Large scale yielding for dynamic crack growth in a strip geometry

Abstract

Dynamic crack growth in a strip geometry has been studied by a convective formulation of the finite element method. The strip is assumed to be made of a material described by an elastic-viscoplastic constitutive equation and the loading conditions are plane strain mode I. The plastic strain-rates are characterized by a power-law overstress model giving an asymptotic elastic singularity at the crack tip. Two different types of loading on the strip geometry have been investigated. In the first geometry the horizontal boundaries parallel to the crack plane were subjected to prescribed displacements perpendicular to the crack plane and the crack tip was loaded in essentially the same way as for a crack in a plate subjected to tensile loading perpendicular to the crack. The second type of loading consisted of a prescribed rotation of the trailing edge in the moving finite element mesh. This created primarily bending loading of the structure.

The crack tip energy flow has been calculated for different levels of yielding around the crack tip. The results are compared to the true small scale yielding solution obtained from a boundary layer analysis.

The results reported indicate that for the tensile loading there exists a rather wide range of load levels for which the boundary layer solution gives a good description of the fields around the crack tip. For the bending loading the results indicate that the boundary layer solution is a correct description only in cases of extremely small scale yielding.

Comparisons between large scale yielding and the boundary layer solution are also made for the effective stress and the effective plastic strain.