Theoretical Error Analysis of the T-Stress for a Central Cracked Brazilian Disk Specimen

Abstract

The central cracked Brazilian disk (CCBD) specimen is one of the most favored samples to measure the combined mode fracture resistance of brittle materials. The T-stress in this sample has a great influence on the experimental results, which are extensively used in fracture criteria for evaluating the fracture behavior of CCBD specimens for different materials. Due to the errors in geometric dimension and crack inclination angle for CCBD specimens, it becomes essential to conduct error analysis of T-stress. In this work, a closed-form expression of T-stress for a CCBD specimen under radial concentrated force was presented with weight function method. Based on this expression, two error transfer functions were also derived to study the T-stress error caused by the errors of crack length ratio and crack inclination angle. The theoretical analysis indicated that the relative error of T-stress increases with the increase of crack length ratio and crack inclination angle under the combined modes I and II. It was also found that the crack length ratio has a very little impact on the T-stress error for pure mode I loading. Furthermore, T-stress is more sensitive to the impact of crack length ratio than pure mode II stress intensity factor (SIF).