Grain Boundary Pinning by Particles

Abstract

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.

Precipitation and grain growth modelling in Ti-Nb microalloyed steels

“…Zener [34], originally considered that β = 4. This value is actually overestimated as several experimental and modelling work seem to prove that the correct expression of the driving pressure for grain growth in polycristalline materials is four times lower [35][36][37][38]. Thus, β is taken equal to 1 in the present work.…”

“…Among these expressions, the one given by Zener in 1948 [34], and the one given by Rios in 1987 [41]…”

Grain and nanoparticle coarsening of an ultrafine structured Cu–5vol.%Al2O3 nanocomposite during isochronal annealing

“…(3) is likely to overestimate the average grain size value in the equilibrium state. To accommodate this effect, Manohar et al [29,30] and Rios [31] modified the Zener equation, and proposed the following modified Zener equation:…”

Critical assessment 30: Grain growth – Unresolved issues

“…The knowledge accumulated on normal grain growth in the succeeding years has been thoroughly reviewed in the late 1980s [4]. Around that same time, particle pinning and abnormal grain growth (AGG) were also the subject of an overview [5].…”