Analytical Model For Grain Boundary Migration Pinned By Second-phase Particle

The modifications to the theory of interaction between grain boundary (GB) and the second-phase particle (SPP) have been made over the past six decades since the first analytical model for Zener pinning was proposed. Many developing analytical models for Zener drag have become an integral part of any theory dealing with recovery, recrystallization and grain growth in the processing of metallic and ceramic materials. Zener pinning is routinely used to attain small grain sizes in polycrystalline materials by impeding grain growth through the pinning of boundaries at second phase precipitates or pores.A partial auxiliary model of the structural evolution resulting from the heating process of HSLA and carbon steels was studied. A mathematical expression describing the shape of deformed grain boundary related to the interaction between GB and SPP has been attained. And moreover, on the basis of energy principle, a new analytical model for Zener drag has been established firstly. Under the guide of the validity of a minimum energy principle, catenary's equation specifying the minimum facial size of the catenoid of revolution in the static state was involved as the research object about deformed grain boundary. The thesis attempted to work out the grain boundary equation in relation to GB and SPP in the dynamic state firstly.In line with the theory of work-energy shifting, the thesis analyzed the relation between the pinning force and interface energy. The energy would be increased, which was resulted from the deformed grain boundary caused by SPP. And, on the basis of the GB equation in the dynamic state, the mathematic expression of the interaction distance between GB and SPP was derived.Postulating that the participle shape was a spherical together with Newton's classical theory, a new analytical model was developed successfully under condition that GB was pinned by SPP. It was excluded that the ubiquitous hypothesis that the interaction between GB and SPP was balanced everywhere in the existed models and that the coherence or incoherence hypothesis related to GB and SPP, which were necessary for the model derived from the perspective of geometry.It was observed that this analytical model much more accorded with the process of interaction between GB and SPP, and the predicted results were in good agreement with values determined experimentally, demonstrating that the analytical model newly proposed in the thesis was reasonable.On the assumption that the second-phase participles (SPPs) were dispersed in the matrix, this analytical model predicted the number of SPPs for an individual pinned grain, the required volume fraction of SPPs when the sizes of grain or SPP were given, and the required number of SPPs blocking grain boundary' s shifting on unit grain boundary area. Lastly, an extension of this thesis considered, in detail, the interaction range between GB and SPP.