The Effects Of Crack-tip Plastic Zone On Fracture Behavior

Plastic zone is always present in the vicinity of crack tip for most metal materials,and the fracture behavior of a cracked structure is significantly affected by the shape and size of the plastic zone.The toughening effects of plastic zone shows that the larger the plastic zone size results in higher toughness of materials.In the classical Irwin's model,the singular stress field outside plastic zone is assumed to be a translational shift of linear elastic solution.Irwin thought that the effect of plastic deformation could be taken into account by considering an effective crack,whose length is equal to the physical crack length plus part of the plastic zone size in front of the crack-tip.Irwin's approach leads to the fact that the stress intensity factor of the effective crack is always larger than the corresponding linear elastic one.This is inconsistent with the shielding effects of the crack-tip plastic zone.Moreover,Irwin's model is only suitable for ideally elastic-plastic materials.For materials satisfying Ramberg-Osgood hardening law,the size of plastic zone and the stress outside plastic zone are greatly affected by the value of hardening exponent,and the stress distribution in the plastic zone is absolutely different from the case of ideally elastic-plastic material.Thus,we proposed the improved Irwin's model.Considering that the stress outside plastic zone is greatly affected by the plastic zone,we hold that the stress outside crack-tip plastic zone is different from the linear elastic solution.In order to examine the affected singular stress field near crack-tip by the plastic zone,we propose a principle that the singular stress redistribution induced by the plastic zone must be statically equivalent to the linear elastic singular stress field ahead of the crack-tip in the plasticity-influenced zone.Following this principle,we develop the improved Irwin's model,which applies to both ideally elastic-plastic material and Ramberg-Osgood strain hardening material,and derive the explicit equations so as to quantitatively evaluate the shielding effects of the plastic zone.The improved Irwin's model is capable of quantitatively explaining the shielding and toughening effects of the crack-tip plastic zone.Using the improved Irwin's model,we quantitatively evaluated the effects of the crack-tip plastic zone on near-tip stress intensity factor for infinite plates with a central crack and edge crack.The results of the improved Irwin's model proposed in the present study are qualitatively consistent with those of the method based on transformation toughening theory.