Plasticity in constrained layers: model with point forces

An elasto-plastic stress analysis is carried out to determine the stresses and deformations within a thin ductile layer sandwiched between two semi-infinite elastic blocks. The layer is assumed to contain a crack much longer than the layer thickness and to have a much lower elastic modulus than the constraining blocks. The development of plasticity within the layer is examined for an increasing applied stress normal to the layer, leading to mode I conditions at the crack tips. The normal stress σyy within the layer is found to rise approximately linearly from about 3σY up to 6σY in some cases, while the stress difference σyy−σxx remains approximately constant within that zone. The plastic deformation is restricted to a narrow zone, coplanar with the crack, appearing to suite a line representation such as the Dugdale model. However, the conventional Dugdale model predicts σyy=σxx along the plastic zone. This limitation is shown to be overcome by adding a distribution of point forces to the distribution of climbing edge dislocations which is effectively used in the Dugdale model. These point forces act in the plane of the crack and must satisfy the overall equilibrium requirement that there is no net force on the crack.