PSI - Issue 38

Adrian Loghin et al. / Procedia Structural Integrity 38 (2022) 331–341 A. Loghin et al. / Structural Integrity Procedia 00 (2021) 000–000

332

2

R Cyclic stress ratio, σ min /σ max DOE Design of Experiment GPR Gaussian Process Regression

K Imax Mode I Stress Intensity Factor at maximum load K IImax Mode II Stress Intensity Factor at maximum load ∆ K I Mode I Stress Intensity Factor range, K Imax − K Imin Y 1

Relative distance between initial notch and the hole feature along Y direction Relative distance between initial notch and test specimen centerline

Y 0

a X , a Y Planar position of sequential crack front increments

1. Introduction

It is commonly believed that remeshing process is man-power intensive and generating fine mesh around the crack front is computationally expensive (Peng, et. al. (2018)). Consequently, any mesh convergence study or uncertainty quantification assessment becomes a burden for the engineer in charge of a structural integrity assignment. Under the assumption that a quick runtime model is needed, closed-form solutions for simple crack representations (i.e. elliptical corner crack at a hole under uniform loading) are still developed and used even though they often provide a lower accuracy solution compared to a 3D finite element structural analysis due to the assumptions made in the modeling process. In a realistic fatigue crack growth assessment, far-field loading is not uniform, crack shape might not be elliptical or straight, geometric features can a ff ect the crack path or, interaction of multiple cracks must be considered. Developing closed-form models for each of the potential scenarios is impractical. Instead of developing a generic model specific to a location susceptible for cracking or already containing a crack, the 3D FEA representation of the structure can be utilized to accurately compute crack driving forces and therefore take into account nominal geometry and the stress gradient that controls crack advancement. This can be achieved with e ffi cient remeshing procedures (Loghin (2018)) transparent to the user at a fraction of the runtime cost compared to the solution time. The assessment is more accurate than the closed form equivalent model, but it comes with a higher runtime cost. The advantage of robust remeshing capabilities can be complemented with machine learning algorithms to satisfy both critical crack propagation life assessment requirements: accuracy and low runtime cost. 3D FEA based surrogate modeling development has been reported in the recent literature by Leser et al. (2017), Loghin and Ismonov (2020a), Spear et al. (2011), Shantz (2010), Loghin and Ismonov (2019). Gaussian Process Regression (GPR) is one technique employed to generate surrogate models for a quick computation of mode I stress intensity factors at one or two locations along the crack front. Calibration of the GPR surrogate model makes use of di ff erent 3D FE models that capture the overall geometry and loading configuration of the part, crack shape and size evolution. This is advantageous since these simulations are detached of each other and therefore can be performed as independent processes (Loghin and Ismonov (2020a)) and, secondly, accuracy of the solution is maintained by using representative 3D FEA instead of reduced order models (based on geometric simplifications and weight functions). Radial Basis Function (RBF) based surface response modeling is another technique for developing surrogate models designed to capture the entire crack path and not only the mode I stress intensity factors for a given crack size and shape. Similar to the GPR surrogate model calibration process, a set of independent simulations are performed but, in this case, each simulation is a 3D FEA crack propagation assessment. The outcome of each deterministic assessment consists of a crack surface evolution and associated loading cycles. The main question is how the damage tolerance design community will accommodate more accurate component level fatigue crack growth representations instead of handbook solutions or reduced order models for crack propa gation life assessments. For a simple corner crack at a hole, the elliptical crack front assumption (commonly used in reduced order models) produces a 36% conservative loading cycles estimation relative to a three-dimensional FE model where no crack front shape constraint is used (Loghin (2021)). Sobotka and McClung (2019) point out another lack of accuracy source in crack propagation life assessment: accuracy of stress intensity factor solution. According to Sobotka and McClung (2019) a 10% error in stress intensity factor calculation may translate into 30% to 50% error in computed loading cycles.