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Ni-base superalloy single crystals are superior metallic structure materials for high temperature applications e.g. for combustion chambers and blades in gas turbines. To be able to simulate creep and/or low cycle fatigue in the parts under the operation conditions, the knowledge of constitutive equations for creep in superalloy single crystal under multiaxial loading is necessary.
The state of the superalloy in a representative volume element is given by parameters characterizing the precipitate and dislocation microstructure (structure parameters) and the constitutive equations provide the creep strain rate tensor as well as the rates of the structure parameters as function of the temperature and of the stress tensor in the representative volume element. Such constitutive equations can be then used in FEM code to simulate the behaviour of the part.
Creep in superalloy single crystal can be treated by non-equilibrium thermodynamics. The following processes are taken into account: Dislocation slip in channels and concurrent multiplication of the dislocations. These dislocations remain deposited on the interfaces.
Dynamic recovery of the dislocation structure. The dislocation loops spanning around the particles move by the combination of slip and climb along the interfaces and shrink towards the apices of the particles.
Morphological changes of the particles by migration of the interfaces. The rates of the structure parameters and of the creep strain follow directly from standard phenomenological equations or they are obtained by application of the thermodynamic extremal principle.
The principle is described in introduction. A unit cell model providing the constitutive equations is described in detail and simulations based on the model are performed and compared with experiments. The comparison indicates that the model explains all features of the uniaxial creep curves and a signficant quantitative agreement is also obtained.

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