To investigate different responses of direct and indirect tensile strengths to loading rate, direct and indirect tension tests were performed on sandstone, rust stone, and granite specimens. Typical load curves indicate that a peak tensile stress frequently appears before the second peak stress, used to calculate the tensile strength in indirect tension tests. As expected, increase in the loading rate increases the tensile strength. In addition, the calculated tensile strengths of the indirect tension tests are frequently higher. Interestingly, the increase ratio of the tensile strength with the increase in the loading rate in indirect tension tests is higher. To verify the above results, crack propagation and stress evolution in direct and indirect tension tests were dynamically monitored using PFC 3D. For direct tension tests, specimens fail at the peak tension point, corresponding to the tensile strength. However, for indirect tension tests, minor cracks, composing of continuous microcracks, form before the peak stress and accompany with the decreased slope of the compression curve. At the peak point, tensile stresses significantly concentrate at the crack tips and further cause large-scale crack propagation. In addition, the initiation stress instead of the peak tensile stress is closer to the tensile strength, obtained from the direct tests for the same loading rate.

中文翻译：

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加载速率对直接和间接拉伸强度的影响：实验室和数值方法

为了研究直接和间接拉伸强度对加载速率的不同响应，对砂岩、锈石和花岗岩试样进行了直接和间接拉伸试验。典型的载荷曲线表明峰值拉伸应力经常出现在第二个峰值应力之前，用于计算间接拉伸试验中的拉伸强度。正如预期的那样，加载速率的增加会增加拉伸强度。此外，间接拉伸试验的计算拉伸强度通常更高。有趣的是，在间接拉伸试验中，随着加载速率的增加，拉伸强度的增加比例更高。为了验证上述结果，使用 PFC 3D 动态监测直接和间接拉伸试验中的裂纹扩展和应力演化。对于直接拉伸试验，试样在峰值张力点失效，对应于拉伸强度。然而，对于间接拉伸试验，由连续微裂纹组成的微小裂纹在峰值应力之前形成并伴随着压缩曲线的斜率减小。在峰值点，拉应力显着集中在裂纹尖端，并进一步引起大规模裂纹扩展。此外，初始应力而不是峰值拉伸应力更接近拉伸强度，这是从相同加载速率的直接测试中获得的。拉应力显着集中在裂纹尖端，并进一步引起大规模裂纹扩展。此外，初始应力而不是峰值拉伸应力更接近拉伸强度，这是从相同加载速率的直接测试中获得的。拉应力显着集中在裂纹尖端，并进一步引起大规模裂纹扩展。此外，初始应力而不是峰值拉伸应力更接近拉伸强度，这是从相同加载速率的直接测试中获得的。