THERMAL PULSE-INDUCED EDGE CRACKING OF COATINGS BASED ON TIME-FRACTIONAL HEAT CONDUCTION
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摘要: 热震边裂是涂层的常见失效模式之一, 严重影响涂层的防护性能, 因此准确预测涂层边缘裂纹的热致扩展行为至关重要. 本文基于Caputo分数阶导热模型, 研究热脉冲作用下涂层边缘裂纹扩展驱动力. 首先, 采用拉普拉斯变换和有限余弦积分变换得到瞬态温度场及热应力场的封闭解; 其次, 运用叠加原理及权函数法计算边缘裂纹尖端的热应力强度因子. 探讨了分数阶阶次、无量纲裂纹长度、无量纲时间等参数对热应力强度因子的影响规律. 结果表明: 热应力强度因子的峰值随着分数阶阶次的增大而提高; 与分数阶超扩散情形相比较, 经典傅里叶导热将低估热流脉冲对边缘裂纹的扩展驱动力; 与分数阶亚扩散情形相比较, 经典傅里叶导热则会高估热流脉冲对边缘裂纹的扩展驱动力; 热流脉冲作用下, 短裂纹的热应力强度因子峰值更高, 因而更易扩展.Abstract: Edge cracking due to thermal shock is a common failure mode of coatings that seriously affects their protective performance, so it is crucial to accurately predict the thermally induced growth behavior of edge cracks. In this paper, based on the Caputo time-fractional heat conduction model, the crack driving force for an edge crack in the coating is investigated under a heat flow pulse. Firstly, the closed-form solutions are obtained for transient temperature and thermal stresses by using techniques of Laplace transform and finite cosine integral transform. Secondly, the thermal stress intensity factor (TSIF) for an edge crack is determined by using the princicipal of superpostion and weight function method. The dependence of TSIF is examined on such parameters such as the fractional-order, normalized crack length as well as normalized time. The results show that, the peak value of the TSIF increases as the fractional-order increases. Compared with the case of fractional order super-diffusion due to a heat flow pulse, the classical Fourier thermal diffusion underestimates the crack driving force for an edge crack, while compared with the case of fractional order sub-diffusion, the classical Fourier thermal diffusion overestimates the crack driving force. Under a heat flow pulse, the peak value of TSIF for a shorter edge crack is higher and thus shorter edge cracks are more prone to propagation.
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图 2 无量纲温度$\bar \theta $在不同时间$\kappa $下的分布
Figure 2. The distribution of the dimensionless temperature $\bar \theta $ for various times $\kappa $
图 3 无量纲应力$\bar \sigma $在不同时间$\kappa $下的分布
Figure 3. The distribution of the dimensionless stress $\bar \sigma $ for various times $\kappa $
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