PSI - Issue 12

Venanzio Giannella et al. / Procedia Structural Integrity 12 (2018) 479–491 V. Giannella/ Structural Integrity Procedia 00 (2018) 000 – 000

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In particular, a main cycle and a secondary cycle are extracted, with respectively a (relatively) high and a (relatively) low range of Stress Intensity Factors (ΔK ); for both of them the corresponding Crack-Growth Rates (CGRs) are calculated, without allowance for sequence effects. The adopted DBEM fracture code does not allow the use of temperature-dependent parameters in the Paris ’ law, consequently C, m and K th were calibrated at the mission maximum temperature, in order to be on the safe side: as a matter of fact, in the range of temperature considered, the growth rates for a given ΔK are monotonically increasing vs. temperature and K th monotonically decreasing vs. temperature. The FEM and DBEM codes used in this work are ANSYS (ANSYS, 2015) and BEASY (BEASY, 2016) respectively.

Nomenclature C

Paris’ law coefficient da/dN Crack-Growth Rate (CGR) E Young’s modulus G Shear modulus J J -integral K Stress Intensity Factor (SIF) K th Threshold value for K K c Critical value for K K eff Effective value for K n Paris’ law exponent W Strain energy density Γ υ Poisson’ ratio

Closed contour around crack tip

2. FEM analyses

2.1. FEM modelling The global FEM model (Fig. 1a) is related to a statoric segment of a low pressure turbine stage of an aircraft engine, composed by six airfoils, one of them affected by crack propagation (Fig. 1b). The material is a typical turbine blade superalloy, with isotropic mechanical and thermal material properties (Fig. 2). The fluid pressure is modeled by a mechanical load applied on both sides of the airfoils; in addition a temperature field, previously calculated by thermo-fluid-dynamic FEM analyses, is applied on the whole mesh. Cyclic symmetry boundary conditions are enforced on the casing that couples with the statoric segment, in order to simulate the periodicity of the whole stage. Surface to surface contacts are applied on the interfaces between the statoric hooks and the casing. Six different thermomechanical load sets are separately applied on the same FEM global model in order to simulate the behavior of the engine for the six main mission points of: pre take-off 1, pre take-off 2, take-off, cruise, reverse and shut down (Fig. 3). Results coming from these six global FEM analyses are then used as inputs for a multiaxial fatigue analysis, where the rainflow counting method is adopted to decompose the complex spectrum in blocks of baseline constant amplitude cycles. Such fatigue analysis points out the most critical regions where to perform the subsequent fracture analysis (in the DBEM environment). Namely, the crack is assumed nucleating by High Cycle Fatigue (HCF), in the most critical material point and, subsequently, propagating throughout the DBEM subdomain. The fatigue load spectrum considered in both fatigue and fracture analyses is assumed to be, in principle, comprehensive of the six abovementioned mission points (Fig. 3).