STRESS STATE DEPENDENCE OF THE SHAPE PARAMETER OF THE 3-PARAMETER WEIBULL DISTRIBUTION IN RELATION TO FRACTURE OF CERAMICS

The present author showed theoretically in a previous paper that the magnitude of the shape parameter of a three-parameter Weibull distribution, m3, depends on stress states. Specifically, it was shown that m3 = alpha - 1/2 for equi-biaxial tension (sigma-1, sigma-2, sigma-3) = (sigma, sigma, 0) and m3 = alpha - 1 for equi-triaxial tension (sigma-1, sigma-2, sigma-3) = (sigma, sigma, sigma) when uniaxial fracture strength follows a three-parameter Weibull distribution with m3 = alpha where sigma-1, sigma-2, and sigma-3 are the principal stresses. This result raises a question of whether m3 for combined tension-compression stresses exceeds that for uniaxial tension. In the present paper, this problem is investigated theoretically. It is shown that even for the case of (sigma-1, sigma-2, sigma-3) = (-k-sigma, -k-sigma, sigma) with k > 0, m3 is equal to alpha. This result together with the previous result indicates that the shape parameter of a three-parameter Weibull distribution for any multiaxial stress state does not exceed that for uniaxial tension.