Showing papers on "Representative elementary volume published in 1995"

An improved Gurson-type model for hardenable ductile metals

Abstract: The aim of this paper is to improve the modelling of strain hardening within the framework of the famous Gurson model for porous ductile metals. Indeed, although the original derivation of this model, for an ideal-plastic matrix, was based on a micromechanical analysis of some representative volume element, namely a hollow rigid-plastic sphere loaded axisymmetrically, the extension to the case of a hardenable matrix was of purely phenomenological and macroscopic nature, and this entailed a number of drawbacks. The phenomenological model was incompatible with the classical, exact solution to the problem of a hollow rigid-hardenable sphere loaded hydrostatically; also, the prediction that for any loading path corresponding to a fixed triaxiality, the curve representing porosity as a function of equivalent strain depended only on the initial porosity and the triaxiality but not on the hardening exponent, was incorrect. A new model solving these difficulties, based on an approximate analysis of a hollow rigid-hardenable sphere subjected to some axisymmetric loading, is proposed. Two types of hardening are considered: isotropic, as in Gurson's original model, and kinematic, as in Mear and Hutchinson's variant of Gurson's model. Comparisons with some finite element simulations evidence the improvements brought.

Thermoelastic theory for the response of materials functionally graded in two directions with applications to the free-edge problem

Abstract: A recently developed micromechanical theory for the thermoelastic response of functionally graded composites with nonuniform fiber spacing in the through-thickness direction is further extended to enable analysis of material architectures characterized by arbitrarily nonuniform fiber spacing in two directions. In contrast to currently employed micromechanical approaches applied to functionally graded materials, which decouple the local and global effects by assuming the existence of a representative volume element at every point within the composite, the new theory explicitly couples the local and global effects. The analytical development is based on volumetric averaging of the various field quantities, together with imposition of boundary and interfacial conditions in an average sense. Results are presented that illustrate the capability of the derived theory to capture local stress gradients at the free edge of a laminated composite plate due to the application of a uniform temperature change. It is further shown that it is possible to reduce the magnitude of these stress concentrations by a proper management of the microstructure of the composite plies near the free edge. Thus by an appropriate tailoring of the microstructure it is possible to reduce or prevent the likelihood of delamination at free edges of standard composite laminates.

Experimental Damage Investigation of a SiC-Ti Aluminide Metal Matrix Composite

Abstract: Experimental investigations and procedures for the determination of damage are presented for the macro- and micro-analysis of SiC-Titanium Aluminide metal matrix composite (MMC). Uniaxial tension tests are performed on laminate specimens of two different layups. The layups are balanced symmetrically and given as (0/90)s and (±45)s, each containing four plies. Dogbone shaped flat plate specimens are fabricated from each of the layups. Specimens for the different layups are loaded to various load levels ranging from rupture load down to 70% of the rupture load at room temperature. By loading specimens to various load levels damage evolution is experimentally evaluated through a quantitative micro-analysis technique. Micro-analysis is performed using scanning electron microscopy (SEM) on three mutually perpendicular representative cross sections of all specimens for the qualitative and quantitative determination of damage. Together these representative cross sections form a representative volume element (RVE...

Elastoplastic analysis of thermal cycling: Ceramic particles in a metallic matrix

Abstract: Elastoplastic deformation induced by the thermal cycling of a particle-reinforced metal is studied analytically and numerically. The representative volume element considered for analysis is a spherical ceramic particle embedded within a hollow sphere of the metallic matrix. Closed-form solutions are derived for four characteristic temperatures which signify certain critical conditions for the onset and spread of plasticity in the composite during thermal fluctuations. These conditions are then evaluated for a wide variety of commonly studied metal-ceramic composites. The effective coefficient of thermal expansion is derived and is shown to be in agreement with finite element results obtained for an Al-SiC composite. Numerical simulations addressing plastic strain accumulation and interfacial decohesion during thermal cycling are also discussed with the objective of providing some guidelines for the estimation of thermal fatigue life.

