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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.
On the Connection between Continuum Crystal Plasticity and the Mechanics of Discrete Dislocations
(2003)
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.
Experimentshow that the strength of Ni-base superalloystrongly depends on the actual morphology of the microstructure. This makes a multiphase micro-mechanical modelling indispensable for a reliable safety analysis. Unfortunately, the classical crystal plasticity theory leads to erroneous predictions, when applied to the scale of the microstructure. This paper suggests that this failure is related to a breakdown of the meaning of plastic strain at the scale of the size of dislocation loops. We propose a global modelling of the compound that overcomes the deficiencies of local crystal plasticity at this description level.
The calculation of the glide force on a dislocation in finite elasticity requires a suitable description of the variation of the deformation due to dislocation motion. This is achieved in this paper by extending the linear Somigliana-type dislocation model to finite strains. The core is modeled by a strip of finite width where the displacement jump continuously decreases with the distance to the dislocation tip. In the case of finite transformations, this distance can be defined in the deformed or in the undeformed state. By defining it in the undeformed natural state of the crystal, we show that the work dissipated by friction in the core region only depends on the dislocation motion. Using the principle of virtual work, the equation of the dislocation motion and several alternative expressions for the glide force are derived. The obtained force may be interpreted as a generalization of Eshelby's configurational forces for a noncoherent singular surface. In the linear case, the glide force of Peach and Koehler as well as the well-known expression of the self-force due to De Wit and Koehler are retrieved.
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.
The present work focuses on the cubic slip phenomenon in single crystal superalloys with a high fraction of γ' precipitates at high temperature.
The macroscopically apparent cubic slip mechanism is known to significantly reduce the tensile and creep strength of <1 1 1> oriented specimens. However, recent results obtained by 3D dislocation dynamics (Vattré et al., 2009) suggest a new interpretation of the so-called pseudo-cubic slip related to the nature of the dislocation network formation at the interfaces. These results are taken into account in a micromechanical model to improve the estimation of the strain hardening anisotropy. In accordance with the discrete simulations, it is shown that a key role is played by the combination of the activated octahedral slip systems as a function of the crystal orientation. In the <1 1 1> case, the contribution of the activated systems to kinematical hardening compensate, whereas strain hardening remains high for the <0 0 1> case. The experimental dependence of plastic flow on the orientation is also explained at the dislocation-scale mechanisms.
Results are presented for the alloy CMSX-4 in several orientations.