The presented simulations show that free surface dissolution of stressed crystals can initiate instabilities that may lead to brittle failure and grain size reduction. The simulation results are in accordance with predictions of linear stability analysis of previous studies [Srolovitz 1989; Gal et al. 1998]. The wavelength of the structures depends on the elastic energy, which is a function of the strain on the system, the elastic properties of the crystal and the free surface energy. The surface energy is dependent on the size of the system. For the ATG-instability the surface energy mainly plays a role in the absolute size and shape of small perturbations on the crystal surface that can trigger the instability. This parameter is hard to quantify. If the crystal surface is too smooth no instability will develop. However if a strain rate is applied on the system the instability will eventually be initiated in order to accommodate the strain as long as no other mechanism takes over. If the breaking strength of the crystal is reached before the instability develops the crystal will simply fracture. If dissolution at confined contacts is faster, strain will be released and the instability will not develop. How important free surface dissolution is in comparison with other mechanisms during deformation has to be established. Recent experiments however indicate that free surface dissolution can play a major role in dissolution precipitation creep [Koehn et al. 2004].

The simulations shed light on a previously known discrepancy between numerical models of the ATG-instability and the experiments of den Brok and Morel (2001). Numerical simulations by Ghoussoub and Leroy (2001) produce cusp instabilities but no quasi-stable dissolution grooves like the experiments of den Brok and Morel (2001). Animation 2 that was presented in section 3.1 shows clearly that the cusp instability is not necessarily stable but can develop into groove like structures. How stable these grooves are is not yet clear and needs to be studied in a numerical model that includes dissolution as well as growth and diffusion of mater in the fluid.

The question remains how fast systems will develop anti-cracks that may initiate failure and under what conditions grooves develop. This is not a straight-forward question. Anti-cracks like the ones shown in section 2.2 that develop out of rough surfaces have yet to be established in experiments. There are however similarities to lens like structures that develop at the olivine to spinel phase transition in the mantle of the Earth [Green and Burnley 1989]. However, the pressure maybe more important in the spinel anti-crack structures than the elastic energy that drives the ATG at free surfaces.

The discreteness of the model has to be treated with care. If the particles are too large the dissolution of a particle by itself will trigger the instability. However the size of the simulations presented in this paper should be sufficiently large so that surface energies of single particles are very high and the removal of a particle by itself does not induce the ATG. This is definitely true for the simulation shown in animation 1 where a rough surface is smoothened by surface energies. In this simulation the particles are small enough so that a wavelength on the surface has to be quite pronounced in order to let the roughness grow.