Abstract
An elastic-viscoplastic mechanics model is used to investigate asymptotically the mode III dynamically propagating crack tip field in elastic-viscoplastic materials. The stress and strain fields at the crack tip possess the same power-law singularity under a linear-hardening condition. The singularity exponent is uniquely determined by the viscosity coefficient of the material. Numerical results indicate that the motion parameter of the crack propagating speed has little effect on the zone structure at the crack tip. The hardening coefficient dominates the structure of the crack-tip field. However, the secondary plastic zone has little influence on the field. The viscosity of the material dominates the strength of stress and strain fields at the crack tip while it does have certain influence on the crack-tip field structure. The dynamic crack-tip field degenerates into the relevant quasi-static solution when the crack moving speed is zero. The corresponding perfectly-plastic solution is recovered from the linear-hardening solution when the hardening coefficient becomes zero.
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References
Östlund S. On numerical modeling and fracture criteria of dynamic elastic-viscoplastic crack growth[J]. International Journal of Fracture, 1990, 44(4):283–299.
Sung J C, Achenbach J D. Heating at a propagating crack tip in a viscoplastic material[J]. International. Journal of Fracture, 1990, 44(4):301–309.
Yang Tingqing. The constitutive theories of elastic-visco-plasticity and their applications[J]. Advances. in Mechanics, 1992, 22(1):10–29 (in Chinese).
Gao Y C. Uniparameter plastic field near a dynamic crack-tip[J]. Mechanics Research Communications, 1988, 15(5):307–313.
Jia Bin, Wang Zhenqing, Li Yongdong. The elastic-viscoplastic field at mode I steadily propagating crack-tip[J]. Chinese Journal of Theoretical and Applied Mechanics, 2005, 37(4):421–427 (in Chinese).
Jia Bin, Wang Zhenqing, Li Yongdong, Liang Wenyan. A visocoplastic solution to the field at steadily propagating crack tip in linear-hardening materials[J]. Applied Mathematics and Mechanics (English Edition), 2006, 27(4):527–533. DOI:10.1007/s10483-006-0413-1
Fineberg J, Gross S P, Marder M et al. Instability in the propagation of fast crack[J]. Physics. Review B, 1992, 45(12):5146–5154.
Jia Bin, Li Yongdong, Wang Zhenqing. Structure analysis of mode III quasi-static propagating crack tip field in creeping materials[J]. Journal of Harbin Institute of Technology, 2007, 39(3):412–415 (in Chinese).
Jia Bin, Tang Jing, Wang Zhenqing. Viscoelastic-perfectly-plastic field at the tip of mode III steadily propagating crack[J]. J Harbin Institute of Technology, 2004, 36(6):718–721 (in Chinese).
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Jia, B., Wang, Zq. & Li, Yd. Field structure at mode III dynamically propagating crack tip in elastic-viscoplastic materials. Appl. Math. Mech.-Engl. Ed. 29, 919–925 (2008). https://doi.org/10.1007/s10483-008-0710-x
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DOI: https://doi.org/10.1007/s10483-008-0710-x
Key words
- elastic-viscoplastic materials
- dynamically propagating crack
- mode III crack
- crack tip field
- zone structure