Phase field approach to dislocation evolution at large strains: Computational aspects

Computational aspects of the phase field simulations of dislocation nucleation and evolution are addressed. The complete system of equations for the coupled phase field approach to dislocation nucleation and evolution and nonlinear mechanics for large strains is formulated. Analytical solutions for a stationary and propagating single dislocation, dislocation velocity, core energy, and core width are found. Dislocation parameters for nickel are identified based on existing molecular dynamics simulations. In contrast to all previous efforts that are based on the spectral approach, finite element method (FEM) is utilized, which allowed us to treat large strain problems and nonperiodic boundary conditions. The single dislocation order parameter profile and the stationary distance between two neighboring dislocations at a semicoherent sharp austenite martensite interface are in perfect agreement with analytical expressions. The main focus is on proving that the new points of the developed theory can be confirmed in simulations, including possibility of obtaining the desired dislocation height for aligned and inclined dislocations, eliminating spurious stresses, resolving dislocation cores and interaction between cores of different dislocations. Mesh independence of the solutions is demonstrated and the effect of approximating finite element polynomials is analyzed, exhibiting possibility of significant numerical errors when special care is not taken of. Problems of nucleation and evolution of multiple dislocations along the single and multiple slip systems near martensitic lath, and along the sharp austenite martensite interface, the activity of dislocations with two different orientations in a nanograined material under shear and pressure, and the interaction between two intersecting dislocation systems are studied. Surfacemodified partial dislocation was revealed. These problems represent the first step in the future Email address: [email protected] (Valery I. Levitas) Preprint submitted to International Journal of Solids and Structures October 28, 2015