Transient crack-tip fields for mixed-mode power law creep

Abstract

Mixed-mode stationary crack-tip fields are obtained for an elastic-nonlinear viscous power law creeping solid under conditions of plane strain and small-scale creep. Power law exponents of 2 and 5 are considered which are representative of the creep response of a wide range of ceramics and metals. The imposed far-field mixity ranges from pure mode I to pure mode II. Crack tip fields are calculated during the transient regime using a detailed finite element analysis and are shown to be governed by a Hutchinson-Rice-Rosengren type singularity over the inner one fifth of the creep zone. Dominance of universal mixed-mode near-tip fields within the inner creep zone is found for several mixtures of far-field mode I and mode II. The pronounced effects of the amount of mixity on the size and shape of the creep zone as well as on the time required to reach extensive creep conditions are determined. For a creep exponent of 5, it is estimated that the creep zone grows about seven times faster in mode II than in mode I, with a corresponding decrease in the transition time from small-scale to extensive creep. For a creep exponent of 2, the creep zone grows about six times faster in mode II than in mode I. Finally, the mixed-mode creep fields are used to assess possible beneficial effects of crack deflection or branching in metals and ceramics at elevated temperatures.