J-integral path-independence inside the plastic zone?

[pettervu]

Hi all,

I am working on a pretty basic J-integral problem on a 2D geometry.

I have been told that the J-values should be path-independent even inside the plastic zone in ABAQUS. However, I get path-dependent values of J on all contours inside the plastic zone, I was therefore wondering whether I have been missinformed or whether I am doing something wrong when making my model.

I do get good path-independence outside of the plastic zone.

Thanx,
Petter

 

[mrgoldthorpe]

Petter,

You get proper path-independence if the material is non-linear elastic, power-law hardening (Ramberg-Osgood). However, elastic-plastic material response generally gives path-dependent results for J close to the crack tip in the plastic zone.

One reason for this is the non-proportional increase in the fields of stress and strain close to the crack tip; the J-integral formulation in ABAQUS assumes proportional behaviour as you would get in a non-linear elastic material. Another reason is that elastic-plastic hardening response is generally not of a power-law nature.

A further reason could be the limit of the stress versus equivalent plastic strain behaviour you input (*PLASTIC). ABAQUS assumes non-hardening behaviour beyond the last *PLASTIC data point. Depending on the mesh refinement, material points close to the crack tip can yield beyond that point. This generally gives lower results for contors in that region because of this change in the local hardening respone - it's effectively a 'different' elastic-plastic material.

You get path independence in the elastic region because the response is proportional along the contour of integration.

 

[pettervu]

Thank you for your good answer mrgoldthorpe!

I've tried increasing the last value of my elastic-plastic material as I realised that the stresses close to the crack tip were acctually larger than my last plastic data point. This did however not have an impact on the results.

I guess I'll just have to make sure to calculate on contours outside of the plastic zone.

 

[xerf]

The J-integral path independence relies on a set of assumptions. As far as I remember one of them is that path does not intersect the plastic region at the crack-tip.