Grain boundary area, grain boundary curvature and particle pinning in an Al-1mass%Mn alloy containing Al6Mn precipitates

The usual expression to calculate the limiting grain radius due to particle pinning is R-L = alphar/f, where r is the particle radius, f is the volume fraction of the particles, R-L is the limiting grain radius and alpha is a constant equal to 1/6 according to Rios[Acta Metall. Vol. 35 (1987) p. 2805]. This form is not convenient for comparison with experimental measurements. In this work two alternative expressions are proposed: 1) S-VL = 3S(VP) where S-V is the grain boundary area per unit of volume and S-VP is the interface area per unit of volume and 2) H = S-VP where H is the total grain boundary curvature. These expressions are compared with experimental measurements carried out in a high purity Al-1mass%Mn alloy containing Al6Mn precipitates annealed for 3600 s at temperatures ranging from 500 to 620degreesC. Good agreement is obtained between theory and experiment. The relative merits and shortcomings of each expression are discussed in detail from a fundamental and experimental point of view. It is concluded that the first expression is probably the best choice for practical purposes.