On the Dislocation Theory of Plastic Deformation

A detailed study has been made of the lattice imperfections which are assumed to account for plastic deformation. Calculations of the strain energy associated with these dislocations have been made in the following cases: a dislocation in a uniform shear stress, two dislocations in an infinite medium, and a dislocation near a surface. The force acting on a dislocation is found by taking the gradient of the strain energy. A force is found which tends to attract dislocations toward the surface of a specimen. It is shown that about twice as much energy is required to produce a certain amount of slip inside a solid as is required to produce the same amount of slip at the surface. The energy required to produce a dislocation is found to be several electron volts per atomic plane, the exact amount depending on where it is located and how it was produced. Finally the energy stored in a material during work hardening is calculated by assuming that the dislocations are arranged in a regular two-dimensional lattice in the material. The density of dislocations found for severely work hardened material agrees with the predictions of other investigators. Numerical values found for the energy stored during work hardening are in agreement with experiment.