Crack-Tip Fields in a Viscoplastic Material.
Abstract
An integral representation for the particle velocity in terms of a Green's function and certain linear combinations of the inelastic strain rates was used in this study, both for a numerical method to compute full field solutions and to develop unequivocal asymptotic expressions for the near-tip fields. Specific results have been obtained for a stationary crack in 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 to the 1/2 power, and the higher-order terms are of the forms r logr and r. Expressions were derived for the angular variations and for the multiplying time-dependent intensity factors. The r logr term is absent for the Mode-II case. Two questions were addressed in further detail: the dependence of the multiplying terms 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 was compared with a one-term asymptotic representation. The two curves diverge at very small values of time. Inclusion of a second term in the asymptotic expression for the stress gives very acceptable agreement as time increases.
Document Details
- Document Type
- Technical Report
- Publication Date
- Apr 01, 1986
- Accession Number
- ADA168014
Entities
People
- J. C. Sung
- Jan D. Achenbach
- Nobuhiko Nishimura
Organizations
- Northwestern University