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Simultaneous determination of dynamic fracture toughness and tensile strength through a single three-point bending test

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Abstract

The fracture process zone (FPZ) has been assumed to activate microcrack evolution and influence the mechanical parameters of the rock specimen. This can be linked to the grain size of the rock specimens located in the path of the crack propagation. However, few studies have considered the effect of the grain distribution on the size of the FPZ, especially under dynamic loadings. In this paper, we analyze the mechanism by which the strain rate and grain distribution affect the FPZ and the dynamic mechanical parameters. We selected three kinds of sandstone specimens to represent the mesostructure heterogeneities characterized by the fractal dimensions. Also, the size of the FPZ can be calculated by the grain size and the dynamic fictitious crack length under the quantified mesostructure heterogeneities and the concept of the box dimension method. Based on the results, the dynamic strength and fracture toughness can be obtained with unknown coefficients. The unknown coefficients were then determined via the dynamic fracture test, in which the processed semicircle bending (SCB) specimens were used for the pendulum hammer-driven split Hopkinson pressure bar (SHPB) apparatus. Finally, the results were validated using the existing experimental methods recommended by the International Society for Rock Mechanics (ISRM). This study provides a valid and simpler method for the simultaneous determination of the dynamic fracture toughness and tensile strength of rock specimens.

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Abbreviations

\(R\) :

Radius

\(B\) :

Thickness

\(a_{0}\) :

Notched length

\(P\) :

Dynamic loading

\(\varepsilon \) In :

Incident strain

\(\varepsilon \) Re :

Reflected strain

\(\varepsilon \) Tr :

Transmitted strain

\(A\) :

Cross-sectional area of the compressive bars

\(l_{0}\) :

Initial length

\(P\) max :

Maximum load

\(\sigma _{n}\) :

Nominal stress

S:

Span length

\(\Delta a_{\mathit{fic}}\) :

Fictitious crack growth length

\(g\) ave :

Average grain size near the notched tip

\(\delta \) :

Grain size of the rock specimen

\(d_{i}\) :

Characteristic mineral particle

\(d_{\mathrm{M}}\) :

Maximum grain size

\(M_{\mathrm{T}}\) :

Total particle mass

\(D\) :

Fractal dimension

\(V\) :

Impact velocity

\(f_{t}\) :

Dynamic tensile strength

\(K\) IC :

Dynamic fracture toughness

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Funding

This work was funded by the National Key Research and Development Program of China (2020YFA0710500), National Science Foundation of China (Grant Nos. 12002004 and 51304037), the Fundamental Research Funds for the Central Universities (Grant Nos. N160104008 and N160103005), Natural Science Foundation of Liaoning Province (2022-MS-038), fundamental research project of SIA(2022JC1K06) and State Key Laboratory of Robotics (Grant No. 2022-Z09).

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Authors and Affiliations

  1. State Key Laboratory of Robotics, Shenyang Institute of Automation, Chinese Academy of Sciences, Shenyang, 110016, China

    Miao Yu, Haitao Luo & Hongdi **g

  2. Institutes for Robotics and Intelligent Manufacturing, Chinese Academy of Sciences, Shenyang, 110169, China

    Miao Yu, Haitao Luo & Hongdi **g

  3. School of Physical and Mathematical Sciences, Nan**g Tech University, Nan**g, 211816, China

    Shuang Wang

  4. State Key Laboratory for Turbulence and Complex Systems, Department of Mechanics and Engineering Science, BIC-ESAT, College of Engineering, Peking University, Bei**g, 100871, China

    Hongyuan Li

Authors
  1. Miao Yu
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  2. Haitao Luo
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Contributions

Yu and Luo conducted the experiment and wrote the main manuscript. **g, Li and Wang prepared the figures and tables. All authors reviewed and revised the manuscript.

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Yu, M., Luo, H., **g, H. et al. Simultaneous determination of dynamic fracture toughness and tensile strength through a single three-point bending test. Mech Time-Depend Mater (2023). https://doi.org/10.1007/s11043-023-09639-3

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