Prediction of the energy dissipation rate in ductile crack propagation

Abstract

In this paper, energy dissipation rate D vs. Δa curves in ductile fracture are predicted using a ‘conversion’ between loads, load-point displacements and crack lengths predicted by NLEFM and those found in real ELPL propagation. The NLEFM/ELPL link was recently discovered for the DCB testpiece, and we believe it applies to other cracked geometries. The predictions for D agree with experimental results. The model permits a crack tip toughness R(Δa) which rises from Jc and saturates out when (if) steady state propagation is reached after a transient stage in which all tunnelling, crack tip necking and shear lip formation is established. JR is always greater than the crack tip R(Δa) and continues to rise even after R(Δa) levels off.

The analysis is capable of predicting the usual D vs. Δa curves in the literature which have high initial values and fall monotonically to a plateau at large Δa. It also predicts that D curves for CCT testpieces should be higher than those for SENB/CT, as found in practice. The possibility that D curves at some intermediate Δa may dip to a minimum below the levelled-off value at large Δa is predicted and confirmed by experiment. Recently reported D curves that have smaller initial D than the D-values after extensive propagation can also be predicted. The testpiece geometry and crack tip R(Δa) conditions required to produce these different-shaped D vs. Δa curves are established and confirmed by comparison with experiment.

The energy dissipation rate D vs. Δa is not a transferable property as it depends on geometry. The material characteristic R(Δa) may be the ‘transferable property’ for scaling problems in ELPL fracture. How it can be deduced from D vs. Δa curves (and by implication, JR vs. Δa curves) is established.