I am working on simulation of aluminum alloy A356 solidification. However, in real phenomena, it undoubtedly involves hydrogen porosity. However, all phase field models tell you about grain growth, but not on gas and shrinkage porosity. Are Phase-field methods incapable of simulating microstructure with defects?
The cracks propagate when strain field inside a material fails to hold strain energy beyond a certain limit. At the crack-void interface and inside the void in between adjacent crack surfaces, there is no strain energy. Further away from the cracked surface, the strain energy is released (by formation and propagation of crack) in less and less amount. This is basic of phase-filed fracture modelling. But since there is no inherent (i.e. not caused by external force, the 1+2b/a inglis stress concentration may be still there) stress concentration near a round porosity, there is no strain field (unless, perhaps solidification shrinkage or void gas pressure exists) for a void/ porosity. Now, one can model the "phase field" of the defect by exploiting difference between energy of solid atoms/molecules in contact with solids only vs in contact with both solid and gas, (that is, surface atoms exposed at crack/porosity surface). Although i suspect, then the decay of "phase field" of fracture may not be exponential. The summary is
- Phase-field method likely provides not-so-satisfactory results where a strain field (yearning to release its energy by cracking) is not present, especially the one responsible for growth of size of the aforementioned defect.
- Change of "surface" energy at discontinuity interface relative to bulk may be used as a "proxy" for phase field techniques, for porosities (effect of surface decays at interior) although it might require major revamping of models and formulae.
I cannot really appreciate how hard it would be to tweak the codes at basic level, but still i think that will not be easy.
I cannot comment about the applicability of these methods to.simulate the solidification of aluminum castings. However, I would.like to caution you that pores are extrinsic defects, caused by entrainment damage. Without any entrainment damage, pores, whether shrinkage or hydrogen, cannot nucleate even heterogenously. Therefore the entrainment damage needs to be known for simulation. This is extremely complex and damages are additives, i.e., ingots come usually with extreme levels of damage and there is more damage in the production system as well. Therefore it is quite a challenge to simulate pore formation, except in badly damaged castings, where you can assume that pores will form when a certain level of hydrogen or negative pressure level is reached.
Well, I will give a brief answer, I think the others already gave enough detail : At best of my knowledge, there is no such kind of study in the literature. Theoretically, PF simulations can simulate the hydrogen diffusion . There are also applications of PF method in fracture mechanics. However, I think that we still don`t know the mechanism well enough to model it and even so, it will probably require a very sophisticated PF code involving heat transfer, diffusion ,solidification, fluid flow and fracture mechanics.
If you can express your constitutive equation of defect evolution in terms of energy functional, I think you in principal can.
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