On the path-dependence of the fracture locus in ductile materials – Analysis

The effect of loading path on the fracture locus was examined theoretically by means of cell model calculations. Two-dimensional axisymmetric finite element analyses were conducted to simulate plastic deformation of a material containing a periodic distribution of initially spherical voids. In the cell model, failure is defined to correspond to an abrupt loss of overall load bearing capacity. The cylindrical unit cells were subjected to loading along several radial paths, characterized by constant values of stress triaxiality. The strain-to-failure was recorded for each path and the locus relating it to triaxiality was thus uniquely determined. The process was repeated for a set of non-radial loading paths in which uniaxial loading was applied up to some strain level, followed by loading at constant triaxiality. For these cases, the time-weighted average value of stress triaxiality was used to plot the fracture locus. It was found that the failure locus for nonradial loadings differs substantially from that for radial paths. In fact, the nonradial locus does not represent a one-to-one relationship between average triaxiality and strain-to-failure. In addition, by varying the strain level image at which the load path is changed, a family of failure loci is generated, indexed by image.