Ductile crack propagation by plastic collapse of the intervoid ligaments

Abstract

In the present study ductile crack initiation and propagation is investigated by means of a micro-mechanical model under small-scale yielding conditions. Voids are resolved discretely in the fracture process zone where steep gradients occur during the loading history and are taken into accounted by a homogenized porous plasticity law elsewhere. The size of the region of discrete voids is not set a priori but is determined consistently. The results show that effective crack growth occurs by plastic collapse, i.e. purely geometric softening of the intervoid ligaments without incorporating material separation. Due to this mechanism a limit load exists coinciding with the maximum fracture toughness. In addition, it turns out that the shielding due to the growth of voids around the crack plane has a considerable influence on the computed R-curves compared to models neglecting this effect. Depending on the void arrangement a diffuse softening zone or even crack branching is observed. A comparison with experimental data from literature indicates that plastic collapse and the formation of diffuse zones of void growth are realistic mechanisms of ductile crack propagation.

Micromechanisms of fracture in nodular cast iron: From experimental findings towards modeling strategies – A review

“…In [63,119] the homogenized behavior outside the discrete void region was modeled by Mises plasticity with identical parameters of the matrix material. In [57] such simulations were compared to simulations allowing also for void growth around the process zone. The void growth around the process zone, which is observed in experiments as well as discussed in Section 2.4.1, was incorporated by resolving several layers of discrete voids and by embedding this discrete zone in a homogenized region modeled by the GTN-model.…”

Micromechanical modeling of crack propagation in nodular cast iron with competing ductile and cleavage failure

“…to the distance X 0 of the voids. However, preliminary studies of the purely ductile mechanism [13,14] showed that void growth in the plastic zone outside the immediate process zone must nevertheless not be neglected. Although possibly of low magnitude, the void growth in the plastic zone shields the process zone from high triaxial stresses thus retarding at least the ductile fracture initiation.…”

“…Several layers of discrete voids (i.e. in planes parallel to the crack plane) have to be incorporated in the process zone where inhomogeneous deformations of the individual unit cells appear that cannot be described adequately by the GTN-model [13,14]. Of course the strongest deformations appear in the void layer in the crack plane which is why a fine mesh is required there.…”

“…In order to deal with such pop-ins and with stationary states of crack propagation which appear under small-scale yielding conditions after sufficient amount of crack growth [34], in the present study dynamic simulations (i.e. including inertia) are performed but with quasi-static loading and implicit time integration as in several preceding studies [13,14,10]. Quasi-static loading means that the time elastic waves need to pass the distance A 0 has to be small compared to the time scale of loading s L .…”

“…Petti and Dodds [24] resolve the microstructure in front of the crack tip discretely in form of a priori existent voids. In general, it is well-known that models with discrete voids within an elastic-plastic matrix predict a plastic collapse and subsequent necking of the intervoid ligaments at sufficient level of loading thus allowing to simulate ductile crack propagation [35,13]. However, Petti and Dodds [24] evaluate possible cleavage only a posteriori locally by means of a Beremin-type criterion, i.e.…”