Near-tip field for steady dynamic crack growth in a compressible elastic-plastic material

Zhang, L.; Zhu, Xiaomeng; Hwang, Keh Chih

doi:10.1016/s0022-5096(96)00100-7

Cited by 4 publications

(7 citation statements)

References 12 publications

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“…1, the hardening material approaches the elastic-perfectly plastic material. It is anticipated that the present solutions can reduce to those proposed by Zhang et al (1997). In fact, when n goes infinity, the Mises equivalent stress r eq approaches the yield stress r 0 in plastic regions.…”

Section: Approximate Behavior Of the Present Solutions As N !mentioning

confidence: 71%

“…However, Leighton et al (1987) demonstrated that the principle of the maximum plastic work prohibits the existence of any dynamic discontinuities in stress, strain, and velocity fields for an incompressible elastic-perfectly plastic material, and successfully constructed a unique asymptotic crack-tip field with fully continuous and bounded stresses, strains, and particle velocities for the material. Similarly using the maximum plastic work principle, Drugan and Shen (1987), Zhu (1995), and Zhang et al (1997) confirmed that dynamic strong discontinuities are not allowed for any field quantities at the dynamic crack tip for non-hardening and hardening materials. Accordingly, Zhang et al (1997) extended the continuous solutions of Leighton et al (1987) to the compressible elastic-perfectly plastic material, and obtained an asymptotic crack-tip field with continuous and bounded stresses and strains.…”

Section: Introductionmentioning

confidence: 83%

“…Similarly using the maximum plastic work principle, Drugan and Shen (1987), Zhu (1995), and Zhang et al (1997) confirmed that dynamic strong discontinuities are not allowed for any field quantities at the dynamic crack tip for non-hardening and hardening materials. Accordingly, Zhang et al (1997) extended the continuous solutions of Leighton et al (1987) to the compressible elastic-perfectly plastic material, and obtained an asymptotic crack-tip field with continuous and bounded stresses and strains. Zhu and Hwang (2002) further extended these continuous solutions to the incompressible power-law hardening materials after a detailed review of the asymptotic solutions for elastic-plastic dynamic crack growth.…”

Section: Introductionmentioning

confidence: 83%

“…0 in (19) and the asymptotic governing (33) and (16) in the second sector can reduce to Eqs. (3.15) and (3.5) given by Zhang et al (1997) for the compressible elastic-perfectly plastic materials. Moreover, the solutions (21) and (32) in the first and third sectors reduce to the corresponding ones given by Zhang et al (1997).…”

Section: Approximate Behavior Of the Present Solutions As N !mentioning

confidence: 99%

“…(3.15) and (3.5) given by Zhang et al (1997) for the compressible elastic-perfectly plastic materials. Moreover, the solutions (21) and (32) in the first and third sectors reduce to the corresponding ones given by Zhang et al (1997). Therefore, the present solutions for the compressive hardening materials can reduce to those developed by Zhang et al (1997) for the compressive elastic-perfectly plastic materials in the limit of n !…”

Section: Approximate Behavior Of the Present Solutions As N !mentioning

confidence: 99%

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Asymptotic crack-tip fields for dynamic crack growth in compressive power-law hardening materials

Zhu

Hwang

2008

International Journal of Solids and Structures

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The effect of material compressibility on the stress and strain fields for a mode-I crack propagating steadily in a powerlaw hardening material is investigated under plane strain conditions. The plastic deformation of materials is characterized by the J 2 flow theory within the framework of isotropic hardening and infinitesimal displacement gradient. The asymptotic solutions developed by the present authors [Zhu, X.K., Hwang K.C., 2002. Dynamic crack-tip field for tensile cracks propagating in power-law hardening materials. International Journal of Fracture 115, 323-342] for incompressible hardening materials are extended in this work to the compressible hardening materials. The results show that all stresses, strains, and particle velocities in the asymptotic fields are fully continuous and bounded without elastic unloading near the dynamic crack tip. The stress field contains two free parameters r eq0 and s 330 that cannot be determined in the asymptotic analysis, and can be determined from the full-field solutions. For the given values of r eq0 and s 330 , all field quantities around the crack tip are determined through numerical integration, and then the effects of the hardening exponent n, the Poisson ratio m, and the crack growth speed M on the asymptotic fields are studied. The approximate behaviors of the proposed solutions are discussed in the limit of m ! 0.5 or n ! 1.

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Section: Approximate Behavior Of the Present Solutions As N !mentioning

confidence: 71%