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On loading ceramic-like materials using split Hopkinson pressure bar

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Abstract

In Hopkinson pressure bar experiments on ceramics, the stress inequilibrium and indentation of the specimen to bar ends are critical issues due to the brittle nature and high strength of ceramics. Theoretical analysis is employed to reconstruct the loading process for investigating the influence of the stress inequilibrium. The results indicate that it has little influence on the accuracy of stress–strain curves and accurate peak stress measurements during the dynamic test can be made. The optimized bilinear incident wave is formulated for achieving the stress equilibrium and constant strain rate loading on the specimen, and the experimental verification demonstrates the feasibility and merits of the bilinear wave in testing brittle materials. Numerical simulations are also performed to see the effect of bar indentation on stress–strain curves, and simulation results show strain concentration at both ends of the specimens resulting in premature failure. A specimen with a dogbone configuration is proposed which can greatly reduce the strain concentration and facilitate the accurate measurement of stress–strain for brittle materials.

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Abbreviations

\(A_\mathrm{s}\) :

Cross-sectional area of the specimen

c :

Wave speed of material or bar

\(c_\mathrm{B}\) :

Wave speed of the bar

e :

Error coefficient

E :

Elastic modulus

\(E_\mathrm{fitted}\) :

Fitted slope of the calculated stress–strain curves

\(E_\mathrm{input}\) :

Input value of the elastic modulus

F :

Reflection coefficient

\(F_\mathrm{BS}\) :

The reflection coefficient of the stress wave from bar to specimen

\(F_\mathrm{SB}\) :

The reflection coefficient of the stress wave from specimen to bar

k :

Times of stress wave reverberating between the specimen/bar interfaces

\(l_\mathrm{s}\) :

Length of the specimen

N :

Mechanical impedance ratio of bar to specimen

R(t):

Stress inequilibrium ratio in the specimen

T :

Transmission coefficient

\(T_\mathrm{BS}\) :

The transmission coefficient of the stress wave from bar to specimen

\(T_\mathrm{SB}\) :

The transmission coefficient of the stress wave from specimen to bar

\(\varepsilon _\mathrm{i}\) :

The incident strain wave

\(\varepsilon _\mathrm{r}\) :

The reflected strain wave

\(\varepsilon _\mathrm{t}\) :

The transmitted strain wave

\(\varepsilon _\mathrm{true}\) :

True strain

\(\varepsilon _\mathrm{engi.}\) :

Engineering strain

\(\dot{\varepsilon }_\mathrm{d}\) :

Desired constant strain rate

\(\alpha \) :

Area ratio of the bar to the specimen

\(\sigma _\mathrm{r}\) :

Reflected stress wave

\(\sigma _\mathrm{i}\) :

Transmitted stress wave

\(\sigma _\mathrm{I/S}\) :

Stress at the interface of incident bar/specimen

\(\sigma _\mathrm{T/S}\) :

Stress at the interface of transmitted bar/specimen

\(\sigma _\mathrm{true}\) :

True stress

\(\sigma _\mathrm{engi.}\) :

Engineering stress

\(\triangle l\) :

Distance if two couples of strain gauges cemented on the bar

\(\tau \) :

Characteristic time of specimen

\(\tau _{\mathrm{s}}\) :

Rise time of stress wave

\(\rho \) :

The mass density of the bar material

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Acknowledgements

I would like to thank the financial support by National Natural Science Foundation of China (#11602202, #11602201 and #11527803). Sincere appreciations are also given to Prof. Luming Shen from the University of Sydney for the helpful discussions, and Mr. Zakir Sheikh for the language modification.

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Authors and Affiliations

  1. Joint International Research Laboratory of Impact Dynamics and its Engineering Applications, School of Aeronautics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Y. G. Miao

  2. Shaanxi Key laboratory of Impact Dynamical and Engineering application, School of Aeronautics, Northwestern Polytechnical University, Xi’an, Shaanxi, 710072, China

    Y. G. Miao

  3. State Key Laboratory for Strength and Vibration of Mechanical Structures, Department of Engineering Mechanics, School of Aerospace Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi, 710049, China

    Y. G. Miao

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Miao, Y.G. On loading ceramic-like materials using split Hopkinson pressure bar. Acta Mech 229, 3437–3452 (2018). https://doi.org/10.1007/s00707-018-2166-7

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  • DOI: https://doi.org/10.1007/s00707-018-2166-7

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