Crack-tip fields in a viscoplastic material

J. D. Achenbach*, N. Nishimura, J. C. Sung

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


An integral representation for the particle velocity in terms of a Green's function and certain linear combinations of the inelastic strain rates has been used in this paper, both for a numerical method to compute full field solutions and to develop unequivocal asymptotic expressions for the fields near a stationary crack tip. Specific results have been obtained for a solid whose constitutive behavior is represented by the Bodner-Partom model. It is shown that the leading term of the near-tip particle velocity is of order r 1 4, and the higher-order terms are of the forms r log r and r. Expressions have been derived for the angular variations and for the multiplying timedependent intensity factors. The r log r term is absent for the Mode III case. Two questions have been addressed in further detail: the dependence of the intensity factors on time and the importance of the higher-order terms. The numerical results show a stress intensity factor which decays with time. At a small distance from the crack tip the numerically computed normalized opening stress τ22(x1,0,1)/τ22(X1,0 ,0) has been compared with a one-term asymptotic representation, i.e. with K1(t)/K1(0). The two curves diverge at very small values of time. The inclusion of a second term in the asymptotic expression for the stress gives very good agreement over a larger time range.

Original languageEnglish (US)
Pages (from-to)1035-1052
Number of pages18
JournalInternational Journal of Solids and Structures
Issue number7
StatePublished - 1987

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering
  • Applied Mathematics


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