Verification of Stress-Intensity Factor Solutions by Uncertainty Quantification

Abstract

This paper summarizes an emerging process to establish credibility for surrogate models that cover multidimensional, continuous solution spaces. Various features lead to disagreement between the surrogate model's results and results from more precise computational benchmark solutions. In our verification process, this disagreement is quantified using descriptive statistics to support uncertainty quantification, sensitivity analysis, and surrogate model assessments. Our focus is stress-intensity factor (SIF) solutions. SIFs can be evaluated from simulations (e.g., finite element analyses), but these simulations require significant preprocessing, computational resources, and expertise to produce a credible result. It is not tractable (or necessary) to simulate a SIF for every crack front. Instead, most engineering analyses of fatigue crack growth (FCG) employ surrogate SIF solutions based on some combination of mechanics, interpolation, and SIF solutions extracted from earlier analyses. SIF values from surrogate solutions vary with local stress profiles and nondimensional degrees-of-freedom that define the geometry. The verification process evaluates the selected stress profiles and the sampled geometries using the surrogate model and a benchmark code (abaqus). The benchmark code employs a Python scripting interface to automate model development, execution, and extraction of key results. The ratio of the test code SIF to the benchmark code SIF measures the credibility of the solution. Descriptive statistics of these ratios provide convenient measures of relative surrogate quality. Thousands of analyses support visualization of the surrogate model's credibility, e.g., by rank-ordering of the credibility measure.

Stress Intensity Factors for Corner Cracks under Arbitrary Stress Fields in the Finite Plates Based on the Point Weight Function Method

“…The SIF considered in this paper is a mode I corner crack in rectangular geometry with finite length and width, as shown in Figure 1. The SIFs for two points along the corner cracks, A and B, are critical for the crack propagation calculation [31].…”

“…The SIFs for two points of corner cracks, A and B, shown in Figure 1, are critical for the crack propagation calculation [31]. It is worth mentioning that the reference solutions are determined as the SIFs taken at 2.5 °inside the two points A and B.…”

“…Orynyak et al then developed point weight functions for elliptical cracks [29,30]. Finally, the point weight function method was applied on the corner cracks at holes for calculating SIFs under bivariant stress gradients and implemented in production software for design and life management [31][32][33]. However, few efforts have been devoted to explaining the details for establishing point weight functions for corner cracks in three-dimensional finite rectangular plates.…”

Machine learning‐based efficient stress intensity factor calculation for aeroengine disk probabilistic risk assessment under polynomial stress fields

“…In the fracture mechanic module of the risk assessment, stress intensity factor (SIF) calculation is essential in which efficiency and accuracy are the main considerations: First, due to the requirement of the crack propagation calculation 2 and Monte Carlo simulation in risk assessment, numerous SIF solutions should be conducted for various types of cracks in complex geometries and stress fields; second, 10% of the sustained errors in the SIF solutions may lead to 30-50% life prediction bias. 3 The main approaches of SIF calculation nowadays are analytical methods, numerical methods, and the weight function method. For analytical methods mentioned in Murakami 4 and Al Laham and Ainsworth 5 and some other handbooks, although the results are accurate, the scope of application is limited.…”

“…Probability failure risk assessment is considered an effective method for rotor disk life management, which has been recommended by airworthiness regulations 1 to evaluate aeroengine safety. In the fracture mechanic module of the risk assessment, stress intensity factor (SIF) calculation is essential in which efficiency and accuracy are the main considerations: First, due to the requirement of the crack propagation calculation 2 and Monte Carlo simulation in risk assessment, numerous SIF solutions should be conducted for various types of cracks in complex geometries and stress fields; second, 10% of the sustained errors in the SIF solutions may lead to 30–50% life prediction bias 3 …”