Effect of shear-coupled grain boundary motion on coherent precipitation

Abstract

We examine the interaction between precipitates and grain boundaries, which undergo shearcoupled motion. The elastic problem, emerging from grain boundary perturbations and an elastic mismatch strain induced by the precipitates, is analysed. The resulting free elastic energy contains interaction terms, which are derived numerically via the integration of the elastic energy density. The interaction of the shear-coupled grain boundary and the coherent precipitates leads to potential elastic energy reductions. Such a decrease of the elastic energy has implications on the grain boundary shape and also on the solubility limit near the grain boundary. By energy minimisation we are able to derive the grain boundary shape change analytically. We apply the results to the Fe-C system to predict the solubility limit change of cementite near an α-iron grain boundary. arXiv:1905.03068v1 [cond-mat.mtrl-sci]

Influence of Interface Proximity on Precipitation Thermodynamics

“…The carbon solubility in ferrite is very low; hence, the description as a dilute alloy is appropriate. According to Equations (3) and (7), the reduction of the solubility limit for carbon near a shear-coupled grain boundary in ferrite is approximately 50% (blue curves) relative to the bulk elastic situation (black curves) for an array of precipitates at room temperature, as discussed in detail in [14].…”

“…As we detailed in [14], the situation changes if the grain boundary has the potential for morphological reorganizations, which can lead to a mechanical stress relaxation. In this sense, the grain boundary is not a fixed shape "passive" interface, but "reacts" to the presence of a nearby precipitate.…”

“…In this sense, the grain boundary is not a fixed shape "passive" interface, but "reacts" to the presence of a nearby precipitate. In [14], we considered the shear-coupled motion of a grain boundary as a potential stress relaxation mechanism, which is related to the amplitude equation and analytical modeling in [18][19][20]. Shear coupling describes the resulting normal motion of a grain boundary, if the two grains are shifted laterally against each other; see Figure 4.…”

“…Notice that an inversion of the tangential velocity also changes the orientation of the normal interface motion. As a result of the normal grain boundary motion, the marker line develops a kink [14].…”

“…This effect is expected to play a role whenever precipitates show a lattice mismatch with the matrix, and the effect will play the largest effect for coherent interfaces between them. We will discuss here two limiting cases that we have elaborated during the past years for phase separation near free and confined surfaces [12,13] and shear-coupled grain boundaries [14] and show what may happen near interfaces between different phases as a consequence of coherent-incoherent transitions. The aforementioned two limiting cases also lead to a distinction of what we call here "reactive" and "passive" surfaces and interfaces, which influence the range of interaction between interfaces and precipitates in the spirit of a strong thermo-chemo-mechanical coupling.…”