论文标题
垂直于材料界面的裂纹的能量释放速率的近似公式
Approximate formulas for the energy release rate of a crack perpendicular to a material interface
论文作者
论文摘要
岩层通常的特征是存在于地质时间尺度和不断发展的应力场上的骨折存在。在机械分层的系统中，这种裂缝可以变成地层或渗透到相邻的地层中。脆性材料中断裂的生长通常取决于能量释放速率，但是当材料界面接近裂纹尖端时，没有封闭形式的分析解决方案。在这项研究中，我们提出了新的经验公式，用于计算垂直于对称3层系统中材料界面的裂纹尖端的能量释放速率。在这些公式中，归一化的能量释放速率表示为基本项的乘积，该基本项会在裂纹长度上整合归一化的刚度模量，并且是校正因子，该校正因子说明了材料界面的存在。假定后者取决于两个数量：裂纹长度与内层厚度的比率，以及内层和外层之间物质刚度的对比度。校正因子是通过将精心选择的表达式的参数拟合到一组有限元溶液中来获得的，以产生准确的预测，这些预测可准确地超过数值结果的百分之一。
Rock formations are very often characterized by the presence of fractures that have grown subcritically over geological time scales and under evolving stress fields. In mechanically layered systems, such fractures can either become layer-bound or penetrate into adjacent strata. The growth of fractures in brittle materials is generally dependent on the energy release rate, however no closed form analytical solutions exist for these when a crack tip is in the proximity of a material interface. In this study, we present new empirical formulas for calculating the energy release rate at the tip of a crack perpendicular to a material interface in a symmetric 3-layer system. In these formulas, the normalized energy release rate is expressed as the product of a base term that integrates the normalized stiffness modulus over the crack length, and a correction factor that accounts for the presence of a material interface. The latter is assumed to be dependent on two quantities: the ratio of the crack length to the inner layer thickness, and the contrast in material stiffness between the inner and outer layers. The correction factors are obtained by fitting the parameters of carefully chosen expressions to a set of finite element solutions in order to yield predictions that are accurate to within one percent of the numerical results.
