On motion decomposition and constitutive relations in geometrically nonlinear elastoviscoplasticity of crystallites

Abstract

The formulation of geometrically nonlinear boundary value problems is a necessary component in modeling real technological processes of thermomechanical material processing, wherein the main issues are the description of nonlinear kinematics and the formulation of constitutive relations. Most of the existing works do not explicitly consider the used method of motion decomposition that implies the extraction of the part responsible for quasi-rigid motion from the motion of a deformed solid. On our opinion, when choosing a method of motion decomposition and the corresponding corotational frame, the latter must be associated with the material to correctly describe the loading history and symmetry properties of the modeled body. Note that crystalline materials (including metals and alloys) at different scale levels are always anisotropic to a certain extent, and their properties can differ significantly in different directions. Even initially isotropic (at the level of the representative macrovolume) polycrystalline materials also become anisotropic under severe plastic deformation due to texturing. A multilevel approach allows the determination of symmetry elements (planes and axes of symmetry) at the crystallite level in metals, and we propose to relate these elements to the axes of the corotational frame that defines quasi-rigid motion. A new way of motion decomposition is proposed, namely, a multiplicative representation of the deformation gradient with an explicit extraction of the corotational frame motion. Elastoviscoplastic constitutive relations are formulated in terms of a stress free configuration. As the used stresses and strains are energetically conjugate, the requirements of no stress hysteresis and no energy dissipation in arbitrary closed elastic strain cycles are automatically satisfied, which is exemplified for anisotropic crystals. ©hus, an approach is proposed for the construction of geometrically nonlinear kinematic and constitutive relations for metal crystallites using a physically justified method of motion decomposition, with taking into account the symmetry properties of materials.