Institute of Metals Division - The Relationship Between the Boundary Area and Hardness of Recrystallized Cartridge Brass

It has long been supposed that, regardless of the mechanism by which grain boundaries increase the hardness of a ductile metal, the effect should be linearly proportional to the grain boundary area. At the present time two methods for determining grain boundary area in an isotropic aggregate are available. The first, derived by Angus and Summers,' presumes that the grain boundary area is equal to 3vn, where n is the number of grains per sq mm in a random section through the metal. This estimate is based upon the assumption that the grains are equivalent to cubes whose faces correspond with the grains as observed in the micro-section. Measurements on copper, bronze, and a brass showed that a nearly linear relation exists between 3vn and hardness. This is illustrated, for the case of brass, in Fig. 1. The second method, developed independently by Smith and Guttman2 and by Duff in, Meussner, and Rhines,3 is absolute and employs a simple linear intercept count for measuring grain boundary area. It involves no assumptions with respect to the shape and distribution of the grain boundaries. The total surface in unit volume is 2 NL , where NL is the number of intercepts between grain boundary and unit length of a test line passed randomly through the sample. In practice, NL,, the average number of grain boundaries intercepted by unit length of traverse across a prepared microsection, is ob-