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An improved diffusion model is proposed for pore annihilation during HIP of single-crystal nickel-base superalloys. The model assumes the pore dissolution by emission of vacancies and their sink to the low angle boundaries. Calculation, considering distribution of the pore sizes, predicts the kinetics of pore annihilation similar to the experimental one.
A stochastic model for fatigue short crack growth is presented. It takes into account the interaction between the crack-tip plastic zone and grain boundaries. The process is Markovian. It is completely described by the crack length and the size of the plastic zone. The integro-differential equation giving the evolution of the transition probability distribution is derived.
Simulations of cavitation processes on a grain boundary under creep conditions have been carried out, taking into account nucleation, growth, coalescence and sintering of multiple cavities. Cavity growth rates have been calculated through a resolution procedure based on the use of holomorphic complex functions. Three dimensionless parameters have been identified that are responsible for the cavitation development. Parameter studies have been carried out in order to characterise the mechanisms that are responsible for the cavitation development. These studies have been used to develop a physically motivated, simplified model in order to describe the cavitation development of the simulations in terms of global state variables. The simplified model is able to reproduce the cavitation development for all considered combinations of the dimensionless parameters and allows the description of the thickening behaviour of a cavitating grain boundary.
A constitutive model for the mechanical behavior at high temperatures of superalloys with a high volume fraction of the ? ? phase is derived from an analysis of the main deformation mechanisms. The model assumes periodically distributed cubic ? ? 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 ? 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 ? channels and the scalar dislocation density in the ?/? ? interfaces for each slip system.