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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1. Introduction

Design of aircraft engines ask for cutting edge modelling capabilities since their components undergo high temperatures, sharp thermal gradients, complex mechanical loads, and corrosive environments. Moreover, long lifetimes are expected and, in case of occurrence of a structural failure, the consequences could be catastrophic. The turbine loading conditions vary drastically from take-off to landing, with temperatures reaching up to 1300 K, imposing to the materials severe thermo-mechanical loadings. Extreme temperature gradients and transients induce cyclic thermal-stresses on the turbine vanes with consequent Thermo-Mechanical Fatigue (TMF) conditions. It is therefore of interest to accurately evaluate the impact of structural defects on these components. Usually, large structures are modeled with Finite Element Method (FEM) because of the versatility of such method; however, modelling crack-growth with FEM involves particularly complex remeshing strategies as the crack propagates, especially under mixed-mode conditions (Citarella et al. 2010, 2008, 2015a; Maligno et al. 2015). The Dual Boundary Element Method (DBEM) simplifies the meshing processes and accurately captures the strong gradients of the stress field near the crack front (Citarella et al., 2003, 2005, 2008, 2010, 2014a, 2018; Calì et al., 2003). As proved in recent works, the two methods can efficiently work together when tackling large structures (Citarella et al. (2013, 2014b), residual stresses generated by plastic deformations (Citarella et al. 2014c, 2015b, 2016a; Carlone et al., 2015) as well as load spectrum effects (Citarella et al., 2014d). Generally, when using a FEM-DBEM approach to solve a fracture problem, FEM is used to work out the main global displacement-stress-strain fields and, subsequently, a DBEM submodel, extracted from the global FEM model, is used to tackle the local fracture problem. Such coupling between FEM and DBEM can be implemented in different ways: • a “ Fixed Displacements/Load ” (FD/FL) approach (Citarella et al., 2013, 2014c, 2016b; Carlone et al., 2015), where temperatures and either displacements or tractions, as evaluated in the global FEM model, are applied on the DBEM submodel boundaries. In this way, the FEM global stress field is reproduced in the DBEM uncracked subdomain, with a higher accuracy due to the refined mesh adopted in the submodel; then the crack is inserted and propagated throughout the DBEM subdomain. • a “ Loaded Crack ” (LC) approach (Citarella et al., 2016b; Giannella et al., 2017a, 2017b), where tractions, as calculated by an FEM global analysis of the uncracked domain, are applied on the DBEM crack faces. Differently from the previous approaches (FD/FL), the FEM stress field is not reproduced in the DBEM submodel; the latter will just provide the fracture parameters useful to drive the crack growth (e.g. SIFs), as enabled by the superposition principle (Wilson, 1979). As the crack propagates, traction loads (available from the FEM global analysis) are added on the newly step-by-step generated crack surfaces. The LC approach offers some advantages in terms of reduced runtimes and enhanced accuracy if compared with FD/FL approaches and therefore will be adopted in this work. In particular, it enables a fast convergence rate vs. mesh refinement (on the crack faces) and a simpler DBEM analysis that does not involve thermal-stress but just pure stress calculations, with a consequent reduction of the computational burden (Citarella et al., 2016; Giannella et al., 2017a, 2017b). As a matter of fact, when adopting the LC approach, the DBEM submodel boundary conditions are just involving tractions, to be applied on crack faces and evaluated by the FEM global analyses on the uncracked component, in correspondence of the surface traced by the advancing crack. In this application, the fracture analysis is performed considering an initial crack, whose position is defined by a multiaxial fatigue analysis, preliminary performed on the whole turbine vane segment, undergoing the considered fatigue load spectrum. Such load spectrum is built up considering a sequence of six main mission points, whose stress scenarios are evaluated by six corresponding FEM analyses, representative of the following flight phases: taxiing, pre take-off, post take-off, cruise, reverse and shut down (the latter two are representative of the landing phase). After producing the crack initiation, the same load spectrum is also driving the fatigue crack-growth simulation. Applying the rainflow algorithm to the abovementioned load spectrum, it is possible to obtain two different baseline cycles that, iteratively applied, will drive the crack-growth simulation. Actually, from the rainflow implementation more than two baseline cycles come out but those corresponding to negative K I values are discarded (these are not considered effective in driving a crack growth).