A Thermodynamically Consistent Phase Field Framework for Anisotropic Damage Propagation

MANY PHASE FIELD FORMULATIONS HAVE BEEN DEVELOPED TO SIMULATE DAMAGE EVOLUTION TAKING INTO ACCOUNT DIFFERENT PHENOMENA SUCH AS PLASTICITY, LARGE DEFORMATION, ANISOTROPY AND FRACTURE BEHAVIOR OF MATERIALS. IN THE PRESENT WORK, A THERMODYNAMIC CONSISTENT FORMULATION IS ADAPTED INCLUDE EFFECT PREFERENTIAL CLEAVAGE PLANES EVOLUTION. SCALAR VARIABLE ASSOCIATED WITH EACH PREDEFINED DIRECTION CRACK PROPAGATION. ANY OTHER POSSIBLE PENALIZED BY PARAMETER (BETA ? 1) THAT REPRESENTS DEGREE FRACTURE. DEFINING BETA = 0, ISOTROPIC CASE RECOVERED. MORE THAN ONE DIRECTION, MATERIAL CONSIDERED TOTALLY FRACTURED WHEN VARIABLES REACHES ONE. SIMULATIONS SHOWED MODEL CAN REPRODUCE EXPECTED PROPAGATION PATTERN FOR MATERIALS TWO DIRECTIONS. WAS SUCCESSFUL SIMULATING ZIGZAG COMMONLY OBTAINED DOUBLE CANTILEVER BEAM STUDIES SPINEL CRYSTALS.