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A theoretical and numerical approach to the plastic behaviour of steels during phase transformations. I: Derivation of general relations. II: Study of classical plasticity for ideal-plastic phases. (English) Zbl 0585.73200

Summary: Part I: Empirical models have been proposed for the anomalous plastic behaviour of steels during phase transformations; they distinguish between classical plasticity (response of the material to variations of the stresses or the temperature) and transformation plasticity (response of the material to variations of the proportion of the phases). This paper uses the Hill-Mandel homogenization method to provide theoretical foundations for such models. Without postulating arbitrarily the existence of an extra plastic strain of a new unknown type on a microscopic scale, it is shown that the distinction between (macroscopic) classical and transformation plasticity is a consequence of the homogenization process; furthermore the transformation plastic strain rate decomposes naturally into two terms which can be interpreted as corresponding to the well-known Greenwood-Johnson and Magee mechanisms. An interesting property of dilatometric diagrams is also proved in the course of the treatment.
Part II: The response of phase-transforming steels to variations of the applied stress (i.e. the \(\Sigma\)-term of the classical plastic strain rate \(E^{cp}\) defined in Part I) is studied both theoretically and numerically for ideal-plastic individual phases. It is found theoretically that though the stress-strain curve contains no elastic portion, it is nevertheless initially tangent to the elastic line with slope equal to Young’s modulus. Moreover an explicit formula for the beginning of the curve is derived for medium or high proportions of the harder phase, and a simple upper bound is given for the ultimate stress (maximum Von Mises stress). The finite element simulation confirms and completes these results, especially concerning the ultimate stress whose discrepancy with the theoretical upper bound is found to be maximum for low proportions of the harder phase. Based on these results, a complete model is proposed for the \(\Sigma\)-term of the classical plastic strain rate \(E^{cp}\) in the case of ideal-plastic phases.

MSC:

74A15 Thermodynamics in solid mechanics
74C99 Plastic materials, materials of stress-rate and internal-variable type
74S05 Finite element methods applied to problems in solid mechanics
82D35 Statistical mechanics of metals
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