Combined Model of Strain-Induced Phase Transformation and Orthotropic Damage in Ductile Materials at Cryogenic Temperatures

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Abstract
Ductile materials (like stainless steel or copper) show at cryogenic temperatures three principal phenomena: serrated yielding (discontinuous in terms of dσ/dε), plastic strain-induced phase transformations and evolution of ductile damage. The present paper deals exclusively with the two latter cases. Thus, it is assumed that the plastic flow is perfectly smooth. Both in the case of damage evolution and for the 0 phase transformation, the principal mechanism is related to the formation of plastic strain fields. In the constitutive modeling of both phenomena, a crucial role is played by the accumulated plastic strain, expressed by the Odqvist parameter p. Following the general trends, both in the literature concerning the phase transformation and the ductile damage, it is assumed that the rate of transformation and the rate of damage are proportional to the accumulated plastic strain rate. The 0 phase transformation converts the initially homogenous material to a two-phase heterogeneous ”composite”. The kinetics of phase transformation is described by the relevant linearized law of evolution of the volume fraction of 0 martensite in the austenitic matrix [Garion, C. and Skoczen, B. (2002a). The evolution of orthotropic damage is characterized by the fact that the principal directions of damage are generally not colinear with the principal directions of stress. The damage rate tensor depends linearly on the strain energy density release rate tensor (conjugate force) and on the material properties tensor C, that reflects the orthotropy level. The relevant kinetic law of damage evolution and the combined constitutive model, including phase transformation, are developed in the present paper. The model is particularly suitable to describe the evolution of highly localized damage fields in thin-walled shells, subjected at cryogenic temperatures to the loads far beyond the yield point. It has been applied to the prediction of the response of the bellows expansion joints (corrugated thin-walled shells) designed for the inter-connections of the Large Hadron Collider at CERN.