# ANSYS modeling of dissimilar mateials - non-zero shear stresses on free-edge!

Dear iMechanica community,

I am a metallugist interested in ANSYS modeling of metal ceramic joints - particularly the singularity at the free-edge. I have created a polar mesh that many in the literature (see below for references) suggest in order to capture the r^(-w) singularity where 0<w<0.5, accurately. The model is simple - two square pieces (metal and ceramic) in 2D with perfect bonding at the interface are modeling and the bottom line-boundary of the ceramic block is constained in y-direction. As I simulate an elastic condition with cooling from high temperature to room temperature (3D, Plane 183 8 node quad elements), Sx, Sy and Sxy should develop at the interface and only Sy should develop on the free-edge. Moreover, the singularity (as calculated on a log-log plot of stresses very close to the free-edge contact point with the interface) should be the same for all the stresses.

However, the Sx and especially the Sxy values are non-zero on the free-edge and the Sx and particularly Sxy values do not give the same value for the singularity as the Sy. I studied a simple case and compared it with analytically calculated value of the singularity 'w' and they match well with Sy but are in error by 10% for Sx and 50% for Sxy. This also correlates well with the higher Sxy values found on the free-edge.

So, my question is - am I missing something simple? How to make ANSYS give me zero free-edge stresses, since I am hoping that this would solve the singularity issue above and also correct the shear stress prediction at the interface. Please advise. Thank you very much.

The literature is copious on this topic, starting from the 1960s till recent times.

References: Please see links below - the NASA papers (1-2 below) gives you the FEM polar mesh modeling near the singularity. This problem is a classic one and I think the composite community routinely handles this problem.