ANALYSIS OF THE EFFECT OF GRAIN-SIZE UNIFORMITY ON THE FLOW-STRESS OF POLYCRYSTALS .1. STUDIES OF THE RELATIONSHIP BETWEEN THE VARIANCE OF GRAIN VOLUME AND THE VARIANCE OF THE GRAIN AREA ON POLYCRYSTAL CROSS-SECTION

Grains in polycrystals form populations characterized by distribution functions of the size and shape. Discussed is a relationship between the standard deviations of the grain volume distribution function SD(V) and the grain area distribution function SD(A). The former conveniently describes the degree of uniformity of the size of grains from the theoretical point of view; the latter is easily measured under experimental conditions. The relationship between the standard deviations is discussed in terms of grain shape, type of grain size distribution function, and the resolution limit delta. Numerical results have been obtained with the use of special computer programs. Solutions are presented that help one to estimate the variance of the grain volume from the results of grain area measurements.