Constitutive Model Based on the Multiplicative Decomposition of Deformation Gradient in Arbitrary Orthogonal Coordinate System

According to general crystallographic slip constitutive laws, the stress-strain analysis of nickel based single crystal superalloy (NBSCS) in arbitrary coordinate system were based on material coordinate system (SRCS method). Ignoring the other symmetry of NBSCS, only the symmetry of plane families {001} were considered, which bring considerable errors into the stress-strain analysis. In this paper, the variation regulation of micro-physical systematical property about this alloy in arbitrary directions was investigated. From the arrangement of atoms in different crystal planes, NBSCS has four symmetry plane families, {001}, {110}, {112} and {111}. According to these symmetry planes, three reference orthogonal coordinate systems were established. Based on these coordinate systems and the coordinate rotation method (TRCS method), the stress-strain relationship of crystallographic slip constitutive model in arbitrary coordinate system was established. Meanwhile elastic constants in arbitrary directions were obtained. Comparing the results of the tensile stress-strain curves obtained from TRCS method with that from SRCS method, it is found that by the TRCS method the elastoplastic stress-strain simulation error of the NBSCS could be effectively reduced.