Theoretical analysis of stress intensity factors and interactions of collinear flaws with unequal lengths in brittle solids under uniaxial tensile conditions

Abstract

Interactions between multiple flaws with different sizes in brittle solids are a key factor that induce failure. Previous studies have focused on the initiation, propagation and coalescence behaviors of multiple flaws in brittle solids. Nevertheless, there have been few theoretical or quantitative analyses of interactions between multiple flaws. In the present study, based on the Kachanov method, we first proposed theoretical analytical solutions of the stress intensity factors (SIFs) for two and three collinear flaws with unequal lengths under uniaxial tensile conditions. Then, a theoretical analysis of the effects of various geometric factors, such as flaw interval, flaw length and flaw number, was performed. The results supported the following findings: (1) For two collinear flaws, interactions between the primary and secondary flaws gradually weakened with increasing flaw interval, and the flaw length ratio gradually became the main factor that determined the interaction. (2) For three collinear flaws, when the interval between the primary and secondary flaws was not less than 1.5 times the length of the secondary flaw, the interaction had no effect on the propagation of the primary flaw. (3) The increase in the number of collinear flaws significantly enhanced the effect on propagation reinforcement between the flaws. Finally, numerical simulations were conducted to verify the results of the theoretical analysis, and good consistency was found. These research results are of great theoretical significance and engineering value for quantitatively understanding the failure mechanism of brittle solids containing multiple flaws and proposing effective measures to prevent cracking and ensure the safety of brittle solid structures.