When voids are present in a ductile material subject to a shear dominated stress state under low stress triaxiality the voids collapse to micro-cracks, which subsequently rotate and elongate in the shear field. In the present plane strain analyses for cylindrical voids a surface load normal to a plane connecting the ends of the micro-crack is used as an approximate representation of contact stresses during frictionless sliding. In a previous study of the same problem the author applied hydrostatic pressure inside the nearly closed micro-crack to approximate contact conditions. The transverse surface loads used in the present analyses avoid the tendency to unrealistically elongate the voids. It is found that even though the model applied here gives significantly later occurrence of a maximum overall shear stress than that found by using hydrostatic pressure, the present model does predict a maximum in all the cases analyzed and thus illustrates the micro-mechanism leading to failure of the material by localization of plastic flow.

Behaviour of voids in a shear field

Shear deformation of voids with contact modelled by internal pressure

One of the basic mechanisms for fatigue crack growth in ductile metals is that depending on crack–tip blunting under tensile loads and re-sharpening of the crack–tip during unloading. In a standard numerical analysis accounting for finite strains it is not possible to follow this process during many cycles, as severe mesh distortion at the crack–tip results from the huge geometry changes developing during the cyclic plastic straining. In the present numerical studies, based on an elastic–perfectly plastic material model, crack growth computations are continued up to 200 full cycles by using remeshing at several stages of the plastic deformation. Three different values of the load ratio R = K min / K max are considered. It is shown that the crack–tip opening displacement, CTOD, typically undergoes a transient behaviour, with no crack closure during many cycles, before a steady-state cycling with crack closure at the tip starts to gradually develop.

On fatigue crack growth in ductile materials by crack-tip blunting

The growth of voids in a thin ductile layer between ceramics is analysed numerically, using an axisymmetric cell model to represent an array of uniformly distributed spherical voids at the central plane of the layer. The purpose is to determine the full traction-separation law relevant to crack growth by a ductile mechanism along the thin layer. Plastic flow in the layer is highly constrained by the ceramics, so that a high level of triaxial tension develops, leading in some cases to cavitation instabilities. The computations are continued to a state near the occurrence of void coalescence.

Thomas Ørts Pedersen

Papers

Remeshing in analysis of large plastic deformations