On Isotropic Damage Distributions and Evolutions of HRR Field

Abstract

Damage distribution and evolution of the HRR field are characterized by means of a two-scalar damage variable approach under the consideration of isotropic damage. This theory is based on the definition of thermodynamic conjugate forces and the postulation that the plastic damage surface corresponds to the initiation of plastic damage. An asymptotic solution is applied for the non-linear plastic damage evolution equations. It is shown that both the damage variables may be expressed as a function of the accumulated amount of overall damage respectively in exponential and tangential types, which determine the damage characteristics in different areas. It is also revealed that the damage evolution coefficient plays an important role to determine the distributions of the damage variables, effective Young’s modulus and Poisson’s ratio. The obtained largest damage variable, which characterizes the deterioration of the material, and the lowest effective Young’s modulus around the crack tip locate at and respectively for Mode I and II problems.