Abstract
This paper discusses the problem of finding the eigenvalue spectrum in determining the stress and strain fields at the tip of an antiplane-shear crack in a power-law material. It is shown that the perturbation method provides an analytical dependence of the eigenvalue on the material nonlinearity parameter and the eigenvalue of the linear problem. Thus, it is possible to find the entire spectrum of eigenvalues and not only the eigenvalue of the Hutchinson-Rice-Rosengren problem.
Similar content being viewed by others
References
J. W. Hutchinson, “Singular behavior at the end of tensile crack in a hardening material,” J. Mech. Phys. Solids, 16, 13–31 (1968).
J. R. Rice and G. F. Rosengren, “Plane strain deformation near a crack tip in a power-law hardening material,” J. Mech. Phys. Solids, 16, 1–12 (1968).
J. R. Rice, “A path independent integral and the approximate analysis of strain concentration by notches and cracks,” Trans. ASME, Ser E: J. Appl. Mech., 34, 287–298 (1967).
S. Yang, F. G. Yuan, and X. Cai, “Higher order asymptotic elastic-plastic crack-tip fields under antiplane shear,” Eng. Fracture Mech., 54, No. 3, 405–422 (1996).
Y. J. Chao, X. K. Zhu, and L. Zhang, “Higher-order asymptotic crack-tip fields in a power-law creeping material,” Int. J. Solids Struct., 38, No. 21, 3853–3875 (2001).
Y. Chao and S. Yang, “Higher order crack tip field and its application for fracture of solids under mode II conditions,” Eng. Fracture Mech., 54, No. 3, 405–422 (1996).
L. Xia, T. C. Wang, C. F. Shih, “Higher-order analysis of crack tip fields in elastic power-law hardening material,” J. Mech. Phys. Solids, 41, No. 4, 665–687 (1993).
S. Yang, Y. J. Chao, and M. A. Sutton, “Higher order asymptotic crack tip fields in a power-law hardening material,” Eng. Fracture Mech., 45, No. 1, 1–20 (1993).
G. P. Nikishkov, “An algorithm and a computer program for the three-term asymptotic expansion of elastic-plastic crack tip stress and displacement fields,” Eng. Fracture Mech., 50, No. 1, 65–83 (1995).
B. N. Nguyen, P. R. Onck, and E. Van Der Giessen, “On higher-order crack-tip fields in creeping solids,” Trans. ASME, Ser. E: J. Appl. Mech., 67, No. 2, 372–382 (2000).
C. Y. Hui and A. Ruina, “Why K? High order singularities and small scale yielding,” Int. J. Fracture, 72, 97–120 (1995).
L. V. Stepanova and M. E. Fedina, “On the geometry of the completely damaged material region at the antiplane-shear crack tip in the conjugate formulation of the problem (creep-damage coupling),” Vestn. Sam. Gos. Univ., No. 2, 87–113 (2001).
M. Lu and S. B. Lee, “Eigenspectra and order of singularity at a crack tip for a power-law creeping medium,” Int. J. Fracture, 92, 55–70 (1998).
A. H. Nayfeh, Introduction to Perturbation Techniques, Wiley. New York, (1984).
M. Anheuser and D. Gross, “Higher order fields at crack and notch tips in power-law materials under longitudinal shear,” Arch. Appl. Mech., 64, 509–518 (1994).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 173–180, January–February, 2008.
Rights and permissions
About this article
Cite this article
Stepanova, L.V. Eigenvalues of the antiplane-shear crack problem for a power-law material. J Appl Mech Tech Phys 49, 142–147 (2008). https://doi.org/10.1007/s10808-008-0021-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10808-008-0021-7