The Theory of Critical Distances applied to multiscale toughening mechanisms

The Theory of Critical Distances (TCD) is an approach used for predicting the effect of cracks and notches on fracture and fatigue behaviour. In recent years it has been successfully applied to a wide range of problems across all classes of materials. The approach relies on the identification of a material constant known as the critical distance, L, which can only be determined by fitting predictions to experimental data. It has been argued that L is related to the size of microstructural features which affect crack growth, but this argument becomes problematic in the presence of multiple toughening mechanisms operating at different scales. In the present work, this matter was approached through the use of thought experiments conducted on model microstructures. It was found that if two mechanisms operate at different length scales, then the use of the normal TCD approach is still possible, though accuracy is reduced and the value of L obtained falls between the length scales of the two mechanisms. A more sophisticated approach however can successfully identify two relevant L values and thus provide insights into the underlying mechanisms. A practical example is given: the analysis of short and long crack toughness data for bone, for which mechanisms at the hundred-micron and millimetre scales were successfully identified. Some general conclusions emerge about the effect of hierarchical toughening mechanisms: in particular it was found that the mechanisms operating at the small length scales may control the strength of the material but have relatively little effect on its toughness.