Advanced Reliability Assessment Approach of Power Modules Under Low-Cycle Thermal Fatigue Through Redefined 3-D J-Integral

Power modules are crucial components in core applications, including electrified vehicles and renewable energy systems. However, high-performance power modules often generate significant heat or experience large thermal fluctuations, leading to substantial thermal fatigue in their solder layers. This fatigue can threaten their reliability and shorten their lifespan. Traditionally, these phenomena have been analyzed using stress and strain measurements, but these force-based methods often fail to accurately predict the initiation and propagation of solder cracks. To address the limitations of conventional approaches, this study focuses on a fracture mechanics parameter known as the J-integral. Specifically, among the various modified versions of the J-integral, this work proposes applying the redefined J-integral, also referred to as the 3-D <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$T_{\varepsilon }^{\ast }$ </tex-math></inline-formula>-integral, for the first time to precisely analyze solder cracks in power modules. Using this proposed approach, the redefined J-integral range, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta J$ </tex-math></inline-formula>, is calculated through thermal cycling simulations and compared with experimentally achieved crack growth rates, dA/dN. Our analysis confirms a strong power-law correlation between the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\Delta J$ </tex-math></inline-formula> and dA/dN (with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${R} ^{2}$ </tex-math></inline-formula> of approximately 0.9344), resembling Paris’ law. Therefore, the proposed application of the redefined J-integral can effectively assess the lifespan of power modules under thermal fatigue conditions.