Liquid Metal Embrittlement can be described as the penetration of a liquid metal with a low melting point along the grain boundaries of a material with a higher melting point, and a subsequent ductile-to-brittle transition, which leads to dramatic material failure. Nowadays the motivation of a good understanding of LME has a background in many areas of civilian engineering, including large parts of energy infrastructure and traffic infrastructure to just mention two big areas where this type of failure interferes severely with our everyday life; Hot dip galvanized steels can suffer from LME near weld points via Zink penetration into the polycrystalline metal. Unfortunately, the phenomenon LME involves various intricate effects and exhibits dependencies on distinct parameters. These include the grain boundary type and structure, the grain size, the liquid properties, the applied stress and the temperature. This complicated structure of the problem demands an approach which for each partial process of LME is as rigorous as possible. Consequently, it is suggested to pursue a mainly analytic ansatz to investigate the limitation of the penetration by diffusional kinetics especially in an initial stage which we complement by different numerical approaches. On a more general level, there are important links between the kinetics of phase transitions and fracture, which we have explored extensively over the past years.