Acta Mechanica Solida Sinica

, Volume 19, Issue 3, pp 241–247

Application of the digital moiré method in fracture analysis of a cracked rubber sheet

• Xiaolei Li
• Yilan Kang
• Wei Qiu
• Xia Xiao
Article

Abstract

This paper deals with the mode I crack problem of a cracked rubber sheet under plane stress condition using the delicate digital moiré technique. Through the four step phase-shifting method of automated fringe analysis, the displacement fields in the Cartesian coordinate system are given. By the coordinate-transform equation, the radial and circular displacement distributions in the polar coordinate system are obtained. The displacement isoline distributions and displacement vector distributions near the crack tip are discussed. The strain isoline distributions near the crack tip are also analyzed in this paper. Finally, the distribution rules for the mechanical fields near the crack tip are discussed with the sector division method.

Key words

digital moiré method rubber-like material large deformation phase-shifting method

References

1. [1]
Wong, F.S. and Shield, R.T., Large plane deformation of thin elastic sheets of neo-Hookean material, Zeitschrift für angewandte Mathematik und Physik, Vol.20, No.2, 1969, 176–199.
2. [2]
Le, K.Ch. and Stumpf, H., The singular elastostatic field due to a crack in rubberlike materials, Journal of Elasticity, Vol.32, 1993, 183–222.
3. [3]
Balankin, A.S., Physics of fracture and mechanics of self-affine cracks, Engineering Fracture Mechanics, Vol.57, No.2-3, 1997, 135–203.
4. [4]
Knowles, J.K. and Sternberg, E., An asymptotic finite-deformation analysis of the elastostatic field near the tip of a crack, Journal of Elasticity, Vol.3, 1973, 67–107.
5. [5]
Knowles, J.K. and Sternberg, E., Finite deformation analysis of the elastostatic field near the tip of a crack-reconsideration and high-order results, Journal of Elasticity, Vol.4, 1974, 201–233.
6. [6]
Gao, Y.C., Elastostatic crack tip behavior for a rubber-like material, Theoretical and Applied Fracture Mechanics, Vol.14, 1990, 219–231.
7. [7]
Gao, Y.C., Large deformation field near a crack tip in rubber-like material, Theoretical and Applied Fracture Mechanics, Vol.26, 1997, 155–162.
8. [8]
Chen, S.H., Zhou, Z. and Gao, Y.C., Theoretical analysis and numerical calculation of large deformation for a wedge tensioned by concentrated force, Acta Mechanica Sinica, Vol.32, No.1, 2000, 117–125 (in Chinese).Google Scholar
9. [9]
Chen, S.H. and Li, Y.F., Large deformation analysis of a rubber wedge contracting with a rigid notch, Acta Mechanica Sinica, Vol.32, No.4, 2000, 412–419 (in Chinese).
10. [10]
Gao Y.C. and Zhou, L.M., Interface crack tip in a kind of rubber materials, International Journal of Solids and Structures, Vol.38, 2001, 6227–6240.
11. [11]
Gao, Y.C. and Zhou, L.M., Crack tip behavior of bio-materials, Theoretical and Applied Fracture Mechanics, Vol.35, 2001, 219–228.
12. [12]
Li, L., Analysis of an incompressible rubber edge contacting with a rigid notch, Acta Mechanica Solida Sinica, Vol.17, No.3, 2004, 196–201.Google Scholar
13. [13]
Kang, Y.L., Wang, S.B., Wang, Y.G. and Lu, H., Experimental analysis for singularities in crack normal to bimaterial interface, Acta Mechanica Solida Sinica, Vol.11, No.2, 1998, 180–186.Google Scholar
14. [14]
Qiu, W., Kang, Y.L., Sun, Q.C., and Qin, Q.H., et al., Stress analysis and geometrical configuration selection for multilayer piezoelectric displacement actuator, Acta Mechanica Solida Sinica, Vol.17, No.4, 2004, 323–329.Google Scholar
15. [15]
Xia, Y., Li, W. and Xia, Y.M., Test and characterization for the incompressible hyperelastic properties of conditional rubbers under moderate finite deformation, Acta Mechanica Solida Sinica, Vol.17, No.4, 2004, 307–314.Google Scholar
16. [16]
Asundi, A. and Yung, K.H., Logical moiré and applications, Exp. Mec., Vol.31, No.3, 1991, 236–242.
17. [17]
Zhang, H.B. and Wu, X.P., The 3-D shape measurement with phase-shift and logical moiré method, Acta Optica Sinica, Vol.14, No.4, 1994, 408–411 (in Chinese).Google Scholar
18. [18]
Zhang, H.B. and Wu, X.P., The displacement and strain field measurement by phase shifting and logical moiré, Acta Mechanica Solida Sinica, Vol.15, No.2, 1994, 121–127 (in Chinese).Google Scholar
19. [19]
Zhang, H.B., Wu, X.P., and Asundi, A., Two dimensional phase shift and logical moiré—A fast and automatic method for whole field fringe pattern analysis, Journal of Experimental Mechanics, Vol.9, No.3, 1994, 181–191 (in Chinese).Google Scholar
20. [20]
Xie, H.M., Zhao, B. and Dai, F.L., et al., Experimental study on nanometer moiré method, Optical Technique, Vol.26, No.3, 2000, 193–195 (in Chinese).Google Scholar
21. [21]
Xie, H.M., Liu, Z.W. and Fang, D.N., et al., A study on the digital nana moiré method and its phase shifting technique, Measurement Science and Technology, Vol.15, No.9, 2004, 1716–1721.