Modelling of fatigue crack growth at the microstructural level

Since the 1960s we have used the stress intensity parameter K to characterise the growth of fatigue cracks. More recently it has been demonstrated experimentally that this parameter does not work for small cracks: these cracks tend to grow faster than would be predicted using linear elastic fracture mechanics, they show lower threshold values for growth, and the one-to-one relationship between growth rate and stress intensity range breaks down. One reason for this behaviour is that these cracks are of the same order of size as the microstructure––typically <10 grain diameters. Material homogeneity can no longer be assumed; the behaviour of an individual crack depends on the local microstructure. Two modifications are required to the modelling equations: (i) the use of statistical parameters to describe behaviour, and (ii) the introduction of parameters related to the microstructure. This paper reviews the state of the art and describes some recent work which applies the same concepts to a model of fatigue in bone. The introduction of short-crack growth relationships helps us to model damage development and understand the dynamic relationship between fatigue and repair in this living material.