Some aspects of deformation behavior
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INTRODUCTION
THE deformation response of single-phase polycrystalline materials (SPPM) is well documented in terms of dislocation theory. I~ 81Conventionally, the strength of an SPPM is accounted by several factors, such as grain size, tL21 solid solution strengthening, t3i precipitation strengthening, N dislocation strengthening, substructure strengthening, i6'7] texture strengthening, tsj and the internal stress of the material. But an understanding of the above factors is not sufficient to predict deformation response of multiphase materials with coarse structures (MPMCS), though a large number of such materials, e.g., ferrito-pearlitic steels, dual-phase steels (DPS), duplex stainless steels, a-/3 Ti alloys, a-/3 brass, and AI-Si alloys, are commercially produced for structural applications. These MPMCS possess a good combination of strength and ductility, where the strength is controlled by the hard phase and the ductility is governed by the soft phase. Typically for these structures, the grain sizes of the constituent phases are of the order of 1 ~ m or above. An understanding of the deformation response of MPMCS requires consideration of all of the factors affecting the deformation behavior of their individual constituents as well as of the following aspects: 19~ (1) (2) (3) (4)
the relative amount of the phases, the morphology of the phases, the nature of distribution of the phases, and the orientational relationship between the constituents.
As a consequence, the prediction of strength for an MPMCS is difficult; and one finds a series of continuing investigations in the literature, a brief account of which is given by Cho and Gurland. I")l The prediction of strength for MPMCS is primarily based on the linear law of mixture for estimating the K.K. RAY, Assistant Professor, and D. MONDAL, Research Scholar, are with the Department of Metallurgical Engineering, Indian Institute of Technology, Kharagpur 721302, India. Manuscript submitted August 7. 1991.
METALLURGICAL TRANSACTIONS A
strength of fiber-reinforced composites, as suggested by Kelly:l ~q ~, = cr, V, + o-~V~
111
where or, is the yield strength, tensile strength, or flow stress of the composite (or phase mixture) and o-,~(or o't3) and V, (or Vt3) are the strength and the volume fraction, respectively, of a particular constituent designated as a (or/3). This law cannot fully describe the strength behavior of most of the metallic MPMCS investigated so far. Several attempts 19,"),~2-~51 have been made to modify this law of mixture primarily for two-phase metallic materials with coarse structures (TPMMCS). Interestingly, the first modification is for ferrito-pearlitic structures by Gladman et al. ,[ ~21using a nonlinear law as depicted below: O', = o-leVfne + Orp(1 -- V~e )
I21
where o-re and O-p are the strengths of ferrite and pearlite, respectively, Vfe is the volume fraction of ferrite, and n is an empirical constant having a value of 1/3. In this formulation, crfe and typ are considered as functions of (a) grain size or interlamellar spa
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