Critical sizes for coherent to semicoherent transition in precipitates

Abstract

Abstract A coherent precipitate, on growth beyond a critical size, can become semicoherent through the formation of interfacial misfit dislocations. This investigation pertains to the finite element simulation of the state of stress of a coherent precipitate, its growth and the change in state of stress on the formation of an interfacial misfit dislocation loop. Critical radii are determined from the simulations based on: (i) global energy minimum (r*) and (ii) local force balance along the radial direction (r c). The concept of local force balance as existing in literature is extended to the circumferential direction, to calculate a new critical size (r t). Local force balance gives radii at which the interface is the stable position for the dislocation loop. Off-interface stability of the dislocation loops is also investigated. The Cu–γFe system is used as an example to illustrate the new methodology developed and validate the results of the simulation. The power of the methodology is shown by considering a configuration (precipitation in a thin disc), where standard theoretical formulations are inadequate.