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Discrete element simulation of dynamic semi-circular bend flexure tests of rocks using split Hopkinson pressure bar

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Abstract

The semi-circular bending (SCB) using a split Hopkinson pressure bar system appears to be a promising method for measuring dynamic flexural strength of rock materials due to its distinct advantages. The quasi-static analysis is adopted for determining the dynamic flexural strength, of which several vital prerequisites have not been thoroughly examined yet. In this study, dynamic flexure tests regarding dynamic force equilibrium, interfacial friction effects, and energy partitioning are numerically investigated based on discrete element method (DEM) modeling. Results show that by virtue of the ramped wave loading, the force equilibrium of the specimen can be effectively achieved and the rupture is precisely measured to synchronize with the peak force, both of which guarantee the quasi-static data reduction method employed to determine the dynamic flexural strength; while the opposite occurs for the test under a rectangular wave loading. Furthermore, dynamic flexural strengths obtained by the numerical SCB tests exhibit approximately linear rate dependence that is identical with the experimental results. The interfacial friction, which is found to significantly influence the measuring results for rather high loading rates, contributes to enhancing the rate dependence of flexural strength and must be taken into account in dynamic flexure tests. In addition, energy partitioning is first numerically performed in the dynamic SCB tests and the nominal fracture energy manifests an S type of rate dependence with loading rates.

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Abbreviations

BPM:

Bonded particle model

DEM:

Discrete element method

ISRM:

International Society for Rock Mechanics

SCB:

Semi-circular bending

SHPB:

Split Hopkinson pressure bar

A s :

Area of the fracture surface (m2)

B :

Thickness of the SCB sample (m)

F Ic :

Force on the incident end of the specimen (N)

F Tc :

Force on the transmitted end of the specimen (N)

G dc :

Fracture energy dissipated per unit area (J/m2)

U f :

Accumulated energy consumed to fracture during the failure process of SCB (J)

P 1 :

Axial force applied on the incident end of the sample (N)

P 2 :

Axial force applied on the transmitted end of the sample (N)

R :

Radius of the SCB sample (m)

S :

Span of the supporting pins (m)

t i :

Instant when the stress wave first arrives at the incident end of the specimen (s)

t t :

Instant when the stress wave first arrives at the transmitted end of the specimen (s)

t b :

Instant when the force equilibrium on both ends of the specimen is first achieved (s)

t f :

Instant when the specimen initially fractures (s)

t p :

Instant when the forces on both ends of the specimen reach the peak value

t d :

Instant when the specimen is destroyed (s)

t e :

Instant when the loading process ends (s)

t m :

Instant of a post-mortem examination (s)

εi :

Incident strain signal on the incident bar

εr :

Reflected strain signal on the incident bar

εt :

Transmitted strain signal on the transmitted bar

μ :

Force equilibrium coefficient

f :

Friction coefficient

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Acknowledgments

The authors are grateful for the financial support from the National Program on Key Basic Research Project (no. 2015CB057903), National Natural Science Foundation of China (no. 51374149, 51579167), and the Youth Science and Technology Fund of Sichuan Province (2014JQ0004).

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Authors and Affiliations

  1. State Key Laboratory of Hydraulics and Mountain River Engineering, College of Water Resources and Hydropower, Sichuan University, Chengdu, Sichuan, 610065, China

    Yuan Xu, Feng Dai, Nu-wen Xu, Tao Zhao & Cheng Zhou

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  1. Yuan Xu
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  2. Feng Dai
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  3. Nu-wen Xu
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  4. Tao Zhao
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  5. Cheng Zhou
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Correspondence to Feng Dai.

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Xu, Y., Dai, F., Xu, Nw. et al. Discrete element simulation of dynamic semi-circular bend flexure tests of rocks using split Hopkinson pressure bar. Arab J Geosci 9, 543 (2016). https://doi.org/10.1007/s12517-016-2574-8

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