Grain Boundary Pinning by Particles
Grain boundary pinning by particles is widely used to prevent grain growth during heat treatment in a variety of commercial alloys. Its practical relevance is matched by a considerable amount of theoretical work that has been devoted this problem. A key issue of boundary pinning is the particle/interface interaction mechanism and its associated pinning force. According to Ashby et al. an interface may interact with a particle in two ways: either it goes through the particles or, more usually, bends round and envelopes the particle. Based on these mechanisms one may derive quantitative expressions relating the characteristics of the particle dispersion and a critical or limiting grain radius. Thus, Zener expression assumes that the interface goes through the particles whereas Rios expression assumes that the interface bends round and envelopes the particle. Both the mechanisms and the resulting expressions are discussed here in detail and compared with available experimental data.
T. Chandra, N. Wanderka, W. Reimers , M. Ionescu
P. R. Rios and G. S. Fonseca, "Grain Boundary Pinning by Particles", Materials Science Forum, Vols. 638-642, pp. 3907-3912, 2010