7 - Approximate Polycrystal Models

Summary

Turning from the rigorous theoretical analysis of Chapter 6 to the subject of (and literature on) the calculation of approximate polycrystalline aggregate models at finite strain, one can identify three prominent themes: the prediction of (i) macroscopic axial-stress–strain curves, (ii) macroscopic yield loci, and (iii) the evolution of textures (that is, the development of preferred crystal orientations in initially statistically isotropic aggregates). The topic of polycrystal calculations is vast and complex, warranting a monograph on its own (and by other hands). In this closing chapter of the present work I primarily shall review selected papers (acknowledging others) from among those contributions that are particularly significant or noteworthy in the more than 50 years' history of the subject.

The Classic Theories of Taylor, Bishop, and Hill

Near the beginning of G. I. Taylor's (1938a) May Lecture to the Institute of Metals is the following splendid sentence. “I must begin by making the confession that I am not a metallurgist; I may say, however, that I have had the advantage of help from, and collaboration with, members of your Institute, whose names are a sure guarantee that the metals I have used were all right, even if my theories about them are all wrong.” More than anything else this statement reflects Taylor's irrepressible humor, for of course his theories were not “all wrong.”