In the high-temperature environment, a larger thermal expansion mismatch of a bimaterial leads to pronounced thermal stresses and interface crack growth. In this paper, a generalized fractional heat conduction model is used to determine the instantaneous thermal fracture behaviors of a bimaterial interface crack. An axisymmetric thermoelastic problem is solved with the aid of Goodier's thermoelastic displacement potential and Love's potential functions. A mixed initial-boundary value problem is then converted to a singular integral equation of second kind by using the Hankel and Laplace integral transforms. Numerical results of the intensity factors of heat flux and thermal stresses are evaluated using Stehfest's Laplace inversion scheme. The influence of fractional kernel functions with power and exponential law are analyzed, respectively, for aluminum-steel and steel-epoxy, respectively. The thermal stress intensity factors exhibit more wave-like behaviors based on Riemann-Liouville and Atangana-Baleanu models which is different from Caputo-Fabrizio and the complete diffusion model.

中文翻译：

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通过广义分数传热研究具有便士形界面裂纹的双材料的瞬时热断裂行为


在高温环境下，双材料较大的热膨胀失配会导致明显的热应力和界面裂纹扩展。在本文中，采用广义分数热传导模型来确定双材料界面裂纹的瞬时热断裂行为。借助 Goodier 热弹性位移势和 Love 势函数解决了轴对称热弹性问题。然后使用汉克尔和拉普拉斯积分变换将混合初始边值问题转换为第二类奇异积分方程。使用Stehfest 的拉普拉斯反演方案评估热通量和热应力强度因子的数值结果。分别针对铝-钢和钢-环氧树脂，分析了具有幂律和指数定律的分数核函数的影响。基于 Riemann-Liouville 和 Atangana-Baleanu 模型的热应力强度因子表现出更多的波状行为，这与 Caputo-Fabrizio 和完全扩散模型不同。