Use of composite cylinder model as representative volume element for unidirectional fiber composites

Abstract: The present work is concerned with the theoretical study of the elastic properties of unidirectional fiber composites. The approach to calculate the effective moduli of composite materials is generally based upon the premise of a representative volume element, or an element in which the strain and stress averages taken over large enough subregions of the specimen are the same for any such subregion. For purposes of computation, some model of a fiber composite must be assumed. The objective of this study is to demonstrate that the composite cylinder model can provide a good simulation for the representative volume element to define the response of a unidirectional composite for a wide range of elastic moduli and volume fraction provided the displacements are prescribed on the external surfaces. Results of the effective elastic moduli and microstresses within the constituents are compared with existing numerical solutions, both with and without partial interphase failure, to demonstrate the effectiveness of...

An evaluation of a coupled microstructural approach for the analysis of functionally graded composites via the finite-element method

Abstract: A comparison is presented between the predictions of the finite-element analysis and a recently developed higher-order theory for functionally graded materials subjected to a thorough-thickness temperature gradient. In contrast to existing micromechanical theories that utilize classical (i.e., uncoupled) homogenization schemes to calculate micro-level and macro-level stress and displacement fields in materials with uniform or nonuniform fiber spacing (i.e., functionally graded materials), the new theory explicitly couples the microstructural details with the macrostructure of the composite. Previous thermo-elastic analysis has demonstrated that such coupling is necessary when: the temperature gradient is large with respect to the dimension of the reinforcement; the characteristic dimension of the reinforcement is large relative to the global dimensions of the composite and the number of reinforcing fibers or inclusions is small. In these circumstances, the standard micromechanical analyses based on the concept of the representative volume element used to determine average composite properties produce questionable results. The comparison between the predictions of the finite-element method and the higher-order theory presented herein establish the theory's accuracy in predicting thermal and stress fields within composites with a finite number of fibers in the thickness direction subjected to a thorough-thickness thermal gradient.

A Theoretical Framework for the Analysis of Thermoelectroelastic Heterogeneous Media with Applications

Abstract: A rigorous theoretical framework is presented for the analysis of thermoelectroelastic heterogeneous media. These materials include, among others, piezoelectric composite media which exhibit pyroelectricity. Formal definitions of a representative volume element, phase constitutive behavior, and numerous averaging theorems are presented. Expression for the average fields in the constituent phases in terms of thermal and electroelastic concentration factors are presented as are exact expressions for the effective moduli in terms of the concentration factors. An approach is presented to estimate the phase concentration factors which is based on the rigorous solution for the auxiliary problem of a single piezoelectric inhomogeneity embedded in an infinite matrix (which is also outlined). The theoretical principles are presented in the framework of a convenient 9 x 9 and 9 x 1 matrix formulation which greatly simplifies their numerical implementation. The framework presented here allows for the clean delineation between exact and assumed relations and allows a clear interpretation of all assumptions. Applications are made to polycrystalline piezoelectric ceramics, cracked piezoelectric solids, and two-phase piezoelectric composites.

Analytical prediction of regular reflection over rigid porous surfaces in pseudo-steady flows

Abstract: An analytical model for solving the flow field associated with regular reflections of straight shock waves over porous layers has been developed. The governing equations of the gas inside the porous material were obtained by simplifying the general macroscopic balance equations which were obtained by an averaging process over a representative elementary volume of the microscopic balance equations as originally done by Bear & Bachmat (1990). The analytical predictions of the proposed model were compared to experimental results of Skews (1992) and Kobayashi, Adachi & Suzuki (1993). Very good to excellent agreement was evident.

