PSI - Issue 38

Paul Catalin Ilie et al. / Procedia Structural Integrity 38 (2022) 271–282 P. C. Ilie et al./ Structural Integrity Procedia 00 (2021) 000 – 000

272

2

1. Introduction The useful fatigue life of in-service aerospace structures is difficult to precisely estimate due to uncertainties related to service loading conditions, deviations from nominal geometry, intrinsic fatigue crack growth scatter, modeling limitations and modeling uncertainties. The formation of fatigue cracks in structural components is influenced by the nature of prior usage as well as the soundness of regular repairs, maintenance and structural improvements [1,2]. Demanding operational environments, economic factors, increased lifetime expectancy and safety requirements have created a need to efficiently assess the safety of current structural elements and future design modifications. Damage tolerance (DT) design philosophy uses fracture mechanics principles to assess the effect of flaws on remaining useful life of structural components sustaining operating conditions. The main design goal for structures considering DT design philosophy is to safely operate within service loads with the presence of material flaws (manufacturing, environmental, accidental) until detection and remedy of the damaged component becomes available [2,3]. In practice, fatigue crack growth life assessment analysis [4] of a component entails the following steps [3]. i. Calculation of stress intensity factor ranges for an assumed or detected cracking site in a serviced part. ii. Use of coupon test data correlating crack growth rate (da/dN) to mode I stress intensity factor range (  K I ). iii. Perform crack propagation simulation to predict maximum allowable crack size or remaining useful life. Fatigue crack growth behavior can be evaluated with closed form solutions of mode I stress intensity factors (K I ) for simple crack geometries while for complex geometry and loading configurations, the weight function technique [5,6] or finite element (FE) methods can be utilized. Closed form solutions for stress intensity factors have been developed for numerous crack shapes, part geometry and loading conditions [7, 8]. The equations can also be found as part of accepted industry practices for fatigue crack growth analysis [9, 10, 11]. The analytical nature of these methods makes them efficient and straightforward to implement however they are known to produce conservative results. Alternatively, finite element-based solvers can be used to calculate stress intensity factor (SIF) values where handbook solutions cannot be applied in case of complex geometries and crack configurations. A three-dimensional (3D) finite element analysis (FEA) based software package such as SimModeler Crack [12] can provide an increased accuracy of SIF solutions and therefore for the predicted crack propagation life for component level representations containing one or several cracks. A two-dimensional analytical model was implemented in MATLAB [13] for predicting planar crack growth. Using three classic geometries, semi-elliptical, corner quarter-elliptical and internal elliptical crack representations in a finite width plate [7, 8], the analytical solution-based crack growth predictions are compared to an explicit 3D FE modeling technique implemented in SimModeler Crack. This initial study serves as a verification benchmark. The 3D FE modeling approach was further validated against experimental data of Al 2024-T3 specimens containing multiple cracks. Two configurations were tested, each with five edge cracks at various locations. The 3D FEA based fatigue crack propagation simulations showed good correlation against the experimental measurements. 2. Modeling Methodology The relation between crack growth rate and stress intensity factor, in its modern form, took shape during the 1960s. This was due in part to experimental evidence and analysis stemming from research by Swanson et al. [14] and experiments by Paris and Erdogan [15]. Swanson [14] concluded that stress and crack length were the main driving parameters to define the stress intensity factor for the crack opening mode i.e. Mode I. This was achieved by adjusting the cyclic loads applied on the sample as the crack grew in length, effectively keeping stress intensity factor range, ΔK I constant. Paris and Erdogan tested aluminum panels with a center crack under uniform remote loading conditions. It was observed that crack growth rate under constant cyclic tension was dependent on stress intensity factor range, ΔK I . The crack growth rate as a function of ΔK I can be expressed mathematically by the Paris-Erdogan equation in Eq. (1). = (∆ ) (1)