discussed. Parametric studies at a microscopic level are conducted for an interphase crack between the fiber and the matrix, and at a macroscopic level for an adhesive layer crack between two laminae.     

Modeling the effective elastic properties of nanocomposites with circular straight CNT fibers reinforced in the epoxy matrix

In the present study, the consistent effective elastic properties of straight, circular carbon nanotube epoxy composites are derived using the micromechanics theory. The CNT composites are known to provide high stiffness and elastic properties when the shape of the fibers is cylindrical and straight. Accordingly, in the present work, the effective elastic moduli of composite are newly obtained for straight, circular CNTs aligned in the specified direction as well as distributed randomly in the matrix. In this direction, novel analytical expressions are proposed for four cases of fiber property. First, aligned, and straight CNTs are considered with transverse isotropy in fiber coordinates, and the composite properties are also transversely isotropic in global coordinates. The short comings in the earlier developments are effectively addressed by deriving the consistent form of the strain tensor and the stiffness tensor of the CNT nanocomposite. Subsequently, effective relations for composites reinforced with aligned, straight CNTs but fibers isotropic in local coordinates are newly developed under hydrostatic loading. The effect of the unsymmetric Eshelby tensor for cylindrical fibers on the overall properties of the nanocomposite is included by deriving the strain concentration tensors. Next, the random distribution of CNT fibers in the matrix is studied with fibers being transversely isotropic as well as isotropic when CNT nanocomposites are subjected to uniform loading. The corresponding relations for the effective elastic properties are newly derived. The modeling technique is validated with results reported, and the variations in the effective properties for different CNT volume fractions are presented.     

Incremental damage theory of particulate-reinforced composites with a ductile interphase

This paper deals with a new micromechanics model of particulate-reinforced composites (PRCs) describing the evolution of debonding damage, matrix plasticity and particle size effect on the deformation. A ductile interphase was considered in the frame of incremental damage theory to analyze the dependence of elastic–plastic–damage behavior on particle size. Progressive debonding damage was controlled by a critical energy criterion for particle–matrix interfacial separation. The equivalent stresses of the matrix and interphase were determined by field fluctuation method. The influences of progressive debonding damage, particle size and interphase properties on the overall stress–strain response of PRC were explained simultaneously. Due to the existence of a ductile interphase, stress transfer and plastic initiation in PRC become very complicated, and thus a unit-cell (UC) based FEM was used to simulate their evolutions and demonstrate the role of the interphase. Finally, particle size effect on the mechanical behaviors of composites was interpreted.     

Electro-mechanical load transfer from a fiber in a 1–3 piezocomposite with an imperfect interface

This paper considers the electro-mechanical interaction between a fiber and a matrix material in a 1–3 piezocomposite due to an axial load and electric charge applied to the fiber. The fiber–matrix interface is assumed to be mechanically imperfect and is represented by a spring-factor model. The interface is either electrically open- or short-circuited. The analytical general solutions corresponding to an infinite piezoelectric fiber with a vertical body force and an electric body charge are derived by using Fourier integral transforms. These solutions together with the analytical general solutions for a transversely isotropic elastic medium are used to formulate the fiber–matrix interaction problem. Selected numerical results for the fiber axial force and vertical electric field, and interfacial stresses are presented for representative 1–3 piezocomposites. The influence of the interface stiffness on the electro-mechanical load diffusion is also examined.     

Finite element modeling of effective thermomechanical properties of Al–B<Subscript>4</Subscript>C metal matrix composites

The present work aims to investigate the influences of thermal residual stresses and material properties on the thermomechanical deformation behavior of Al–B₄C composites. Boron carbide-reinforced aluminum matrix composites having 4, 8, and 12 vol% boron carbide were fabricated using squeeze liquid stir casting method for experimental characterization of their microstructure, effective elastic moduli and effective CTEs at room temperature as well as elevated temperatures. Next, the thermomechanical behavior of fabricated composites was investigated using finite element modeling. The effects of thermal residual stresses on the effective material properties were examined by simulating the cooling process of MMCs from processing temperature to room temperature. The effective elastic moduli and the effective CTEs were predicted considering linear elastic as well as elastoplastic deformation of aluminum matrix, and the results obtained were compared with the experimental values. The effects of voids on effective material behavior are studied by simulating the void growth and nucleation using Gurson–Tvergaard–Needleman model.     

Calculation of effective coefficients for piezoelectric fiber composites based on a general numerical homogenization technique

Numerical unit cell models for 1–3 periodic composites made of piezoceramic unidirectional cylindrical fibers embedded in a soft non-piezoelectric matrix are developed. The unit cell is used for prediction of the effective coefficients of the periodic transversely isotropic piezoelectric cylindrical fiber composite. Special emphasis is placed on the formulation of the boundary conditions that allows the simulation of all modes of overall deformation arising from any arbitrary combination of mechanical and electrical loading. The numerical approach is based on the finite element method (FEM) and it allows the extension to composites with arbitrary geometrical inclusion configurations, providing a powerful tool for fast calculation of their effective properties. For verification the effective coefficients are evaluated for square and hexagonal arrangements of unidirectional piezoelectric cylindrical fiber composites. The results obtained from the numerical technique are compared with those obtained by means of the analytical asymptotic homogenization method (AHM) for different fiber volume fractions.     

