Failure criterion for brittle materials with U-notches: Unification of characteristic length-based and grain size-based criteria

Here, the limitations of characteristic length-based (L_chb) and grain size-based (G_b) criteria with two or three parameters were pointed out employing the apparent toughness tests of 12 different ceramics at a large span range of U-notch root radius (ρ) values. After comprehensively considering the potential influencing factors of stress intensity factor (K_c), ρ divided by critical notch tip radius (ρ_c) was proposed as the independent variable, and the data of 21 materials (covering ceramics, plastics, resins, rocks, and metals) was summarized and discussed to establish a simple and more applicable K_c prediction model. Results indicated that K_c/K_Ic was a power function of ρ/ρ_c with a power exponent n of 0.5 for ideal materials and less than 0.5 for actual materials. It was also found that ρ_c can be calculated simply by K_Ic²/(πσ₀²), where σ₀ represented the inherent strength. This semiempirical criterion succeeded in unifying the L_chb and G_b criteria without introducing more parameters to increase the prediction accuracy of the K_c at the U-notch root for brittle materials like ceramics.