Strains in Crystalline Aggregate

Abstract

Much study has been devoted in many countries to the mechanism of plastic strain in crystals by the formation and movement of dislocations. There has also been much experimental work on the macroscopic relationships between stress, strain and the crystal axes of single crystals. With this background of knowledge the man who contemplates a crystal aggregate and tries to understand how it behaves when forced to flow, is in much the same position as one who knows about the kinetic theories of gases and liquids, understands how the statistical effects of molecular collisions are averaged to yield the laws of viscosity, is familiar with Poisson’s equations for the flow of viscous fluids, and then sets out to study turbulence. Dr. Cottrell has used this analogy in a similar case. Even with the very simple laws summarised in Poisson’s. equations it has proved impossible so far to make any complete representation of turbulent fluid flow. Indeed some people working on that subject have felt so discouraged at their lack of success in finding significant results based on Poisson’s equations that they have concluded that these equations do not apply to turbulent flow and have tried to start again, as in the kinetic theory of gases, from known properties of molecules. Such people have had no success in these despairing efforts; nor are they likely to succeed, because Poisson’s mathematical expression for the stress-rate of strain relations in a fluid represent the simplest possible averaging process for molecular interactions. The sole reason why we have not succeeded in giving a complete description of turbulent flow is not because we don’t know enough about fluids, but because we are not clever enough to find the appropriate solutions of Poisson’s equations.