The influence of aspect ratio on the determination of tearing energy in mode I fracture tests

Abstract

The energy for tearing is a classical measure of fracture toughness for elastic materials at finite strains. The prominent approach to quantify the tearing energy utilizes a tensile test on edge-cut thin rectangular specimens with low height-to-width ratio to determine the critical stretch at which a crack propagates from the tip of the cut. The analysis of the experiment, proposed by Rivlin and Thomas (1953), relies on the assumption that a large portion of the test piece is in a state of plane strain, and that the change of the total elastic energy is equal to the energy release due to the formation of new crack surfaces. While these assumptions are well justified for test pieces with sufficiently low height-to-width ratio, limitations in the availability and homogeneity of various sample materials have enforced the use of specimens with higher height-to-width ratios. In order to analyse the applicability of the classical theory and the corresponding errors, we investigate in the present work the influence of the sample’s height-to-width ratio on the estimation of the tearing energy in mode I fracture tests. Exemplified with experiments and simulations for the elastomer Ecoflex 1:1, we show that reliable measurements can be obtained even for a quadratic sample geometry. For tough materials, however, significant overestimation of the tearing energy is expected already for a height-to-width ratio larger than 1/2. Surprisingly, in very brittle materials the tearing energy is vice-versa prone to be underestimated by up to 10% for ratios up to 1. The error also depends on the non-linear stress–strain characteristics, as illustrated by the use of different constitutive models. While a generally valid geometrical criterion cannot be defined based on the present results, our results suggest that the error hardly exceeds 10% for height-to-width ratios of up to 1/2.