Some simple formulas to predict the variation of stress intensity factors for mode I crack induced by near crack-tip inclusion

Several simple formulas have been developed to predict the variations of stress intensity factors (SIFs) for mode I crack induced by the inclusion within crack-tip field. The derivation of the fundamental formula is based on the transformation toughening theory. The unconstrained mismatch strains between matrix and inclusion, which induce the variation of the near crack-tip field, are estimated from the remote applied SIF K0. As validated by numerical examples, the developed formulas have satisfactory accuracy for wide range of the modulus ratios between inclusion and matrix as long as the inclusion is located in the K0-controlled field.