Theoretical calculation of anisotropie creep and stress-strain behavior for a class of metal-matrix composites
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INTRODUCTION
THIS article is concerned with the development of a unified theoretical model which can account for both the time-dependent creep and the strain-rate sensitivity of the stress-strain curve of a metal-matrix composite at constant temperature. The unified theory is developed based on the observation that creep and plasticity are fundamentally rate processes and that, within approximately the same stress and temperature range, plasticity is not qualitatively different from time-dependent creep. This has been demonstrated by Weertman, tl~ who conducted several constant strain-rate and constant-stress creep tests on pure aluminum and found that the steady-state responses of both tests were almost identical. The composite considered here is made of a ductile metal matrix with unidirectionally aligned, homogeneously dispersed, spheroidal inclusions. For generality, we shall take both the inclusions and the matrix to be capable of creeping (even though in reality the creep activity of most inclusions is an order (or two) of magnitude less than that of the matrix) and then, when applied to a system where the inclusions are strictly elastic, creep activity may be set to zero. To treat both creep and strainrate effects in a unified fashion, both primary (transient) and secondary (steady-state) creep of the constituents must be considered. For simplicity, we shall assume the inclusions and the matrix to be perfectly bonded together without any void nucleation or growth. The spheroidal inclusions are aligned with their symmetric axis pointing toward direction 1, and their common shape, as depicted K. MURALI, formerly Graduate Student, and G.J. WENG, Professor, are wilh the Department of Mechanical and Aerospace Engineering, Rulgers University, New Brunswick, NJ 08903. K. Murali is now a Research Associate, Department of Mechanical Engineering, Florida A&M University and Florida State University, Tallahassee, FL 32316. Manuscript submitted November 30. 1992. METALLURGICAL TRANSACTIONS A
in Figure 1, is represented by the aspect ratio a (the lengthto-diameter ratio). This class of composites covers a wide range of inclusions; they may vary from thin discs (a 0) to oblate inclusions (a < 1), from spherical particles (a = 1) to prolate inclusions (c~ > 1), and all the way to continuous fibers (c~ ~ ~). In this case, the composite as a whole is transversely isotropic and its overall creep behavior will be affected by the volume fraction and aspect ratio of the inclusions. The theory is to be developed so that the influence of inclusion shape and volume concentration on both the creep behavior and the stressstrain curves can be accounted for. While particle and fiber-strengthened composites are abundant, those with aligned discs or oblate or prolate inclusions are not yet as common, and if the analysis points to a superior property for the latter class of composites, it may serve as a guide for future material development. In the case of creep, a constant external stress is applied. Under this condition, the initial re
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