A Further Improved Maximum Tangential Stress Criterion for Assessing Mode I Fracture of Rocks Considering Non-singular Stress Terms of the Williams Expansion

Previous studies showed that the modified maximum tangential stress (MMTS) criterion considering two stress terms (containing r^−1/2 and r^1/2) of the well-known Williams series expansion can better assess the mode I fracture toughness (K_Ic) of rocks than the traditional maximum tangential stress (MTS) criterion. However, this study indicates that in some cases, only using the two stress terms cannot fully describe the tangential stress at the critical distance for rock specimens, and the higher order, non-singular stress terms can also play important roles in the tangential stress. The MMTS fracture criterion might still induce non-negligible errors for assessing mode I rock fracture. Thus, we propose a further improved MTS (FIMTS) criterion. The FIMTS criterion emphasizes that the number of non-singular stress terms used in a MTS-based criterion should be carefully chosen according to the following principle: the tangential stress at the critical distance can be accurately described using the selected stress terms. Mode I fracture tests on two kinds of rocks are conducted using a newly proposed V-notched short rod bend (VNSRB) specimen. The specimen- or loading-configuration-dependence of K_Ic indicated by the experimental data is theoretically assessed using the traditional MTS, the MMTS and the FIMTS criteria, and the last criterion is shown to be the best. Therefore, considering non-singular stress terms of the Williams expansion can better assess mode I fracture of rocks. Our study calls for more attention to the effects of non-singular stress terms on mode I fracture of rocks, especially for small-size specimens and for rocks with relatively large critical distances.