Asymptotic fields of stress and damage of a mode I creep crack in steady-state growth

Asymptotic fields of stress, strain rate and damage of a mode I creep crack in steady-state growth are analyzed on the basis of Continuum Damage Mechanics by employing a semi-inverse method. A damage field D(x) for steady-state crack growth represented by an undetermined power function r(l) of radius r from the crack tip is assumed first, and the corresponding asymptotic stress field of a mode I crack in a non-linear creep damage material is analyzed by solving a two-point boundary value problem of non-linear differential equations. Then, the exponent l of undetermined damage field is determined so that the assumed damage held D(x) may be consistent with the resulting asymptotic stress field and the damage evolution equation. Finally, the relations between exponent p of the asymptotic stress distribution and exponents n and m of power creep constitutive law and the power creep damage law are elucidated. The effects of material damage on the crack-tip stress field in non-linear materials are discussed in detail. Comparison between the results of the present analysis and those of earlier papers of fracture mechanics on the creep-crack growth analyses based on grain-boundary cavitation is also made. (C) 2000 Elsevier Science Ltd. All rights reserved.