Fracture mechanics of weldment using finite elements

It is established that weldments are non-homogeneous anisotropic materials. Hence a new fracture criterion is necessary to predict critical directions for crack propagation as well as critical loads. The proposed criterion is that the crack will propagate in a direction so that the energy release rate is stationary. The magnitude of the critical energy release rate is a material property which is dependent upon the structure of the weldment. To utilize this criterion an existing two-dimensional finite element code has been modified to have the following extra features; special crack tip triangular elements have been developed to account for the singularity at the crack tip; the computer program capabilities have been extended to solve plane stress, plane strain and axisymmetric problems for orthotropic, non-homogeneous, elastic materials whereby different elements have different orientations of their principal material directions; the facility of constraining two nodes to have the same displacement has been added to the code. This is done to allow the finite element model to propagate the crack along different element boundaries without having to increase the number of nodes in the input data when the crack is allowed to propagate. The procedure then is to generate a finite element mesh for the specimen considered and to load it with a known deplacement. The crack is allowed to propagate in a given direction (usually an element boundary) by a distance S and the difference in strain energy per unit thickness U is obtained. The direction of crack propagation is determined by a variational procedure. This theory explains crack branching and irregular crack-propagation directions observed experimentally