The influence of martensite shape, concentration, and phase transformation strain on the deformation behavior of stable
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INTRODUCTION
D U A L - p h a s e steels have gained considerable importance over other commercial steels because o f the high strength and ductility achieved. A n u m b e r o f theoretical models have been developed to exhibit the deformation behavior o f the constituent phases in such a system. As mentioned in the review o f Korzekwa et al.,tt] Davies[2.3] has applied the simple rule-of-mixtures approach, whereas Araki et al.,141 Tamura et a l . 15] and Speich and Miller161 have developed other continuum models based on the constant strain or constant stress in each constituent phase (a strength-of-material type approach). Karlsson and Sundstrrm 17] have used the finite element method to study a similar two-dimensional ferrite-martensite system up to a total strain o f 5 pct. A micromechanical m o d e l was developed by Ashby,lSl who assumed martensite as spherical, nondefomting inclusions. Though useful in their own right, none o f these approaches has considered the influence o f martensite shape, volume fraction, phase transformation strain, and thermal mismatch on the strength and ductility o f the dual-phase system. When a dual-phase steel is quenched from an intercritical annealed temperature, the austenite phase trans-
A. BHATI'ACHARYYA, Graduate Student, and G.J. WENG, Professor, are with the Department of Mechanical and Aerospace Engineering, Rutgers University, New Brunswick, NJ 08903. T . SAKAKI, formerly Visiting Professor, Department of Mechanical and Aerospace Engineering, Rutgers University, is Professor, Department of Precision Engineering, T o k y o Metropolitan University, Hachiouji-shi, T o k y o 192-03, Japan. Manuscript submitted July 1 , 1991. METALLURGICAL TRANSACTIONS A
forms into martensite. The transformation is accompanied by a phase transformation strain, and the martensite may exist in various shapes. The phase transformation strain and the thermal misfit o f the constituent phases, in t u r n , introduce an internal stress in both inclusions and the ferrite matrix, whose magnitude is usually high enough to cause yielding in the ductile matrix. The magnitudes o f the internal stress are strongly dependent upon the volume fraction and the shape o f inclusions. Thus, when the dual-phase system is subjected to an external tensile stress at room temperature, the martensitic inclusions and the ferrite matrix do not start from a stress-free state; in effect, the ductile matrix starts from the plastic state and this, in turn, leads to the widely observed "continuous yielding" in the dual-phase system. Based on a micromechanics analysis, we shall present a theory to account f o r the influence o f thermal misfit, phase transformation strain, and inclusion shape and its volume fraction on the extent o f initial yielding o f the ductile matrix and on the subsequent deformation o f the dual-phase system. W e shall, f o r simplicity, take the shape o f martensite phase to be o f an oblate spheroid, with a common aspect ratio a (thickness-to-the-diameter ratio, 0 < cr -< 1). The transformed marte
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