Research Article: Calculation for tensile strength and fracture toughness of granite with three kinds of grain sizes using three-point-bending test

Date Published: March 29, 2018

Publisher: Public Library of Science

Author(s): Miao Yu, Chenhui Wei, Leilei Niu, Shaohua Li, Yongjun Yu, Jun Xu.


Tensile strength and fracture toughness, important parameters of the rock for engineering applications are difficult to measure. Thus this paper selected three kinds of granite samples (grain sizes = 1.01mm, 2.12mm and 3mm), used the combined experiments of physical and numerical simulation (RFPA-DIP version) to conduct three-point-bending (3-p-b) tests with different notches and introduced the acoustic emission monitor system to analyze the fracture mechanism around the notch tips. To study the effects of grain size on the tensile strength and toughness of rock samples, a modified fracture model was established linking fictitious crack to the grain size so that the microstructure of the specimens and fictitious crack growth can be considered together. The fractal method was introduced to represent microstructure of three kinds of granites and used to determine the length of fictitious crack. It is a simple and novel method to calculate the tensile strength and fracture toughness directly. Finally, the theoretical model was verified by the comparison to the numerical experiments by calculating the nominal strength σn and maximum loads Pmax.

Partial Text

It is well recognized that rock as a heterogeneous brittle material shows a much higher compressive strength than tensile strength (more or less 10 times). Therefore it is important to understand local tensile stress of the rock samples under different mechanical loadings [1–5]. Because of the existing of the microcracks the propagation and coalescence of these defects can easily make the rock samples failure. Therefore, the researches on fracture toughness are also the key problems to the rock mechanical properties and failure modes as important as basic mechanical behaviors [6–9]. Test procedures were suggested by ISRM [10] for rock fracture toughness, where chevron bend (CB) [11], short rod (SR) [12] and cracked chevron-notched Brazilian disk (CCNBD) [13] were adopted as standard specimens. But many scholars [14, 15] thought that neither tensile strength nor fracture toughness can be obtained easily through the physical experiment, and therefore indirect experimental methods such as Brazilian disc and notched three-point-bending samples have been taken into consideration and semi-empirical relations have been built to measure the tensile strength and fracture toughness. Tutluoglu [16] used the three methods (CCNBD, SCB and SNDB) to calculate the fracture toughness of granite and it can be concluded that the growth of fracture process zone is the major factor affecting the experimental results. Dai et al. [17] conducted the numerical simulation to measure the mode I fracture toughness of rocks according to four methods (ISRM suggested). By comparison of the above methods, it can be found that the fracture of the semi-circular bend (SCB) specimen agrees with the measuring principle. Wei et al. [18] analyzed the fracture mechanism of the SCB specimens by both acoustic emission (AE) monitoring and numerical modeling and discussed the relationship between effective crack lengths and fracture toughness. Nasseri et al. [19] used four relatively fine grained and homogeneous granitic rocks to investigate the relationship between their microstructural properties and fracture toughness.

In summary, this paper presents a new method to calculate the tensile strength and fracture toughness of three kinds of granite samples with different notch lengths by using three-point-bending (3-p-b) tests. A modified fictitious model is introduced to describe the fracture process zone (FPZ) around the notch tip and it can link the FPZ with grain size on a micro-scale at the peak load during quasi-static fracture process. Moreover, acoustic emission system can be used to monitor the failure mechanism of samples around the notch tip. The combination methods of physical and numerical tests are performed to validate the model and also acoustic emission system is introduced to monitor the fracture mechanism around the notch tip. The numerical simulation RFPA-Dip version is developed to characterize the microstructure of the rock specimens and can be used to conduct the 3-p-b tests, in which process only peak loads and average grain size of three kinds of samples are needed. The results can be concluded that: (1) a modified fictitious crack model is presented and used to link the microstructure of the rock with fracture process around the notch tip and it is an effective method to calculate the tensile strength and fracture toughness at the peak loads of 3-p-b tests under quasi-static loadings; (2) fracture mechanism is governed by grain size of the rock samples and moreover it is shown that the smaller grain size corresponds to the shear failure and the percentage of tensile failure is gradually larger with the increase of the grain size. (3) fractal concept can be introduced to describe the microstructure and heterogeneity of granites and calculate the fictitious crack growth; (4) numerical experiments of above 3-p-b samples are conducted to understand the fracture mechanism of three kinds of granites and validate the theoretical model in contrast to the results of physical tests and model prediction.




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