Application of anisotropic inclusion theory to the deformation of Ni based single crystal superalloys: Stress–strain curves determination

The development of plastic deformation after uniaxial plastic strain along [0 0 1] is analyzed in two types of domains in γ–γ′ nickel superalloys. These domains are the horizontal matrix channels normal to [0 0 1] and the vertical channels normal to [1 0 0] and [0 1 0]. By using a mean field method, an elastic energy increase due to the introduction of plastic strain (elongation or compression) in the two types of domains is calculated. The analysis of a mixed mode, where horizontal and vertical channel deformation occurs, is also conducted. Results show that plastic deformation is primarily initiated in a particular type of channel. The choice of the deformation configuration is related to the sign of misfit strain. After a critical amount of plastic strain is reached, the deformation expands through all the matrix channels. This conclusion is supported by the dependence of a flow stress on the deformation mode. FEM calculations are also conducted and compared with the analytical calculation. Except when the strain is extremely small, the two methods give almost the same result.