On the Application of the Sliding Box Analogy for an Energy Balance Approach to Fatigue Modeling in Cold Environments

Abstract

This thesis investigates the application and extent of validity of a novel physics-based energy-balance approach with the Sliding Box analogy. The scope focuses on predictive modeling of fatigue crack growth in aluminum alloys at low temperatures. The motivation for this research arises from the increasing demand for reliable fatigue-life prediction methods in the context of hydrogen-powered aviation, where liquid-hydrogen storage tanks and adjacent structures are exposed to cyclic mechanical and thermal loading in cold environments. Traditional empirical approaches, such as Paris’ law, are limited by their reliance on extensive experimental calibration, especially when material properties and environmental factors vary significantly.

The research aims to expand and validate the Energy Balance with the Sliding Box analogy (EBSB) framework by comparing its predictions to a comprehensive experimental dataset covering both room-temperature and low-temperature conditions down to -30°C. The study considers a diversified selection of aluminum alloys with quasi-static property differences that emulate changes expected at low temperature. The investigated materials are 7075-T6, 2024-T3, 6061-T6, and an artificially over-aged 2024-A300. Additionally, thicknesses from 1 to 6.5 mm and two stress ratios, R=0.1 and R=0.5, are varied to evaluate their influence on the modeled fatigue crack-growth response. The methodology combines quasi-static tensile testing to determine case-specific elastic--plastic properties with constant-amplitude fatigue crack-growth experiments on standard geometry specimens. Crack growth is measured via periodic high-contrast image capture. Furthermore, Digital Image Correlation (DIC) is employed to evaluate plastic-zone development from periodic displacement-field measurements around the advancing crack tip.

The results demonstrate that the EBSB model—particularly in its direct sliding-box form—captures the general trends and order of magnitude of fatigue crack growth in aluminum alloys well. However, predictive accuracy is limited by the current formulation of the plastic energy dissipation term and by the treatment of stress-state transitions (plane stress/plane strain). The quantification of plastic-volume growth within the energy balance was varied in an attempt to capture increased energy absorption at low temperature. The model tends to overestimate crack-growth rates, especially for pronounced variations in yield strength and strain hardening relative to the 7075-T6 baseline. This effect is not mitigated by adopting larger plastic-zone approximations. For lower thicknesses of 7075-T6, however, using a larger plastic-zone estimate reduces model error, consistent with better agreement with the plane-stress assumption.

Overall, the EBSB model is sensitive to material-specific strain-energy absorption characteristics, particularly yield strength and the degree of strain hardening. Experimental observations confirm the expected increase in yield strength and work hardening at low temperature, but also reveal an unexpected decrease in ductility for the low-temperature 7075-T6 tests, highlighting the complex coupling between material behavior and environment. Improvements to the EBSB framework are proposed, including a parametrically defined plastic strain energy density derived from quasi-static stress--strain data and the introduction of a damping term to account for crack-shielding effects. Recommendations for future work include expanded cryogenic testing, improved DIC resolution, and the development of more robust analytical and numerical treatments to better capture strain hardening, stress-state transitions, and plastic-zone evolution.