Elastic fields of a wedge disclination in a functionally graded cylinder

Abstract

In this paper, the elastic fields of a wedge disclination in a functionally graded cylinder are obtained in closed-form by directly solving the equilibrium equations. The cylinder material is graded radially according to a power law characterized by a gradient index. The disclination has a small fixed core of nanometer dimension. The results show that: (1) the displacement, radial and transverse stresses vary with the radial coordinate according to a sum of power laws, (2) the gradient index changes the elastic fields through modification of the elastic parameters, and modification of the power law indices of the field dependence on (i) the radial coordinate and (ii) the cylinder dimensions, (3) the stresses at and near the disclination core are generally reduced by both positive and negative gradients, (4) the transverse stress at the disclination core can be reduced to zero and even compressive for small negative gradients, (5) a significant size effect exists for the disclination stresses, and the effect is influenced strongly by the gradient index, (6) the energy of the disclination is a strong, non-monotonic function of the gradient. These results suggest that various relaxation phenomena such as crack nucleation and disclination splitting may be controlled by selecting a suitable gradient for the material variation.