A microstructural model for the monotonic and the cyclic mechanical behavior of single crystals of superalloys at high temperatures

A constitutive model for the mechanical behavior at high temperatures of superalloys with a high volume fraction of the γ ′ phase is derived from an analysis of the main deformation mechanisms. The model assumes periodically distributed cubic γ ′ particles and an homogeneous slip distribution perpendicular to the slip planes inside the matrix channels and the particles. It accounts for octahedral and cubic slip in the γ channels, recovery by climb of loops around the precipitates until complete annihilation, shear of both matrix and precipitates by complete matrix dislocations and partial slip reversal during unloading. The back-stresses of the constitutive law are identified with the long-range internal stresses in the microstructure which are explicitly calculated by Fourier series for a simplified distribution of the plastic strains in the microstructure. In particular the three types of channels are distinguished. The internal variables of the model are the plastic strains produced by each mechanism, the number of mobile loops in the γ channels and the scalar dislocation density in the γ/γ ′ interfaces for each slip system.