We developed a generalized multiphase-field modeling framework for addressing the problem of brittle fracture propagation in quartz sandstones at microscopic length scale. Within this numerical approach, the grain boundaries and crack surfaces are modeled as diffuse interfaces. The two novel aspects of the model are the formulations of (I) anisotropic crack resistance in order to account for preferential cleavage planes within each randomly oriented quartz grain and (II) reduced interfacial crack resistance for incorporating lower fracture toughness along the grain boundaries that might result in intergranular crack propagation. The presented model is capable of simulating the competition between inter- and transgranular modes of fracturing based on the nature of grain boundaries, while exhibiting preferred fracturing directions within each grain. In the full parameter space, the model can serve as a powerful tool to investigate the complicated fracturing processes in heterogeneous polycrystalline rocks comprising of grains of distinct elastic properties, cleavage planes, and grain boundary attributes. We demonstrate the performance of the model through the representative numerical examples.

中文翻译：

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石英砂岩中的脆性各向异性裂缝扩展：相场模拟的启示

我们开发了一种通用的多相场建模框架，以解决微观尺度下石英砂岩中脆性断裂扩展的问题。在这种数值方法中，将晶界和裂纹表面建模为扩散界面。该模型的两个新方面是（I）各向异性抗裂性的公式化，以说明每个随机取向的石英晶粒内的优先劈裂面；（II）降低的界面抗裂性，以便沿晶界结合较低的断裂韧性，这可能导致晶间裂纹扩展。提出的模型能够基于晶界的性质模拟晶间和晶间断裂模式之间的竞争，同时在每个晶粒内展现出优选的断裂方向。在全参数空间中，该模型可作为研究异质多晶岩石中复杂断裂过程的有力工具，该岩石由具有不同弹性特性的晶粒，劈裂面和晶界属性组成。我们通过具有代表性的数值示例来证明模型的性能。