Coupled temperature, stress, phase transformation calculation
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I.
INTRODUCTION
D U R I N G the quenching process, the steel in the piece undergoes temperature variations which give rise to structural transformations. The resulting changes in density in the piece are at the origin of internal stresses (in this paper we are concerned only with stresses of the first orderS). These internal stresses affect themselves the structural transformations and consequently the thermal evolutions in the piece. In order to perform the quantitative prediction of the internal stresses in the piece during quenching, it is thus necessary to model the thermomechanical behavior of the steel during its phase transformations. This behavior can be considered in three aspects: The metallurgical aspect." The overall kinetics of phase transformation during cooling and the changes in density associated with these transformations must be known. It should be mentioned that in the quenching process of steels, the various kinds of transformations in steels may occur: transformations with nucleation and diffusion controlled growth called diffusional transformations (ferritic, pearlitic, and bainitic transformations) and martensitic transformation called diffusionless transformation. The mechanical aspect: The elastic and plastic behavior of the material must be known; it means the mechanical properties as a function of temperature and structure. The interactions between stresses~strains and phase transformations: When phase transformation takes place under an applied stress, the stress affects the kinetics of phase transformation and the mechanical behavior of the steel is modified through transformation plasticity. 2'5 In the quenching process, the steel is not submitted to external applied stresses. The solicitations on the steel are the thermal gradients which result in nonuniform deformations in the part and give rise to internal stresses. These stresses affect the phase transformations. S. DENIS and A. SIMON are with Laboratoire de Science et GEnie des Mat6naux M&alliques (UA 159 C.N.R...S.) Ecole des Mines, Parc de Saurupt-54042-Nancy-Cedex, France S. SJOSTROM is with Division of Solid Mechamcs and Strength of Materials, Lmk~Sping Institute of Technology, Link~Sping, Sweden. Manuscript submitted October 8, 1986 METALLURGICAL TRANSACTIONS A
On a general point of view models can be developed at different levels: either models are based on a microscopical analysis of the local behavior (at the phase, grain, or lattice level) or they describe the macroscopic behavior of the material (at the specimen level). These models are either theoretical (based on the theory of dislocations, on thermodynamics... ) or phenomenological (when they describe a phenomenon by a mathematical expression identified to experimental results). Concerning phase transformations in metals, if models for describing the mechanism of transformation exist (theory of nucleation, theory of growth~), they are most often insufficient for describing quantitatively the phenomena in steels. For diffusional transformation they don't allow for
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