Strain gradient plasticity

A constitutive model for anisotropic damage in fiber-composites

Effective properties of composite materials with periodic microstructure : a computational approach

This paper presents a review of the principal developments in functionally graded materials (FGMs) with an emphasis on the recent work published since 2000. Diverse areas relevant to various aspects of theory and applications of FGM are reflected in this paper. They include homogenization of particulate FGM, heat transfer issues, stress, stability and dynamic analyses, testing, manufacturing and design, applications, and fracture. The critical areas where further research is needed for a successful implementation of FGM in design are outlined in the conclusions. DOI: 10.1115/1.2777164

https://web.mst.edu/~vbirman/papers/Modeling%20and%20Analysis%20of%20FGM_Review_2007.pdf

Modeling and Analysis of Functionally Graded Materials and Structures

Dislocation generation due to differences between the coefficients of thermal expansion

A new method is proposed for evaluation of local fields and overall properties of composite materials subjected to incremental thermomechanical loads and to transformation strains in the phases. The composite aggregate may consist of many perfectly bonded inelastic phases of arbitrary geometry and elastic material symmetry. In principle, any inviscid or time-dependent inelastic constitutive relation that complies with the additive decomposition of total strains can be admitted in the analysis. The governing system of equations is derived from the representation of local stress and strain fields by novel transformation influence functions and concentration factor tensors, as discussed in the preceding paper by G. J. Dvorak and Y. Benveniste. The concentration factors depend on local and overall thermoelastic moduli, and can be evaluated with a selected micromechanical model. Applications to elastic-plastic, viscoelastic, and viscoplastic systems are discussed. The new approach is contrasted with some presently accepted procedures based on the self-consistent and Mori-Tanaka approximations, which are shown to violate exact relations between local and overall inelastic strains.

Transformation field analysis of inelastic composite materials

HE DEVELOPMENT OF a satisfactory theory for cross-ply laminates which have been damaged by transverse matrix cracking under monotonic loading has attracted a substantial number of investigators. The formulation of a shear lag model appears to have been first proposed in a series of papers by Bailey and his co-workers [1,2,3,4,5,6]. This work, in turn, relies on some studies of unidirectional composites by Aveston and Kelly [6]. Subsequent contributions to the theory have geen given by Wang [7], Highsmith and Reifsnider [8], Flaggs and Kural [9], Nuismer and Tan [10], Manders, Chou, Jones and Rock [11], Fukunaga, Chou, Peters and Schulte [12], Flaggs [13], Ohira [14] and Ogin, Smith and Beaumont [15,16]. Doubtless a diligent search of the literature would disclose other related work.

Progressive Transverse Cracking In Composite Laminates

The effect of local eigenstrain and eigenstress fields, or transformation fields, on the local strains and stresses is explored in multiphase elastic solids of arbitrary geometry and material symmetry. The residual local fields caused by such transformation fields are sought in terms of certain transformation influence functions and transformation concentration factor tensors. General properties of these functions and concentration factors, and their relation to the analogous mechanical influence functions and concentration factors, are established, in part, with the help of uniform strain fields in multiphase media. Specific estimates of the transformation concentration factor tensors are evaluated by the self-consistent and Mori-Tanaka methods. It is found here that although the two methods use different constraint tensors in solutions of the respective dilute problems, their estimates of the mechanical, thermal, and transformation concentration factor tensors, and of the overall stiffness of multiphase media have a similar structure. Proofs that guarantee that these methods comply with the general properties of the transformation influence functions, and provide diagonally symmetric estimates of the overall elastic stiffness, are given for two-phase and multiphase systems consisting of, or reinforced by, inclusions of similar shape and alignment. One of the possible applications of the results, in analysis of overall instantaneous properties and local fields in inelastic composite materials, is described in the following paper.

On transformation strains and uniform fields in multiphase elastic media

Elastic response of selected plane-array models of graded composite microstructures is examined under both uniform and linearly varying boundary tractions and displacements, by means of detailed finite element studies of large domains containing up to several thousand inclusions. Models consisting of piecewise homogeneous layers with equivalent elastic properties estimated by Mori-Tanaka and selfconsistent methods are also analysed under similar boundary conditions. Comparisons of the overall and local fields predicted by the discrete and homogenized models are made using a C/SiC composite system with very different Young's moduli of the phases, and relatively steep composition gradients. The conclusions reached from these comparisons suggest that in those parts of the graded microstructure which have a well-defined continuous matrix and discontinuous second phase, the overall properties and local fields are predicted by Mori-Tanaka estimates. On the other hand, the response of graded materials with a skeletal microstructure in a wide transition zone between clearly defined matrix phases is better approximated by the self-consistent estimates. Certain exceptions are noted for loading by overall transverse shear stress. The results suggest that the averaging methods originally developed for statistically homogeneous aggregates may be selectively applied, with a reasonable degree of confidence, to aggregates with composition gradients, subjected to both uniform and nonuniform overall loads.

Micromechanical models for graded composite materials

The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debo...

George J. Dvorak

Papers

Transformation field analysis of inelastic composite materials

Progressive Transverse Cracking In Composite Laminates

On transformation strains and uniform fields in multiphase elastic media

Micromechanical models for graded composite materials

Analysis of Progressive Matrix Cracking In Composite Laminates II. First Ply Failure