The sensitivity of a Weibull failure criterion to singularity strength and local geometry variations

Abstract

Previous experimental evidence has shown scale sensitivity of adhesives both in terms of ultimate stress and strain to failure; this sensitivity may be modelled using Weibull statistics. The implications of this on the sensitivity of strength predictions to mesh density around singularity points and small changes in local geometry is investigated using an idealised model of an enclosed corner in an adhesive joint. The sensitivity of two other failure criteria are also compared to the Weibull method. It is seen that there is a critical relationship between the Weibull shape parameter, m, and the singularity strength, λ. This relationship marks the transition between mesh insensitivity and mesh sensitivity, even with a singular stress (or strain) field present. If the singularity is removed by localised rounding, then the Weibull method of failure prediction shows much less sensitivity to the exact local geometry variation than other methods of failure prediction.