Numerical development of a new correlation between biaxial fracture strain and material fracture toughness for small punch test

Abstract The miniaturized specimens are used to determine mechanical properties of the materials, such as yield stress, ultimate stress, fracture toughness etc. Use of such specimens is essential whenever limited quantity of material is available for testing, such as aged/irradiated materials. The miniaturized small punch test (SPT) is a technique which is widely used to determine change in mechanical properties of the materials. Various empirical correlations are proposed in the literature to determine the value of fracture toughness (JIC) using this technique. bi-axial fracture strain is determined using SPT tests. This parameter is then used to determine JIC using available empirical correlations. The correlations between JIC and biaxial fracture strain quoted in the literature are based on experimental data acquired for large number of materials. There are number of such correlations available in the literature, which are generally not in agreement with each other. In the present work, an attempt has been made to determine the correlation between biaxial fracture strain (eqf) and crack initiation toughness (Ji) numerically. About one hundred materials are digitally generated by varying yield stress, ultimate stress, hardening coefficient and Gurson parameters. Such set of each material is then used to analyze a SPT specimen and a standard TPB specimen. Analysis of SPT specimen generated biaxial fracture strain (eqf) and analysis of TPB specimen generated value of Ji. A graph is then plotted between these two parameters for all the digitally generated materials. The best fit straight line determines the correlation. It has been also observed that it is possible to have variation in Ji for the same value of biaxial fracture strain (eqf) within a limit. Such variation in the value of Ji has been also ascertained using the graph. Experimental SPT data acquired earlier for three materials were then used to get Ji by using newly developed correlation. A reasonable comparison of calculated Ji with the values quoted in literature confirmed usefulness of the correlation.