This study introduced a simplified thermodynamic model based on the regularized phase field method for simulating the thermally induced fractures of rocks pretreated by microwave. A thermo-mechanical model comprises three main parts developed to evaluate the fractures: the heat generation of the rock specimen is determined via the heat balance equation; the calculation of thermally induced stress is performed in the second part by taking into account the thermal stress due to temperature change; the third part calculates the fracture induced by microwave heating using the phase field equation. Combining these three parts enables simulations of rock fractures due to thermally induced stress. The first simulation is the quenching test of ceramics to validate the robustness of the phase field method in modelling the thermo-mechanical fracture. Then, examples of microwave-induced fracture are presented and discussed in comparison with microwave test results. A good agreement is achieved from the results of numerical analysis and experiments, which proves the feasibility of the proposed thermo-mechanical coupling fracture (phase field) model for the simulation of thermal-mechanical fractures. It is further found that the power level is crucial in influencing the fractures given the same energy input. More specifically, a higher power level leads to an increased non-uniformity of a thermal gradient, which, as a result, leads to a higher stress gradient and more fractures generated eventually. Furthermore, the energy utilization ratio also benefits under a more intensive microwave power level. The developed model quantitatively enriches the understanding of fractures produced by microwave irradiation and advances the application of the microwave-assisted rock breakage technique in industry and academics.

中文翻译：

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使用相场法对火成岩中微波诱发裂缝进行计算建模

本研究提出了一种基于正则化相场方法的简化热力学模型，用于模拟微波预处理岩石的热致断裂。热力模型包括三个主要部分，用于评估裂缝：通过热平衡方程确定岩石样本的热量产生；在第二部分中进行热致应力的计算，考虑由于温度变化而产生的热应力；第三部分利用相场方程计算微波加热引起的断裂。将这三个部分结合起来可以模拟由于热致应力引起的岩石破裂。第一个模拟是陶瓷的淬火测试，以验证相场方法在热机械断裂建模中的稳健性。然后，介绍了微波诱发断裂的实例，并与微波测试结果进行比较进行讨论。数值分析和实验结果吻合良好，证明了所提出的热力耦合断裂（相场）模型用于模拟热力断裂的可行性。进一步发现，在相同能量输入的情况下，功率水平对于影响裂缝至关重要。更具体地，较高的功率水平导致热梯度的不均匀性增加，其结果是导致较高的应力梯度并最终产生更多的断裂。此外，在更密集的微波功率水平下，能量利用率也将受益。该模型定量地丰富了对微波辐照产生裂缝的认识，推动了微波辅助岩石破碎技术在工业和学术界的应用。