Self-Similarity of the Near Crack-Tip Fields under Creep Regime Taking into Account Damage Augmentation

The paper analyzes a series of computer experiments aimed at identifying the self-similar behavior of stresses and continuity (damage) near the crack tip in a steady-state creep mode in a damaged medium. Finite element computations of crack-tip fields under creep regime were carried out using the interdisciplinary, universal finite element platform SIMULIA Abaqus FEA using the UMAT utility, which integrates the process of damage augmentation into the FEM computational scenario. The paper implements computational simulations of uniaxial stretching of a plate weakened by a central horizontal crack in the steady-state creep mode, which includes damage growth that evolves over time according to the mathematical model of damage growth by Kachanov – Rabotnov (KR) according to a power law for various values of exponents of the kinetic equation and the power constitutive equations. The study and analysis of the FE for the crack-tip stress and continuity (integrity) fields for a number of material constants clearly reveal a selfsimilar behavior of stress and damage fields near the front tip. The structure of the solution is revealed and the values of the exponents in the self-similar variable and the self-similar representation of the solution are found, which can be interpreted as an intermediate self-similar solution of the second type according to the classification of G.I. Barenblatt. It is elucidated that the revealed property of self-similarity of the solution can be interpreted as the intermediate asymptotes of the far field of damage and stress. The obtained figures also clearly show the asymptotes of the near-field stress, characterized by the absence of a singularity in the immediate vicinity of the crack.