Abstract The development of a fracture process zone (FPZ) (microcrack zone) ahead of a fracture tip is a prominent fracture characteristic of rock-like materials. At present, understanding of the quasi-static loading-rate effect on the FPZ development of a mixed-mode (I-II) fracture remains challenging for rock-like materials. In this paper, the centrally cracked Brazilian disk (CCBD) specimens of artificial rock-like materials were tested to create mixed-mode (I-II) fractures at different quasi-static loading rates (0.02–2 mm/min), and the centrally crack in each specimen is prefabricated at 15° (tensile-shearing mixed-mode), 45° (compressive-shearing mixed-mode) and 0° (pure mode-I) to the loading direction. The digital image correlation (DIC) was employed to identify FPZ, with the discontinuous characteristics of DIC-measured displacement and strain field ahead of the fracture tip. Based on test results, a couple of outcomes were obtained. (1) The geometries of mixed-mode (I-II) fractures changed barely at different quasi-static loading rates. (2) At mixed-mode (I-II) fracture tips, the DIC-measured tensile displacement fields presented remarkable discontinuity; in contrast, the DIC-measured sliding displacement fields were nearly continuous. Consequently, at different quasi-static loading rates, the tensile-shearing and compressive-shearing mixed-mode (I-II) just represents the fracture bearing tensile-shearing and compressive-shearing stresses for rock-like materials. Still, at the mixed-mode (I-II) fracture tip, the deformation in FPZ and the generation of the real fracture surface is tensile. (3) With the loading rate increasing, the FPZ length of mixed-mode (I-II) fracture increased roughly from 5 mm to 17 mm, which is similar to the pure mode-I fracturing (FPZ length: 4.5–17.3 mm). The rate-dependent FPZ length of mixed-mode (I-II) fracture follows a power-law, consistent with the mode-I fracture. (4) The peak load (an index indicating the fracture resistance) of mixed-mode (I-II) and pure mode-I fracturing was strengthened with the increasing loading rate, linearly correlated to the increasing FPZ length. It indicates that rate-dependent FPZ is supposed to strengthen the fracture resistance of mixed-mode (I-II) cracks with loading rates increasing. This research can provide a basis for controlling mixed-mode (I-II) fracturing of rock-like materials in underground excavation projects and geo-energy exploitation, such as the deflecting propagation of hydraulic fractures.

中文翻译：

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准静态加载速率对类岩材料中混合模式 (I-II) 裂缝断裂过程区发展的影响

摘要 裂隙尖端前发育断裂过程带（FPZ）（微裂纹带）是类岩石材料的显着断裂特征。目前，对于类岩石材料，了解准静态加载速率对混合模式（I-II）裂缝的 FPZ 发展的影响仍然具有挑战性。在本文中，对人造岩石类材料的中央裂纹巴西盘 (CCBD) 试样进行了测试，以在不同的准静态加载速率 (0.02–2 mm/min) 下产生混合模式 (I-II) 裂缝，并且每个试件的中心裂纹与加载方向成 15°（拉剪混合模式）、45°（压剪混合模式）和 0°（纯模式-I）预制。数字图像相关（DIC）被用来识别FPZ，具有 DIC 测量的断裂尖端前位移和应变场的不连续特征。根据测试结果，获得了几个结果。(1) 在不同的准静态加载速率下，混合模式 (I-II) 裂缝的几何形状几乎没有变化。(2) 在混合模式 (I-II) 断裂尖端，DIC 测量的拉伸位移场表现出明显的不连续性；相比之下，DIC 测量的滑动位移场几乎是连续的。因此，在不同的准静态加载速率下，拉剪和压剪混合模式（I-II）仅代表岩石类材料的裂缝承受拉剪和压剪应力。尽管如此，在混合模式 (I-II) 断裂尖端，FPZ 中的变形和真实断裂面的产生是拉伸的。(3)随着加载速率的增加，混合模式(I-II)裂缝的FPZ长度大致从5 mm增加到17 mm，与纯I型压裂(FPZ长度：4.5-17.3 mm)相似. 混合模式 (I-II) 断裂的速率相关 FPZ 长度遵循幂律，与模式 I 断裂一致。(4)混合模式(I-II)和纯模式-I压裂的峰值载荷(指示抗裂性的指标)随着加载速率的增加而增强，与FPZ长度的增加呈线性相关。这表明速率相关的 FPZ 应该随着加载速率的增加而增强混合模式 (I-II) 裂纹的抗裂性。该研究可为地下开挖工程和地能开发中类岩材料混合模式（I-II）压裂的控制提供依据，