J Integral Independence 3D Mesh

[bfillery]

Hi All,

Was wondering if anybody who is experienced with the J Integral (Fracture mechanics) option can answer the following.

When performing a J-Integral analysis in a 3D cylinder, I find the J Integral values at the intersection of the crack line with a free body surface is path dependent. I define the crack extension direction by way of q-vectors, and as per the analysis manual manually specify node normals (*Normal) for these free surface nodes involved in the J Integral calculation. Has anybody either experienced this before and have any suggestions as to how to recover the path independence, or has somebody solved this problem?

Thanks

bfillery

 

[xerf]

J-integral is used to characterize the stress field at a crack-tip.

The value of J-integral in a domain without a crack-tip (i.e. a singularity) I think it does not make much sense.

The path independence of J-integral relates to its theoretical definition where it is defined as a a integral along a curve (path) encompassing the crack-tip. In FEM approach (one of them) the curve integral is converted to an equivalent area integral. This is numerically computed by integration on a domain formed by subsequent rings of elements (i.e. contours) around the crack-tip.

In general, to improve the accuracy of the J-integral you can increase the number of contours (i.e. enlarge the domain) used for computation until J(using n contours)=J(using n+1 contours).

If the material is elasto-plastic, the number of contours should be sufficient such that the integration domain to encompass the whole region of plastic deformation at the crack tip.

 

[xerf]

So far I saw J-integral path independence shown for 2D domains only and assuming:
- time independent fracturing
- no body forces
- small strains
- single homogeneous hyperelastic material
- traction-free crack edges

Violations of the above assumptions need additional terms in the definition of J-integral in order to conserve path independence. However, according to ABAQUS theory manual, no extra terms are used for computation of J-integral when the above assumptions are violated. Therefore, one cannot expect path independence.

 

[bfillery]

Thanks xerf

The J Integral works fine for me in 3D (including under thermal stress/strain -> body force) in all cases but at a free surface intersection at the moment, where in this case the users manual it stipulates that for increased path independence, nodal normals defining the free surface normal should be defined. However, even in doing so, path independence at a free surface intersection is not seen (at least for me), even upon increasing the number of contours extensively.

Thanks again