Slip and the need for dislocations

If a solid is stressed beyond its elastic limit, it will acquire a permanent deformation. The deformation can be either brittle or ductile depending on (i) the material, (ii) the hydrostatic pressure, (iii) the temperature, and (iv) the strain rate. In general, a solid is more likely to deform in a brittle manner at low hydrostatic pressures, low temperatures, and at high strain-rates. Convesely, high hydrostatic pressures and temperatures and low strain-rates favor ductile deformation. 

Most crystalline materials which can undergo a large permanent strain without fracture deform in a complex manner that is neither viscous nor perfectly plastic. At low temperatures, such materials deform by a process 

For crystals of reasonably pure, well-annealed metals at a given temperature, slip begins when the resolved shear stress reaches a certain critical value, which is characteristic of each metal. In the case of aluminum, for example, the observed critical shear stress Uco is usually about 4x10 N/m ( 4 bars = 0.4 MPa). Theoretically, for a perfect crystal, the resolved shear stress is expected to vary periodically as the lattice planes slide over each other and to have a maximum value that is simply related to the elastic shear modulus /t. This was first pointed out in 1926 by Frenkel who, on the basis of a simple model, estimated that the critical resolved shear stress was approximately equal to h/Itt (see Kittel 1968). In the case of aluminum (which is approximately elastically isotropic), = C44 = 2.7x10 N/m, so the theoretical critical resolved shear stress is about lO wco for the slip system 100 (100). 

An explanation of the tendency for crystalline solids to deform plastically at stresses that are so much smaller than the calculated critical resolved shear stress was first given in 1934 independently by Taylor, Oro-wan, and Polanyi. They introduced the concept of the dislocation into physics and showed that the motion of dislocations is responsible for the deformation of metals and other crystalline solids. At low temperatures, where atomic diffusion is low, dislocations move almost exclusively by slip. 

The theory of dislocations - what they are, what they do, and how they produce macroscopic effects that can be observed and measured - was highly developed (Read 1953) before individual dislocations were routinely observed directly by transmission electron microscopy. Dislocations and 

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