Grain boundary relaxation question

[Vincent Péron]

Dear Mr Miller,

I am trying to reproduce some of your results available in the paper named "An adaptative finite element approach to atomic-scale mechanics - the quasicontinuum method" by Shenoy et al. My aim is to study the interaction between grain boundary (GB) and dislocation. In the part 6 of this last paper you describe this kind of interaction. The Figure 14 shows the computational box before indentation. My question is quite simple : did you relax the GB before indenting the material ?

My indenter is rigid and rectangular as in « Nanoindentation and incipient plasticity » and I use the boundary conditions as E. Tadmor did in his paper. When I relax the GB properly using the Displacement shift lattice theory (DSC) or by seeking the best energy configuration before relaxation, the indented surface is not homogeneous. Consequently, the indentation is not as clean as it shoud be. To get a realisitic GB we need to let a little spacing between grains ( F. Sansoz and J. F Molinari acta mat 2004) to allow for GB volumic expansion. This relaxation has a strong influence on the homogeneity of my indented surface.

If you did relax your GB, how did you do to keep an homogeneous surface ? I have tried many things to make it works and I would really appreciate your help.

I will participate to your course in Aachen next august.

Best regards,

Péron Vincent

PS: the attached file gives an idea of the inhomogeneity observed after GB relaxation.

[Ron Miller]

Whew... that was a long time ago for me, so I can't remember the details, but I'll try.  I believe you are correct that the boundary relaxation could propagate some disturbance to the surface.  It seems that it would depend on the choice of the boundary and its orientation.  The image looks almost like a partial dislocation has emitted from the GB and moved to the surface, but its hard to tell from what you sent.  I believe that would indeed be the relaxed configuration for some boundaries (i.e. they would spontaneously emit such dislocations).  In that case, making the top grain thicker (moving the GB away from the surface) would fix the problem if the potential has a reasonable stacking fault energy.. I don't think you mentioned what potential you are using.  If the potential doesn't have a good stacking fault energy (common EAM problem), this dislocation could move a long way from the boundary before coming to equilibrium.  

So, I am sure that we pre-relaxed the boundary, but perhaps we did a different GB type or maybe we didn't find the correct "global" minimum energy structure.... those were early days with such studies.  We studied Aluminum using the Ercolessi/Adams potential which does have a good stacking fault energy, so that may also be why we didn't have this problem.  I think Curtin and Dewald have done more studies of this type using CADD, and the Sansoz reference is a good place to look for ideas.

looking forward to meeting you in Aachen.
ron