Dislocations

The Italian elastician and mathematician Vito Volterra introduced in 1905 the theory of the elastostatic stress and displacement fields created by dislocating solids. This involves making a cut in a solid, displacing its surfaces relative to one another by some fixed amount, and joining the sides of the cut back together, filling in with material as necessary. The initial status of this work was simply regarded as an interesting way of generating elastic fields, but, in the early 1930s, Geoffrey Ingram Taylor, Egon Orowan, and Michael Polanyi realized that just such a process could be going on in ductile crystals and could provide an explanation of the low plastic shear strength of typical ductile solids, much as Griffith’s cracks explained low fracture strength under tension. In this case, the displacement on the dislocated surface corresponds to one atomic lattice spacing in the crystal. It quickly became clear that this concept provided the correct microscopic description of metal plasticity, and, starting with Taylor in the 1930s and continuing into the 1990s, the use of solid mechanics to explore dislocation interactions and the microscopic basis of plastic flow in crystalline materials has been a major topic, with many distinguished contributors.

The mathematical techniques advanced by Volterra are now in common use by earth scientists in explaining ground displacement and deformation induced by tectonic faulting. Also, the first elastodynamic solutions for the rapid motion of crystal dislocations, developed by South African materials scientist F.R.N. Nabarro in the early 1950s, were quickly adapted by seismologists to explain the radiation from propagating slip distributions on faults. The Japanese seismologist H. Nakano had already shown in 1923 how to represent the distant waves radiated by an earthquake as the elastodynamic response to a pair of force dipoles amounting to zero net torque. (All his manuscripts were destroyed in the fire in Tokyo associated with the great Kwanto earthquake in that same year, but copies of some had been sent to Western colleagues and the work survived.)