连续变化界面层对复合材料弹性性能影响

界面层对复合材料的变形和破坏有着重要的影响,实际界面层的性能是随位置而连续变化的,但目前大多数考虑界面层影响的工作都假设界面层材料性能均匀或分层均匀。假设界面层的性能是空间位置的幂函数形式,给出了具有上述界面层的纤维和球形夹杂在球压和剪切载荷下的解,然后利用平均场方法建立了上述复合材料的有效弹性性质与微结构的联系。还将上述方法与均匀界面层模型进行了比较,计算结果表明,界面层的性质对复合材料有效性质和局部应力的分布有着重要影响。      

Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov–Galerkin method

We analyze plane strain static thermoelastic deformations of a simply supported functionally graded (FG) plate by a meshless local Petrov–Galerkin (MLPG) method. Material moduli are assumed to vary only in the thickness direction. The plate material is made of two isotropic randomly distributed constituents and the macroscopic response is also modeled as isotropic. Displacements and stresses computed with the MLPG method are found to agree very well with those obtained from the analytical solution of the problem. The number of nodes required to obtain an accurate solution for a FG plate is considerably more than that needed for a homogeneous plate.The work was partially supported by the Office of Naval Research grant N00014-98-1-0300 to Virginia Polytechnic Institute and State University with Dr. Y. D. S. Rajapakse as the program manager. L. F. Qian was also supported by the China Scholarship Council.     

Thermo-mechanical fatigue modeling of advanced metal matrix composites in the presence of microstructural details

An analytical model developed for predicting the inelastic response of metal matrix composites subjected to axisymmetric loading is employed to investigate the behavior of SiC---Ti composites under thermo-mechanical fatigue loading. The model is based on the concentric cylinder assemblage consisting of arbitrary numbers of elastic or inelastic sublayers with isotropic, transversely isotropic, or orthotropic, temperature-dependent properties. In the present work, the inelastic response of the titanium matrix is modeled by the Bodner-Partom unified viscoplastic theory. These features of the model allow the investigation of microstructural effects (such as the layered morphology of the SCS-6 fiber, including the weak carbon coating, and matrix microstructure) and rate-dependent response of the matrix on the fatigue behavior.

In this paper, we employ the predictions of the multiple concentric cylinder model to study the effects of the layered morphology of the SCS-6 SiC fiber and two-phase microstructure of the Ti-15-3 matrix on the response of a SiC---Ti composite under thermo-mechanical fatigue loading. It is shown that ignoring the microstructure can lead to significant errors in the predictions of the internal stress and inelastic strain distributions.     

Constitutive models for ductile solids reinforced by rigid spheroidal inclusions

We study the effective constitutive response of composite materials made of rigid spheroidal inclusions dispersed in a ductile matrix phase. Given a general convex potential characterizing the plastic “in the context of J₂-deformation theory” behavior of the isotropic matrix, we derive expressions for the corresponding effective potentials of the rigidly reinforced composites, under general loading conditions. The derivation of the effective potentials for the nonlinear composites is based on a variational procedure developed recently by Ponte Castaneda (1991a, J. Mech. Phys. Solids 39, 45–71). We consider two classes of composites. In the first class, the spheroidal inclusions are aligned, resulting in overall transversely isotropic symmetry for the composite. In the second class, the inclusions are randomly oriented, and thus the composite is macroscopically isotropic. The effective response of composites with aligned inclusions depends on both the orientation of the loading relative to the inclusions and on the inclusion concentration and shape. Comparing the strengthening effects of rigid oblate and prolate spheroids, we find that prolate spheroids give rise to stiffer effective response under axisymmetric “relative to the axis of transverse isotropy” loading, while oblate spheroids provide greater reinforcement for materials loaded in transverse shear. On the other hand, nearly spherical “slightly prolaterd spheroids are most effective in strengthening the composite under longitudinal shear. Thus, the optimal shape for strengthening composites with aligned inclusions depends strongly on the loading mode. Alternatively, the properties of composites with randomly oriented spheroidal inclusions, being isotropic, depend only on the concentration and shape of the inclusions. We find that both oblate and prolate inclusions lead to significant strengthening for this class of composites.     

Effective porothermoelastic properties of transversely isotropic rock-like composites

The present work is devoted to the determination of the overall porothermoelastic properties of transversely isotropic rock-like composites with transversely isotropic matrix and randomly oriented ellipsoidal inhomogeneities and/or pores. By using the solution of a single ellipsoidal inhomogeneity arbitrarily oriented in a transversely isotropic matrix presented by Giraud et al. [A. Giraud, Q.V. Huynh, D. Hoxha, D. Kondo, Effective poroelastic properties of transversely isotropic rocks-like composites with arbitrarily oriented ellipsoidal inclusions, Mechanics of Materials 39 (11) (2007) 1006-1024], it is possible to observe the effect of the shape and orientation distribution of inhomogeneities on the effective porothermoelastic properties. Based on recent works on porous rock-like composites such as shales or argillites, an application of the developed solution to a two-level microporomechanics model is presented. The microporosity is homogenized at the first level, and multiple solid mineral phase inclusions are added at the second level. The overall porothermoelastic coefficients are estimated in the particular context of heterogeneous solid matrix. The present model generalizes to transversely isotropic media a recently developed two-level model in the simpler case of isotropic media (see Giraud et al. [A. Giraud, D. Hoxha, D.P. Do, V. Magnenet, Effect of pore shape on effective thermoporoelastic properties of isotropic rocks, International Journal of Solids and Structures 45 (2008) 1-23]). Numerical results are presented for data representative of transversely isotropic rock-like composites.     

Fracture of metal/ceramic interfaces

The present paper examines metal/ceramic interfaces. Energy release rates are calculated with the finite element method for different elastic–plastic material laws of the metal. The local strain field of the metal is measured during a four-point bending test with an optical method and compared with results from the simulations. The aim of the work is to understand the influence of interface strength and material properties on the energy release rate.