Non-linear rate dependent deformation under compression due to state variable friction

Abstract

Observations of strain-rate effects in brittle failure under compression have been interpreted as suggesting that sub-critical crack growth plays an important role in the deformation process. We suggest an alternate interpretation in which strain-rate effects are attributed to rate- and state-dependent friction along parent cracks. Using independently measured friction law parameters we demonstrate that a wing crack model incorporating state variable friction replicates the observed dependence of the stress-strain curve on applied strain rate. Model results are essentially equivalent to those of an earlier model incorporating sub-critical crack growth, suggesting that despite their different conceptual foundations, the validity of either model can not be determined on the basis of the observed strain-rate effects. However, only the rate-dependent friction model reproduces the observed unsteady growth of wing cracks.