Two‐level models of polycrystalline elastoviscoplasticity: Complex loading under large deformations

Abstract

Key words Polycrystal, multilevel models, geometrical nonlinear models, matching of constitutive relations, quasi-rigid motion, loading process image, complex loading, material memory, vector property lagging. This paper considers the application of multilevel mathematical models describing processes of severe inelastic deformations of monocrystals and polycrystals that requires the usage of geometrically and physically nonlinear constitutive relations. In order to describe the behavior of a representative macrovolume, a two-level model based on the physical theory of elastoviscoplasticity is used. The motion of rigid corotating frame describing quasi-rigid motion is determined by a macrolevel motion decomposition hypothesis. The following macrolevel hypotheses are considered: (1) the representative volume total motion is a deformational one; (2) the motion is decomposed into a deformational and a rigid ones with a spin being determined by an averaging of the mesolevel spins; (3) quasi-solid and deformational motions are determined by corresponding skew-symmetrical and symmetrical parts of the macrolevel displacement velocity gradient. In order to describe experimentally known effects observed under complex loading the questions related to the application of monoand poly-crystals inelastic deformation multilevel models based on crystal plasticity theories are discussed. In particular, a polycrystalline metals inelastic deformation of the two-level model is used to consider the scalar and vector properties lagging effects arising during deformation path breakage within the Ilyushin's space: the isotropy postulate fulfillment is discussed and a possible explanation for the effects based on physical consideration is provided.