Finite deformation analysis of crack tip fields in plastically compressible hardening–softening–hardening solids

Effect of crack tip shape on near-tip deformation and fields in plastically compressible solids

“…The particle positions (in the initial undeformed configuration) and time are the independent variables. All field equations are functions of convected coordinates, y i and time t. Similar formulation has widely been in use earlier, like in Hutchens et al [6], Khan et al [8], Mohan et al [16], Needleman et al [18] and Singh and Khan [26,27]. The solution of the problem is obtained on the basis of the linear incremental form of the virtual work principle.…”

“…As these materials have prospective uses in applications like viscoelastic energy absorption, compliant thermal interfaces and biomimetic dry adhesives, these materials have attracted numerous researchers over the past several years. Over the years, a large amount of research works have been carried out for stationary as well as growing cracks for plastically compressible solids under monotonic and fatigue loading to understand the near-tip deformation and stress-strain fields; some studies are based on small deformation formulation [2,7,12,24,28,31,32], while others are found on finite deformation formulation [6,8,10,15,16,18,26,27].…”

“…An important problem is how the shape of a crack tip can influence the near-tip deformation and fields for the above kind of materials. It has been realized from some earlier studies (for example, [8,26,27]) that plastically compressible materials with material softening have some different kinds of deformation pattern and stress field around a circular arc crack tip, but how a crack tip shape (other than circular one) can affect those fields and deformation remains to be looked into. Furthermore, it appears that the crack tip shape entails important information about the crack propagation mechanism because they directly reveal local strain/stress field near the crack tip.…”

“…The material constitutive relation employed in this work is identical as that given in Khan et al [8], Mohan et al [16], Needleman et al [18], Singh and Khan [26,27]. The rate of deformation tensor, d (the symmetric part of ̇ ⋅ −1 , where F is the deformation gradient.…”

“…20 and 21. Although there are different techniques to simulate crack growth using finite elements, like node release schemes [1] or cohesive zone model [19], etc., this investigation focuses simulation of crack growth solely due to the effect of crack tip blunting, Hunnell and Kujawski [4], Khan et al [8], Laird and Smith [11], Singh and Khan [26,27], Tvergaard and Hutchinson [29], Tvergaard [30]. It can be observed that for material B Fig.…”