## 5 Werkstofftechnik

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- 5 Werkstofftechnik (8) (entfernen)

Under cyclic thermomechanical loading conditions, various effects such as strain accumulation, creep damage, ageing, fatigue etc. may occur in the material of a gas turbine blade. Depending on the loading conditions, all these effects contribute to reduce the lifetime of the component. Subject of the present work is the development of a lifetime model able to discriminate between the different damage mechanisms, as well as the development of a material model to describe the mentioned effects and thus providing the input data for lifetime prediction.

Micromechanical investigations and modelling of a copper-antimony-alloy under creep conditions
(2014)

In many practical applications, creep damage is the limiting factor of a components lifetime. A micromechanical model of creep induced grain boundary damage is proposed, which allows for the simulation of creep damage in a polycrystal within the framework of finite element analysis. The model considers grain boundary cavitation and sliding according to a micromechanically motivated cohesive zone model while creep deformation of the grains is described following the slip system theory. The model can be applied to idealised polycrystalline structures, such as a Voronoi tessellation or, like demonstrated here, to real grain structures of miniature creep specimens. Creep tests with pure Cu single crystals and with a coarse-grained polycrystalline Cu-1 wt.% Sb alloy at 823 K have been performed and used to calibrate the polycrystal model. The grain structure of the polycrystalline CuSb specimens has been revealed by the EBSD method. Extensive grain boundary sliding and cavitation has been observed in the crept specimens. Grain boundary sliding has been found to promote wedge-type damage at grain boundary triple junctions and to contribute significantly to the total creep strain. Furthermore, the assumed stress sensitivity of the models grain boundary cavity nucleation rate strongly influences the development of wedge-type damage.

Material modelling and lifetime prediction of Ni-base gas turbine blades under TMF conditions
(2014)

Under cyclic thermomechanical loading conditions, various damage mechanisms such as strain accumulation, creep cavitation, ageing, fatigue surface cracking etc. may take place in the material of a gas turbine blade. Depending on the loading conditions, all these effects can contribute to reduce the lifetime of the component. Subject of the present work is the development of a material model to describe the mechanical effects mentioned above, as well as the development of a lifetime model able to discriminate the different damage mechanisms.

Gas turbines are widely used for a variety of purposes including power generation, compression or as jet engines in aircrafts. The critical components of a gas turbine are the high-pressure turbine blades which operate under severe conditions. These include thermo-mechanical loadings over temperatures ranging from room temperature up to 1100°C.
While a large number of constitutive models for single crystals have been proposed, most applications are restricted to special loading scenarios, temperature range and deformation mechanisms. In particular, a number of models are focused on pure creep. Only a few papers consider application of both creep and fatigue. Applications of the constitutive models to long-term stress relaxation are even scarcer. The new model assumes deformation-induced softening and can properly reproduce the viscous behavior at different time scales.
The model has been calibrated with the uniaxial tests at 800°C and 950°C in [001], [011] and [111] specimens of a nickel-basis superalloy. The predicted creep, short- and long-term relaxation and cyclic tests are in reasonable agreement with the experimental observations.

The creep behavior of single crystals of the nickel-based superalloy CMSX-4 was investigated at 1288 °C, which is the temperature of the hot isostatic pressing treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no gammaPrime-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g., the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-sectional area psi of [001] crystals reached nearly 100 pct, while for a [111] crystal psi = 62 pct. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals did not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. The recrystallization degree was found to be correlated with deformation behavior as well as with dwell time at high temperature. From the analysis of the obtained results (creep anisotropy, stress dependence of the creep rate, traces of shear deformation, and TEM observations), it was concluded that the main strain contribution resulted from <01-1>{111} octahedral slip.

The creep behavior of single-crystals of the nickel-base superalloy CMSX-4 was investigated at 1288°C, which is the temperature of the hot isostatic pressing (HIP) treatment applied to this superalloy in the industry. It was found that at this super-solvus temperature, where no Gamma’-strengthening occurs, the superalloy is very soft and rapidly deforms under stresses between 4 and 16 MPa. The creep resistance was found to be very anisotropic, e.g. the creep rate of [001] crystals was about 11 times higher than that of a [111] crystal. The specimens of different orientations also showed a very different necking behavior. The reduction of the cross-section area psi of [001] crystals reached nearly 100%, while for a [111] crystal psi=62%. The EBSD analysis of deformed specimens showed that despite such a large local strain the [001] crystals didn’t not recrystallize, while a less deformed [111] crystal totally recrystallized within the necking zone. From the shape of deformed specimens and TEM investigations it was concluded that the main strain contribution resulted from <011> {111} octahedral slip.

Single crystal superalloys usually contain pores of sizes 5-10 micro-m after casting and heat treatment. These pores can be reduced under compression by combined creep and diffusion in a subsequent treatment called Hot Isostatic Pressing (HIP). The paper presents a methodology to simulate pore shrinkage under HIP conditions in two dimensions (2D).
At the scale of the pores, which is also the scale of the sub-grains (<50 micro-m) the dislocation sources cannot be assumed to be homogeneously distributed. Thus, the applicability of classical crystal plasticity is questionable. In this case, the transport of dislocations under an applied stress from the location where they are nucleated must be explicitly modelled. This is done by solving the transport equations for the dislocation densities and the elasticity equations in 2D. The dislocations are assumed to be nucleated at Low Angle Boundaries. They glide or climb through the sub-grains with a stress dependent velocity.
The transport equations are solved by the Flux-Corrected Transport method, which belongs to the predictor-corrector class of algorithms. In the first step, an artificial diffusion is introduced, which suppresses spurious oscillations of the solution. In a second step, the solution is corrected in such a way that no additional extremes appear and that the extremes do not grow. The algorithm is validated by simulating the transport of simple distributions with a constant velocity field.
With the dislocation velocities and the computed dislocation densities, the inelastic shear rate at the slip system level is computed by integrating the Orowan equation. In the 2D-setting, three slip systems are considered. The contributions of these slip systems are summed up to obtain the total inelastic strain rate. Dislocation glide and climb and the coupling of climb with vacancies diffusion are considered.
The resolution of the equilibrium equations from the inelastic strains turned out to be prone to numerical instabilities. As an alternative, the stresses are directly computed from the distribution of geometrically necessary dislocations following the method presented in. The resulting boundary value problem is solved by the Least-Square Finite Element method.
Examples of simulations are presented for a representative region under creep tension and for a pore shrinking under external pressure.