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

Asymptotic ®elds 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 ®eld D…x† for steady- state crack growth represented by an undetermined power function rl of radius r from the crack tip is assumed ®rst, and the corresponding asymptotic stress ®eld 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 di€erential equations. Then, the exponent l of undetermined damage ®eld is determined so that the assumed damage ®eld D…x† may be consistent with the resulting asymptotic stress ®eld 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 e€ects of material damage on the crack-tip stress ®eld 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