A strain-based Dugdale model for cracks under generally yielding conditions

摘要

To develop an analytical method for quantifying the growth behaviour of short cracks embedded in notch plastic zones, a critical assessment of the Dugdale model is first made by comparison against finite element analysis for an edge-cracked plate subjected to an applied strain varying linearly along the crack path. It is shown that the conventional stress-based Dugdale model provides accurate estimates for the crack-tip opening displacement and the plastic zone size provided that the applied strain does not exceed one third of the yield strain. These estimates become significantly inaccurate at higher strain levels. To overcome this limitation of the conventional model, a strain-based implementation of the Dugdale model is proposed in which the conventional equilibrium equation is replaced by strain compatibility. Comparison with finite element results shows that this strain-based model provides accurate values for both the crack-tip-opening displacement and the plastic zone size for applied strains up to four times the yield strain and with no evidence of decreasing accuracy with increasing strain. Furthermore, it is shown that the relevant plastic constraint factor to be used for plane strain is that appropriate for the notch plastic zone in the absence of a crack, rather than the more usual choice which is appropriate only for small-scale yielding conditions. This provides a practical and physically plausible approach for extending the scope of current predictive software for fatigue crack growth based on the Dugdale model to include conditions of large-scale yielding.