PSI - Issue 12

Venanzio Giannella et al. / Procedia Structural Integrity 12 (2018) 499–506 V. Giannella Structural Integrity Procedia 00 (2018) 000 – 000

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1. Introduction

Three-dimensional crack-growth simulations have assumed increased relevance over the last few decades. Early works were focused on building the framework to appropriately represent cracks with complex geometries, and calculate the related Stress Intensity Factors (SIFs) along the crack front (Newman et al., 1979). As crack propagation capabilities followed, much of the efforts went to the development of the framework necessary to model the extending crack with minimal user workload, for instance by FEM codes, such as FRANC3D (Wawrzynek et al., 2009), CRACKTRACER3D (Bremberg et al., 2009), ZENCRACK (Citarella et al., 2015a), and by DBEM codes, such as BEASY (Citarella et al., 2018). As shown in recent works, these methods nowadays allow performing automatic 3D fatigue crack-growth simulations for cracks in large structures (Citarella et al., 2014, 2013), in presence of residual stresses generated by plastic deformations (Citarella et al., 2014, 2015b, 2016a, 2016b; Carlone et al., 2015) and with allowance for load spectrum effects (Citarella et al., 2009). Additionally, hybrid FEM - DBEM global-local approaches have been proposed along the years (Citarella et al., 2016c; Giannella et al., 2017a, 2017b): these approaches take advantage of both the FEM versatility, when modelling the global problem, and of the higher efficiency of DBEM for simulating crack-growth in restricted subdomains. Non-planar 3D crack growth algorithms typically utilized 2D mode I/II crack growth theories that worked well for a wide range of engineering applications. However, as the technology to model nonplanar cracks in complex geometries has developed, the problem concerning the crack path assessment has become more demanding, requiring propagation criteria that include HCF/LCF interaction, Mixed Non-Proportional Loading (MNPL), fracture mode asymmetry and both elastic and fracture resistance anisotropy. Traditional crack-growth criteria, such as the Maximum Tangential Stress (MTS) criterion (Erdogan et al., 1963), assume proportional loading (KII/KI = constant during one cycle), and predict crack-growth along a KII ≈ 0 path. For non-proportional loading, the relative proportions of KI, KII, and KIII vary with time throughout the cycle making the setup of effective crack path criteria more complicated. MNPL can result from any structural situation wherein steady and cyclic loads are simultaneously acting along different directions, as for a turbine blade where the steady state centrifugal load couple with the blade vibrations (Fig. 1).

Nomenclature C

Paris’ law coefficient da/dN Crack-Growth Rate (CGR) E Young’s modulus J J -integral K Stress Intensity Factor (SIF) K th Threshold value for K K c Critical value for K K eq Equivalent value for K m Paris’ law exponent w Walker’s parameter υ Poisson’ ratio

2. Experimental tests

Cracks occurring in a fillet radius of a blisk (turbomachine component comprising both rotor disk and blades in a single piece) are subject to LCF in circumferential direction due to the centrifugal loading and HCF in radial direction due to several vibrational blade modes. The question arises whether such an initial crack, which propagates due to the HCF-loading, could turn into the disk due to the centrifugal LCF-loading and consequently leading to a catastrophic failure (Fig. 1).