Relaxation of a precipitate misfit stress state by creep in the matrix

• Precipitation strengthening.
• Precipitation kinetics.
• Creep–elasticity interaction.
• Misfit stress relaxation by creep.
• Analytical formulation of contact pressure evolution.

Designed microstructures, such as the ones of high strength and creep resistant modern steels and Al-alloys, are based in many cases on the understanding of the role of precipitates. The kinetics of precipitation can be significantly influenced by the adaption of their volumetric misfit relative to the matrix where plastification and creep of the matrix are typical accommodation processes in addition to vacancy diffusion-controlled mechanisms. A solution for creep coupled with elasticity as such an accommodation mechanism is presented. The set of governing equations including the according assumptions is provided. First, an efficient numerical algorithm is presented to solve the system of two such governing differential equations. Second, necessary steps to obtain an analytical form of the rate equation of the contact pressure are outlined. This rate equation for the contact pressure can be later implemented into models for treatment of precipitation kinetics in complex systems.