Influence of Test Specimen Geometry on Probability of Failure of Composites Based on Weibull Weakest Link Theory.

Abstract

This paper presents an analytical model that quantifies the stress ratio between two test specimens for the same probability of failure based on the Weibull weakest link theory. The model takes into account the test specimen geometry, i.e., its shape and volume, and the related non-constant stress state along the specimen. The proposed model is a valuable tool for quantifying the effect of a change of specimen geometry on the probability of failure. This is essential to distinguish size scaling from the actual improvement in measured strength when specimen geometry is optimized, aiming for failure in the gauge section. For unidirectional carbon fibre composites with Weibull modulus m in the range 10–40, it can be calculated by the model that strength measured with a straight-sided specimen will be 1–2% lower than the strength measured with a specific waisted butterfly-shaped specimen solely due to the difference in test specimen shape and volume.