Under triaxial deviatoric loading at stresses below failure, rocks generally exhibit nonlinearity and hysteresis in the stress‐strain curve. In 1965, Walsh first explained this behavior in terms of frictional sliding along the faces of closed microcracks. The hypothesis is that crack sliding is the dominant mode of rock inelasticity at moderate compressive stresses for certain rock types. Here we extend the model of David et al. (2012, https://doi.org/10.1016/j.ijrmms.2012.02.001) to include (i) the effect of the confining stress; (ii) multiple load‐unload cycles; (iii) calculation of the dissipated strain energy upon unload‐reload; (iv) either frictional or cohesive behavior; and (v) either aligned or randomly oriented cracks. Closed‐form expressions are obtained for the effective Young's modulus during loading, unloading, and reloading, as functions of the mineral's Young's modulus, the crack density, the crack friction coefficient and cohesion for the frictional and cohesive sliding models, respectively, and the crack orientation in the case of aligned cracks. The dissipated energy per cycle is quadratic and linear in stress for the frictional and cohesive models, respectively. Both models provide a good fit to a cyclic loading data set on polycrystalline antigorite, based on a compilation of literature and newly acquired data, at various pressures and temperatures. At high pressure, with increasing temperature, the model results reveal a decrease in friction coefficient and a transition from a frictionally to a cohesively controlled behavior. New measurements of fracture toughness and tensile strength provide quantitative support that inelastic behavior in antigorite is predominantly caused by shear crack sliding and propagation without dilatancy.

中文翻译：

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岩石三轴应力-应变曲线的非线性和迟滞滑动裂纹模型及其在反蛇纹岩变形中的应用

在破坏以下的应力下，在三轴偏斜载荷下，岩石通常在应力应变曲线中表现出非线性和滞后现象。1965年，沃尔什（Walsh）首先用沿闭合的微裂纹表面的摩擦滑动来解释这种行为。假设是，对于某些类型的岩石，在中等压缩应力下，裂纹滑动是岩石无弹性的主要模式。在这里，我们扩展了David等人的模型。（2012，https://doi.org/10.1016/j.ijrmms.2012.02.001）包括（i）约束压力的影响；（ii）多个装卸循环；（iii）计算卸荷时的耗散应变能；（iv）摩擦或内聚行为；（v）对准或随机取向的裂纹。对于加载，卸载和重新加载过程中的有效杨氏模量，可以获得闭合形式的表达式，作为矿物的杨氏模量的函数，分别针对摩擦和内聚滑动模型的裂纹密度，裂纹摩擦系数和内聚力，以及在对齐裂纹情况下的裂纹取向。对于摩擦模型和内聚模型，每个周期的耗散能量分别是平方和线性应力。这两种模型都基于文献汇编和最新获得的数据，在各种压力和温度下，都非常适合多晶抗蛇纹石的循环载荷数据集。在高压下，随着温度的升高，模型结果表明摩擦系数降低，并且从摩擦控制行为转变为内聚控制行为。