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Interrupted LCF-tests at 850 deg C for Inconel 738LC have been carried out and the specimens have been intensively examined by REM to quantify the evolution of fatigue damage. Surface crack nucleation at oxidatized grain boundaries and coalescence of neighboring flaws occurred during the whole experiment. An anomalous fast single crack growth is observed just after nucleation, followed by a relative stagnation of the propagation in absence of coalescence. A statistical model is proposed that describes these pheonmena. It leads to an integro-differential equation for the crack density f(c,n) after n cycles, similar to the Bolzmann equation which describes the collision of molecules in a dilute gas.
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.
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.