Nonlinear thermoelastic analysis of stress intensity factors in isotropic cracked layers

This paper investigates stress intensity factors (SIFs) in a finite, homogeneous, and isotropic cracked layer with temperature-dependent properties under thermal shock. Unlike previous studies that have predominantly relied on linear or generalized thermoelasticity theories, this work accounts for the nonlinear effects within the framework of classical thermoelasticity – representing the key innovation of this research. This analysis is critical for preventing catastrophic failures in safety-sensitive components where linear theories may underestimate thermal stress effects. Key applications include turbine blades, combustion chambers, and thermal protection systems subjected to rapid heating/cooling cycles; hypersonic vehicle skins; and reactor pressure vessels, among others. The extended finite element method (XFEM) is employed to solve the governing equations, and SIFs are extracted using the interaction integral method. Results show a slight increase in SIFs when using the nonlinear theory compared to the linear theory. For materials with temperature-dependent properties and under large temperature variations a strong increase in SIFs is observed. The results indicate that for temperature-dependent material properties, the maximum increase in SIFs due to nonlinear effects reaches approximately 6% at specific time intervals.