Multiscale modelling of single crystal superalloys for gas turbine blades

T. Tinga

Research output: ThesisPhd Thesis 1 (Research TU/e / Graduation TU/e)

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Gas turbines are extensively used for power generation and for the propulsion of aircraft and vessels. Their most severely loaded parts, the turbine rotor blades, are manufactured from single crystal nickel-base superalloys. The superior high temperature behaviour of these materials is attributed to the two-phase composite microstructure consisting of a g-matrix (Ni) containing a large volume fraction of g'- particles (Ni3Al). During service, the initially cuboidal precipitates evolve to elongated plates through a diffusion-based process called rafting. In this work, a micro-mechanical constitutive framework is developed that specifically accounts for the microstructural morphology and its evolution. In the proposed multiscale approach, the macroscopic length scale characterizes the engineering level on which a finite element (FE) calculation is typically applied. The mesoscopic length scale represents the level of the microstructure attributed to a macroscopic material point. At this length scale, the material is considered as a compound of two different phases, which compose a dedicatedly designed unit cell. The microscopic length scale reflects the crystallographic level of the individual material phases. The constitutive behaviour of these phases is defined at this level. The proposed unit cell contains special interface regions, in which plastic strain gradients are assumed to be concentrated. In these interface regions, strain gradient induced back stresses develop as well as stresses originating from the lattice misfit between the two phases. The limited size of the unit cell and the micromechanical simplifications make the framework particularly efficient in a multiscale approach. The unit cell response is determined numerically at a material point level within a macroscopic FE code, which is computationally much more efficient than a detailed FE based unit cell discretization. The matrix phase constitutive behaviour is simulated by using a non-local strain gradient crystal plasticity model. In this model, non-uniform distributions of geometrically necessary dislocations (GNDs), induced by strain gradients in the interface regions, affect the hardening behaviour. Further, specifically for the two-phase material at interest, the hardening law contains a threshold term related to the Orowan stress. For the precipitate phase, the mechanisms of precipitate shearing and recovery climb are incorporated in the model. Additionally, the typical anomalous yield behaviour of Ni3Al-intermetallics and other non-Schmid effects are implemented and their impact on the superalloy mechanical response is demonstrated. Next, a damage model is proposed that integrates time-dependent and cyclic damage into a generally applicable time-incremental damage rule. A criterion based on the Orowan stress is introduced to detect slip reversal on the microscopic level and the cyclic damage accumulation is quantified using the dislocation loop immobilization mechanism. Further, the interaction between cyclic and time-dependent damage accumulation is incorporated in the model. Simulations for a wide range of load conditions show adequate agreement with experimental results. The rafting and coarsening processes are modelled by defining evolution equations for several of the microstructural dimensions. These equations are consistent with a reduction of the internal energy, which is often considered as the driving force for the degradation process. The mechanical response of the degraded material is simulated and adequate agreement is found with experimentally observed trends. Finally, the multiscale capability is demonstrated by applying the model in a gas turbine blade finite element analysis. This shows that changes in microstructure considerably affect the mechanical response of the gas turbine components.
Original languageEnglish
QualificationDoctor of Philosophy
Awarding Institution
  • Mechanical Engineering
  • Geers, Marc G.D., Promotor
  • Brekelmans, Marcel, Copromotor
Award date7 May 2009
Place of PublicationEindhoven
Print ISBNs978-90-386-1721-3
Publication statusPublished - 2009


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