Using the Volume Averaging Technique to Perform the First Change of Scale for Natural Random Porous Media

Abstract: The volume averaging technique is one of the various theoretical methods providing a rigorous description of the change of scale procedure. Applying this method to pore scale flow through natural porous media gives rise to several theoretical and practical problems. This paper is a progress report of an ongoing effort to solve most of them in order to build physically and structurally realistic models of flow through natural porous media. We present here some recent results concerning the characterisation of the random geometry of those media, the definition of a Representative Elementary Volume (REV) appropriate for the considered change of scale, and the relevance of periodic boundary conditions to solve the closure problem originated in this process.

Finite element based micro-mechanics modeling of textile composites

Abstract: Textile composites have the advantage over laminated composites of a significantly greater damage tolerance and resistance to delamination. Currently, a disadvantage of textile composites is the inability to examine the details of the internal response of these materials under load. Traditional approaches to the study fo textile based composite materials neglect many of the geometric details that affect the performance of the material. The present three dimensional analysis, based on the representative volume element (RVE) of a plain weave, allows prediction of the internal details of displacement, strain, stress, and failure quantities. Through this analysis, the effect of geometric and material parameters on the aforementioned quantities are studied.

Effects of Fiber Morphology in Short Fiber Reinforced Composites

Abstract: The upper and lower bounds of fiber/fiber interaction effects induced by the different fiber morphologies in a short fiber reinforced composite were studied using an axisymmetric finite element (FE) model that employs a periodic hexagonal array of elastic short fibers embedded in an elastoplastic matrix. An equivalent representative volume element (RVE) was modeled to maintain vertical and horizontal constrained boundary conditions for the reduction of modeling efforts. The internal stress fields were evaluated for the ideally aligned single fiber model and compared to a staggered model. It was found that both fiber and matrix stresses in a staggered fiber model are significantly altered from those of the perfectly aligned case. Finally, the hydrostatic stresses in the matrix along the fiber/matrix interface and the evolution of matrix plasticity for each model were illustrated.

Effect of applied boundary condition on the analysis of composites based on woven preforms

Abstract: Textile composites have the advantage over laminated composites of a significantly greater damage tolerance and resistance to delamination. Currently, a disadvantage of textile composites is the inability to examine the details of the internal response of these materials under load. Traditional approaches to the study of textile based composite materials neglect many of the geometric details that affect the performance of the material. The present three dimensional analysis, based on the representative volume element (RVE) of a plain weave, allows prediction of the internal details of displacement, strain, stress, and failure quantities. In the present paper, the effect of boundary condition on the response of the RVE is studied.

On the Micromodelling of Dynamic Response for Thermoelastic Periodic Composites

Abstract: As it is known, the asymptotic homogenization methods for micro-periodic composites, leading to the effective modulus theories, neglect inertial aspects of microstructural features related to the size of constituents (cf [1,2] and the references therein) The main aim of this contribution is to propose a new approach to the formulation of macro-models for micro-periodic thermoelastic composite materials This approach takes into account a length-scale effect on a dynamic response of a composite and is simple enough to be applied in analysis of engineering problems and for quasi-stationary processes reduces to the special effective modulus theory, [3,4] Theories of this type for elastic composite materials and structures were discussed in [5–7] and are termed refined macro-theories In this paper governing equations of the refined macro--thermoelastodynamics are formulated on the basis of heuristic hypotheses concerning the expected form of disturbances in displacement and temperature fields, caused by the micro-inhomogeneity of a composite At the same time a special form of macro-modelling approximations is used The resulting equations are obtained without any reference to a boundary value problem on the representative volume element, that is required in asymptotic homogenization approaches, [1,2] The general considerations are illustrated by the simple example the aim of which is to compare results of the refined macro-theory and those of the effective modulus theory It is shown that the microstructure length scale effects, described by the proposed macro-theory, play an essential role in investigations of the non-stationary behaviour of the composites

Analytical/Experimental Study of Interphase Effects on Composite Compression Strength

Abstract: In this work we present an analytical model of a composite containing coated cylindrical fibers subjected to a compressive loading. The modeling approach used in this paper is a blend of two conventional analytical techniques to predict the composites compression strength as a function of microparameters. The model presented here explicitly includes interphase influences and the circular geometry of the fiber which causes substantial stress concentrations at key locations. Analytical results suggest that a specific coating may increase the compression strength of a composite. Experimental studies are conducted on several composite systems fabricated with coated glass fibers as the reinforcing fiber. Results indicate that coating effects, adhesion, and fiber geometry play a critical role in compression strength. Comparison of the experimental results with the analytical model yield reasonable correlation between the two, thus supporting the theoretical claims of the model.

