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Applications of Digital Image Correlation (DIC) and the Strain Gage Method for Measuring Dynamic Mode I Fracture Parameters of the White Marble Specimen

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Abstract

Digital image correlation (DIC) and the strain gage method are both widely used in characterizing the fracture mechanisms of materials. However, the quantitative comparisons of rock fracture parameters between the two methods have been studied insufficiently. In this paper, dynamic three-point bending impact tests were performed on white marble specimens using DIC and the strain gage method simultaneously. The complete cracking process was recorded by two high-speed cameras situated on either side of the specimen. The crack propagation velocities were obtained and the dynamic stress intensity factors (DSIFs) were calculated by both methods for analysis and comparison. The experimental results show that the crack propagation velocities almost remain constant during the cracking process, and the evolutions of strain values recorded by gages are consistent with the modified strain variations obtained theoretically. DSIFs calculated by DIC show good agreement with the results obtained from strain gages #1 to #4, while the size effect and the multiple stress waves interfere with the strain signals sensed in strain gage #5, causing a relatively larger deviation in the DSIF. In addition, the complete fracture process (including the variations in successive displacement and strain fields) can be obtained by the DIC method, while a rough changing trend in the DSIF can be given by the strain gage method with a limited number of strain gages.

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Abbreviations

\(\left( {x,y} \right)\) :

Coordinate of the testing strain gage

\(\mu\) :

Shear modulus

\(\varepsilon_{\text{g}}\) :

Strain values recorded by gages

\(\varepsilon_{\text{max} }\) :

Maximum value of modified strain curve

\(A_{0} ,A_{1} ,B_{0}\) :

Constant parameters in three-parameter model

\(c\) :

Crack propagation velocity

\(\bar{c}\) :

Average crack propagation velocity

\(c_{1} ,c_{2}\) :

Longitudinal and shear wave velocities, respectively

\(\nu\) :

Poisson’s ratio

\(\alpha\) :

Orientation of strain gage

\(E_{\text{d}}\) :

Dynamic Young’s modulus

\(\rho\) :

Density of the specimen

\(y_{\text{g}}\) :

Perpendicular distance between gage and cracking path

\(u,v\) :

Displacement components

\(\Delta x,\Delta y\) :

Distances between point O and point P

\(\frac{\partial u}{\partial x},\frac{\partial u}{\partial y},\frac{\partial v}{\partial x},\frac{\partial v}{\partial y}\) :

Gradients of displacement components

\(f\left( {x,y} \right),g\left( {x,y} \right)\) :

Gray-level values for reference and deformed image

\(\bar{f},\bar{g}\) :

Average gray-level value of subimage

\(T_{x} ,T_{y} ,R\) :

Rigid-body translation and rotation

\(K_{\text{I}}^{\text{d}}\) :

Dynamic mode I stress intensity factor

DIC:

Digital image correlation

DSIF:

Dynamic stress intensity factor

PMMA:

Polymethyl methacrylate

NSCB:

Notched semicircular bend

ROI:

Region of interest

AESP:

Acoustic emission signal parameter

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Acknowledgements

This research was supported by the National Key Research and Development Program (2016YFC060090X). The authors gratefully acknowledge the editorial staff of RMRE and the reviewers.

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Authors and Affiliations

  1. Department of Mechanics and Civil Engineering, China University of Mining and Technology, Beijing, 100083, China

    Zhongwen Yue, Yao Song, Penghui Li, Shiying Tian, Xiaodan Ming & Zhiyuan Chen

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  1. Zhongwen Yue
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  2. Yao Song
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  3. Penghui Li
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Correspondence to Yao Song.

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Yue, Z., Song, Y., Li, P. et al. Applications of Digital Image Correlation (DIC) and the Strain Gage Method for Measuring Dynamic Mode I Fracture Parameters of the White Marble Specimen. Rock Mech Rock Eng 52, 4203–4216 (2019). https://doi.org/10.1007/s00603-019-01830-8

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