Two different constitutive models are employed to describe creep crack growth under small-scale creep conditions theoretically. The first model combines elastic/nonlinear viscous deformation fields (8 = (r/E + Aa ~) with a critical-strain criterion, e = e,, to be satisfied at a structural distance x,. ahead of the crack. The deformation fields are characterized by three singular fields -the remote elastic field, the HRR field in the creep zone, if one exists, and the Hui-Riedel (HR) field near the growing crack tip. At small stress intensity factors, crack growth is found to become irregular and to tend to instabilities. This is a consequence of the properties of the HR field.
The second model is based on continuum damage mechanics. Creep strain rates are modified by a Kachanovtype denominator, ~ = 6/E + Aa"/(1 -~o) ~, where ~o is a damage parameter which obeys a second differential equation in time. Solutions of these constitutive equations for crack geometries contain crack growth automatically, where co = 1. It could not finally be decided whether a solution of this model for steady-state crack growth exists, but if it exists, the growth rate must be a ~: K] for dimensional reasons in contrast to a oc Kโข in the first model. For non-steady growth, the crack tip and the process zone may either be contained within the creep zone or may grow outside the creep zone. Corresponding to these cases, two types of similarity solutions can be obtained, in which the crack length, the process zone size and the creep zone size increase smoothly as a function of time with no tendency to instabilities. This difference to the first model arises since the HR field is displaced by the process zone. Only for crack growth within the creep zone do the results of the two models coincide (apart from numerical factors) if the stress intensity factor is high enough (K~ > Ee~ ,f-~x,).