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

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Few analytical K I solutions are available in literature. For a practical application, stress intensity factor K I can be computed for a set of predefined geometries using reduced order models while for a general geometry and loading conditions, K I is numerically calculated as part of 3D FEA solvers [4], For an analytic model, crack growth life can be calculated incrementally using the following steps: i. Given the initial crack length, geometry factor and applied far-field loading cycle are used to calculate stress intensity factor range (see Eq. 3). ii. For an assumed number of loading cycles ΔN , numerical integration of the Paris equation (1) is used to calculate the associated crack increment da . An R stress ratio (R=  min /  max ) is assumed to be constant.

Fig. 1. Numerical integration technique for fatigue crack growth.

2.1. Analytical Model Various analytical methods exist which can used to calculate stress intensity factors for surface, corner and embedded elliptical cracks in finite width plates under simple loading conditions. To verify the FE based results, MATLAB scripts were written based on empirical equations of the SIF solution associated with the three crack types as a function of plate geometry, crack dimension and loading conditions [7, 8]. In a realistic application, the analytical solutions provided by Newman and Raju [7, 8] are more runtime efficient than the 3D FEA based sequential crack propagation simulation however, analytical methods generally produce conservative results and at times, depending on how representative the reduced order model is to the specific component failure location the predictions can be non-conservative [16].