Pervasiveness of plasticity at the crack tip

Above a critical yield stress (Tq the singular mode I stresses around sharp cracks are truncated at the yield stress in a plastic zone of extent ( ahead of the crack, which increases with increasing applied stress or stress-intensity factor K. This results in important alterations of the crack-tip stresses. The level of pervasiveness of the plastic zone in parts of finite size governs the nature and extent of the alterations of the crack-tip stresses and strains from those presented in Section 12.2.2 for elastic response only. As the stresses are radically altered around the crack tip in the plastic zone and lose their singularity, the strains become more concentrated. Depending on the different levels of pervasiveness of the plastic zone across the cross section, there occur different forms of alteration of stress and strain fields that govern the eventual forms and mechanisms of crack growth and fracture. 

In Fig. 12.6(b), at higher levels of externally applied stress, the plastic zone is now of extent C D — a), i.e., it is still smaller than the unaffected ligament. This range of pervasiveness of plasticity in the part is called contained yielding. Depending on the type of constitutive plastic response of the material, the distributions of stress and strain both inside and outside the plastic zone are now quite different from those of SSY. 

Finally, in Fig. 12.6(c) the external applied stresses are larger still and the plastic zone has now increased over the entire cross section where D — a). Here the entire part response is importantly altered by the plasticity of the material and the nature of its strain-hardening behavior. 

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