Effect of residual surface stress on the strength distribution of brittle materials

The introduction of residual surface stresses into a material can change the strength distribution simply due to variability in the stress intensity factor of surface cracks. This variability arises from the distribution in surface (critical) crack lengths. A fracture mechanics approach was used to determine the influence of surface compression on the average strength and the standard deviation of the strength distribution. The strengths of the stress-free samples were assumed to fit a two-parameter Weibull distribution, and the increases in strength resulting from the surface compression were determined using fracture mechanics. It was determined from the analysis that the standard deviation/average strength ratio (coefficient of variation) initially increases, passes through a maximum, and ultimately reaches a plateau value below the initial value, as one increases the depth of surface compression. The maximum increase in the strength scatter occurs when the depth of the surface compression is approximately equal to the characteristic crack size. These changes were found to be dependent on the magnitude of the surface stress, as well as the characteristic strength, Weibull modulus, and fracture toughness of the stress-free material.