Modeling of fracture in small punch tests for small- and large-scale yielding conditions at various temperatures

Abstract

We present a systematic numerical study on temperature dependent fracture mode change in small punch tests. Following Needleman and Tvergaard (2000), we model the material as thermo-inelastic, where the ductile fracture mode, by void nucleation, growth and coalescence is accounted for by Gurson׳s porous metal plasticity (Gurson, 1977). The brittle fracture mode by cleavage is accounted for by Ritchie–Knott–Rice׳s deterministic maximum principal stress criterion (Ritchie et al., 1973). The well-known problem of mesh dependence associated with softening material behavior is remedied by using an integral type nonlocal formulation similar to that presented in Tvergaard and Needleman (1995). Two length scales are incorporated into the constitutive relations: the ductile fracture length scale is based on the average inclusion distance and associated with the nonlocal evolution equation for the porosity. The brittle fracture length scale is based on the average grain size and associated with the material region at which the maximum principal stress is averaged out. The material model is used to simulate small punch tests at −196°C, −158°C and 25°C of notched and unnotched specimens of P91 steel representative for small- and large-scale yielding conditions, respectively. The simulated fracture modes and patterns show a very good agreement with experiments: for −196°C brittle fracture propagating normal to the maximum (tensile) principal stress prevails. For 25°C ductile fracture is governed by shear localization with voidage. The simulations also show that the deformation energy is considerably higher for the upper shelf tests compared to the lower shelf tests.