Fracture stability, R-curves and strength variability

Abstract

Variability in fracture strength is examined as a function of the increase in fracture resistance with crack length. The driving force for fracture is modelled generally as the sum of two components, one stabilizing and the other destabilizing crack propagation, leading to a crack extension force displaying a minimum as a function of crack length. The resistance to crack extension, the R-curve, is modelled as an increasing power law. By invoking the equilibrium and instability conditions for fracture, strength is thus shown to have a simple power law dependence on the magnitude of the stabilizing component of the crack driving force. The magnitude of this power law dependence is shown to be inversely related to the rate of increase of the R-curve. This latter result implies that although strengths will increase for a given flaw size in the presence of an R-curve, a more important ramification is that the related increased crack stabilization leads to diminished distributions of strengths for given ranges of flaw sizes. An expression is derived quantifying this conclusion, showing an increasing relation between the Weibull modulus of a strength distribution and the slope of the R-curve. The results substantiate the empirical finding that appropriate R-curve behavior is an effective means of achieving high, narrow strength distributions, independent of randomly introduced flaws.