Thermodynamically consistent phase field approach to dislocation evolution at small and large strains

摘要: Abstract A thermodynamically consistent, large strain phase field approach to dislocation nucleation and evolution at the nanoscale is developed. Each defined by an order parameter, which determines magnitude of Burgers vector for given slip planes directions. The kinematics based on multiplicative decomposition deformation gradient into elastic plastic contributions. relationship between rates parameters consistent with phenomenological crystal plasticity. Thermodynamic stability conditions homogeneous states are formulated satisfied proper choice Helmholtz free energy parameter dependence vector. They allow us reproduce desired lattice instability a stress-order curve, as well obtain stress-independent equilibrium avoid artificial dissipation during deformation. Ginzburg–Landau equations obtained linear kinetic relations rate change conjugate thermodynamic driving forces. crystalline coefficient dislocations periodic step-wise function coordinate along normal plane, provides barrier plane desired, mesh-independent height bands any system orientation. Gradient contains additional term, excludes localization within smaller than prescribed height, but it does not produce interface energy. An term introduced that penalizes interaction different same point. Non-periodic boundary include surface due exit from crystal. Obtained kinematics, thermodynamics, kinetics strains simplified small rotations, well.