Abstract
The near-tip asymptotic field and full-field solution are obtained for a mode III crack in an elastic material with strain gradient effects. The asymptotic analysis shows that, even though the near-tip field is governed by a single parameter B (similar to the mode III stress intensity factor), the near-tip field is very different from the classical KIII field; stresses have r-3/2 singularity near the crack tip, and are significantly larger than the classical KIII field within a zone of size l to the crack tip, where l is an intrinsic material length, depending on microstructures in the material. This high-order stress singularity, however, does not violate the boundness of strain energy around a crack tip. The parameter B of the near-tip asymptotic field has been determined for two anti-plane shear loadings: the remotely imposed classical KIII field, and the arbitrary shear stress tractions on crack faces. The mode III full-field solution is obtained analytically for an elastic material with strain gradient effects subjected to remotely imposed classical KIII field. It shows that the near-tip asymptotic field dominates within a zone of size 0.5l to the crack tip, while strain gradient effects are clearly observed within 5l. It is also shown that the conventional way to evaluate the crack tip energy release rate would lead to an incorrect, infinite value. A new evaluation gives a finite crack tip energy release rate, and is identical to the J-integral.
Original language | English (US) |
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Pages (from-to) | 325-348 |
Number of pages | 24 |
Journal | International Journal of Fracture |
Volume | 92 |
Issue number | 4 |
DOIs | |
State | Published - 1998 |
Funding
Y.H. and K.C.H. appreciate helpful discussions with Drs. J.W. Hutchinson, C.F. Shih, and W. Yang. Y.H. acknowledges the support from the US National Science Foundation (Grant #INT-94-23964 and #CMS-96-10491). L.Z. and K.C.H. acknowledge the support from China National Natural Science Foundation and China State Commission of Education.
Keywords
- Full-field solution
- Strain gradient effects
ASJC Scopus subject areas
- Computational Mechanics
- Modeling and Simulation
- Mechanics of Materials