Evolution of damage and plasticity in
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I.
INTRODUCTION
S T R U C T U R A L designs with metal matrix composites (MMCs) require: (1) a suitable constitutive model, such that stresses and strains can be computed locally (including those at the fiber/matrix level) in a structure, and (2) the establishment of failure criteria which govern functional loss under different loading conditions. Both of these ingredients require detailed knowledge of the material's elastic (recoverable) and inelastic (i.e., permanent) deformation mechanisms. In titanium-based MMCs, permanent deformation can start at very low strains (typically 0.1 to 0.5 pct[~]), which implies that design procedures should adequately take into account inelastic deformation processes. Understanding inelastic deformation also is important from a materials development perspective for optimizing MMC architecture and processing conditions for obtaining higher levels of critical stresses and strains at the onset of inelastic deformation and failure. Against this background, it is interesting to note that a relatively greater number of past studies has concentrated on modeling 12 10j MMC response as opposed to investigating damage and deformation mechanisms. [jL~'~,~31 The reason probably lies in the fact that the current generation of titanium-based MMCs is an extension of the more familiar A I / B and AI/AI203 MMCs, where fiber-matrix bond strengths were high relative to matrix yield strength M 141 and where elastic-plastic models generally were successful in predicting the stress-strain response. [7'~51 However, even for Al-based systems, recent studies involving thermal treatments [j6j and thermal cycling show that interfacial damage is important and should be part of any comprehensive model, in the case of titanium-based MMCs where specimens experience significantly greater loads than aluminum-based MMCs and where it is extremely difficult to avoid brittle reaction zones between matrix and fibers, damage effects B.S. M A J U M D A R , Senior Scientist, is with Universal Energy Systems, Inc., Dayton, OH 45432-1894. G.M. N E W A Z is with Battelle Memorial Institute, Columbus, OH 43201. J.R. ELLIS, Acting Chief, Fatigue and Failure Branch, is with NASA Lewis Research Center, Cleveland, OH 44135. Manuscript submitted June 12, 1992. METALLURGICAL TRANSACTIONS A
become even more relevant. The issue then becomes one of identifying the relative contributions of plasticity and damage and the sequence in which they occur in the MMC. Constitutive models must account for these processes to be realistic, such that calculations of local stresses/strains are accurate. The correlation of model predictions with experimental stress-strain data by itself is not a measure of successful prediction, unless realistic deformation mechanisms are properly accounted for in the model. The need to understand the deformation mechanisms formed the rationale for the work described here. The emphasis in this article is to clarify the sequences of plasticity and damage. By plasticity, we imply processes involving dislocation nu
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