In order to study the mechanical properties of granite at the micro- and nanoscale, the load-displacement curve, residual indentation information, and component information of the quartz, feldspar, and mica in granite were obtained using a nanoindentation test, a scanning electron microscope (SEM), and X-ray diffraction (XRD). The elastic modulus and the hardness of each component of the granite were obtained through statistical analysis. Treating rock as a composite material, the relation between the macro- and microscopic mechanical properties of rock was established through the theory of micromechanical homogenization. The transition from micromechanical parameters to macromechanical parameters was realized. The equivalent elastic modulus and Poisson’s ratio of the granite were obtained by the Self-consistent method, the Dilute method, and the Mori-Tanaka method. Compared with the elastic modulus and the Poisson ratio of granites measured by a uniaxial compression test and the available data, the applicability of the three methods were analyzed. The results show that the elastic modulus and hardness of the quartz in the granite is the largest, the feldspar is the second, the mica is the smallest. The main mineral contents in granite were analyzed using the semiquantitative method by XRD and the rock slice identification test. The elastic modulus and the Poisson ratio of granite calculated by three linear homogenization methods are consistent with those of the uniaxial compression test. After comparing the calculation results of the three methods, it is found that the Mori-Tanaka method is more suitable for studying the mechanical properties of rock materials. This method has an important theoretical significance and practical value for studying the quantitative relationship between macro- and micromechanical indexes of brittle materials. The research results provide a new method and an important reference for studying the macro-, micro-, and nanomechanical properties of rock.

中文翻译：

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基于纳米压痕技术的花岗岩多尺度力学性能评价方法

为了在微米和纳米尺度上研究花岗岩的力学性能，利用纳米压痕测试、扫描电子显微镜获得了花岗岩中石英、长石和云母的载荷-位移曲线、残余压痕信息和成分信息。 (SEM) 和 X 射线衍射 (XRD)。通过统计分析得到花岗岩各组分的弹性模量和硬度。将岩石作为一种复合材料，通过微观力学均质化理论，建立了岩石宏观力学性质与微观力学性质之间的关系。实现了从微观力学参数到宏观力学参数的转变。花岗岩的等效弹性模量和泊松比通过自洽法、稀释法、和森田中方法。将花岗岩单轴压缩试验测得的弹性模量和泊松比与已有数据进行对比，分析了三种方法的适用性。结果表明，花岗岩中石英的弹性模量和硬度最大，长石次之，云母最小。采用XRD半定量方法和岩石切片鉴定试验对花岗岩中的主要矿物含量进行了分析。三种线性均化方法计算的花岗岩弹性模量和泊松比与单轴压缩试验结果一致。通过比较三种方法的计算结果，发现Mori-Tanaka方法更适合研究岩石材料的力学特性。该方法对于研究脆性材料宏观力学指标与微观力学指标之间的定量关系具有重要的理论意义和实用价值。研究成果为研究岩石的宏观、微观和纳米力学性质提供了一种新方法和重要参考。