The asymptotic field of a dynamically growing crack in a viscoelastic materia

Abstract

A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field. It was shown that in the stable creep-growing phase, elastic deformation and viscous deformation are equally dominant in the near-tip field, and stress and strain have the same singularity, namely, (σ, ε) ∝ r ^−1/n−1). The asymptotic solution of separating variables of stress, stain and displacement in the crack-tip field was obtained by asymptotic analysis, and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack. Through numerical calculation, it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M. When n → ∞, the asymptotic solution of a viscoelastic material can be degenerated into that of Freund’s elastic-ideally plastic material by analyzing basic equations.

Keywords

viscoelastic material / mode I crack-tip field / dynamic growing

References

[1] Freund L. B. Dynamic fracture mechanics[M]. 1990, Cambridge: Cambridge University Press, 80-96

[2] Riedel H. Cracks loaded in anti-plane shear under creep conditions[J]. Z Metall, 1978, 69(12): 755-760

[3] Hui C. Y., Riedel H. The asymptotic stress and strain field near the tip of a growing crack under creep conditions[J]. International Journal of Fracture, 1981, 17(4): 409-425

[4] Riedel H. Creep crack growth under small-scale creep conditions[J]. International Journal of Fracture, 1990, 42: 173-188

[5] Gao Y. C. Further study on strain singularity behavior of moving cracks in elastic-viscoplastic material[J]. Theoretical and Applied Fracture Mechanics, 1990, 14(3): 233-242

[6] Gao Y. C., Wang Z. Q. Stress and strain field near tip of mode III growing crack in material with creep behavior[J]. Theoretical and Applied Fracture Mechanics, 1996, 25(2): 113-126

[7] Tang L. Q., Cai Y. H., Liu C. H. Mode III dynamic growing crack-tip field of viscoelastic material[J]. J of Harbin Engineering University, 2002, 23(1): 108-112

[8] Tang L. Q., Cai Y. H. Asymptotic field of mode I dynamic growing crack in visco-elastic material[J]. Acta Mechanics Sinica, 2005, 37(5): 573-577

[9] Leighton J. T., Champion C. R., Freund L. B. Asymptotic analysis of steady dynamic crack growing in an elastic-plastic material[J]. Journal of Mechanics and Physics of Solids, 1987, 35(5): 541-563