Representative volumes for a class of composite materials with periodic structures

Abstract: In this paper we consider the issue of representative volumes to determine the volume averaged effective elastic moduli for a class of composite materials with periodic structures. The existence of representative volumes under a specific group of homogeneous boundary conditions is proved and the dependence of effective elastic moduli on homogeneous boundary conditions is discussed.

Matrix cracking with bonded interfaces in unidirectional fibre-reinforced composites

Abstract: Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6119, USA The mechanical properties of a material can be significantly improved by incorporating strong fibres aligned with the loading direction [1-6]. The initial damage in unidirectional fibre-reinforced composites is often in the form of a crack (or cracks) extending through the matrix with unbroken fibres bridging the crack surfaces. Several models have been proposed to analyse the critical loading stress on the composite for matrix cracking [7-14]. Depending upon the bonding strength between the fibre and the matrix, the interface either remains bonded [8, 9] or becomes debonded [7, 9-14] during the matrix cracking and fibre bridging processes. For the case of debonded interfaces, the analysis has been performed in a companion work [14] and compared with other existing analyses [7, 9]. Hence, the analysis of the present study is limited to the case of bonded interfaces. Firstly, the existing models [8, 9] are summarized, then a new model is proposed. Finally, comparison is made between the present solution and the existing solutions. The steady-state matrix cracking stress with bonded interfaces was first analysed by Aveston and Kelly [8]. A fibre surrounded by a hexagonal matrix was adopted as a representative volume element of the composite. A shear lag model [15] was used to analyse the stress transfer between the fibre and the matrix in the presence of matrix cracking. The stress-transfer solutions were based on the assumption that the average displacement in the matrix could be represented by the displacement in the matrix at a radial distance R from the centre of the fibre. The solutions were then used to calculate the work done by the applied stress during matrix cracking. Finally, the energy balance condition was used to derive the matrix cracking stress, and the result was [8]:

Effective Moduli of Concentrated Particulate Solids

Abstract: The overall elastic constants of a participate composite material are theoretically estimated. The composite consists of a high concentration of randomly arranged spherical particles embedded in an isotropic elastic matrix. Because of the high concentration of particles (volume fraction close to the maximum possible), the load transfer occurs mainly at the regions of near contact between neighbouring particles. The self-consistent approach is therefore unlikely to give an accurate prediction. It is now necessary to estimate the load transfer between two neighbouring particles separated by a thin layer of matrix material. This has been done in the present paper without placing any restrictions on the rigidity of the particles or on the length of contact zone between them. The latter two limiting cases have been previously solved by Batchelor and O’Brien (1977), Phan-Thien and Karihaloo (1982), and Dvorkin, Mavko and Nur (1991). The results of the present study are applicable in particular to cemented granular materials.

Radiation Heat Transfer

Abstract: In this chapter, heat transfer by radiation in porous media is examined. The medium may be treated either as a single continuum or as a collection of particles (i.e., scatterers). In the particle-based analysis, the interaction of radiation with a collection of elements of the solid matrix (e.g., particles in a packed bed) is considered. On the other hand, the continuum treatment attempts to obtain the effective radiative properties of the medium by using the element-based interaction along with a local volume-averaging procedure. This volume averaging is greatly simplified if it is assumed that the interaction of a particle with radiation is not affected by the presence of neighboring particles [i.e., the scattering (or absorption) is independent]. In case the assumption of independent scattering fails, the volume averaging must include dependent effects.