A new strain-based approach to investigate the size and geometry effects on fracture resistance of rocks

In this paper, a new strain-based criterion is suggested for assessing the effects of size and geometry of specimen on the fracture resistance of rocks under mixed-mode (I/II) loading. The new approach named the modified maximum tangential strain (MMTSN) criterion is based on the classical maximum tangential strain (MTSN) criterion, in which the first non-singular term ($T$) of Williams series expansion is considered in addition to the singular terms ($K$). Furthermore, to provide more coherence, the critical distance ($r_c$) from the crack tip is defined according to a new strain-based failure model. Unlike similar strain-based fracture models available in the literature, the critical distance $r_c$ in the MMTSN criterion is assumed to be size-dependent and a semi-empirical formulation is utilized for describing this size-dependency. To assess the ability of MMTSN for considering the size and geometry effects, the experimental data existing in the literature for a number of cracked Brazilian disk (CBD) and semi-circular bend (SCB) specimens manufactured from Guiting limestone are taken into account. It is demonstrated that the MMTSN criterion can predict the experimental data very well by taking into consideration the size and geometry effects without needing to calculate the other higher order terms.