Abstract
This paper presents a study on fracture of materials at microscale (∼ 1 μm) by the strain gradient theory (Fleck and Hutchinson, 1993; Fleck et al., 1994). For remotely imposed classical K fields, the full-field solutions are obtained analytically or numerically for elastic and elastic-plastic materials with strain gradient effects. The analytical elastic full-field solution shows that stresses ahead of a crack tip are significantly higher than their counterparts in the classical K fields. The sizes of dominance zones for mode I and mode II near-tip asymptotic fields are 0.3l and 0.5l, while strain gradient effects are observed within l and 2l to the crack tip, respectively, where l is the intrinsic material length in strain gradient theory and is on the order of microns in strain gradient plasticity (Fleck et al., 1994; Nix and Gao, 1998; Stolken and Evans, 1997). The Dugdale-Barenblatt type plasticity model is obtained to provide an estimation of plastic zone size for mode II fracture in materials with strain grain effects. The finite element method is used to investigate the small-scale-yielding solution for an elastic-power law hardening solid. It is found that the size of the dominance zone for the near-tip asymptotic field is the intrinsic material length l. For mode II fracture under the small-scale-yielding condition, transition from the remote classical KII field to the near-tip asymptotic field in strain gradient plasticity goes through the HRR field only when KII is relatively large such that the plastic zone size is much larger than the intrinsic material length l. For mode I fracture under small-scale-yielding condition, however, transition from the remote classical KI field to the near-tip asymptotic field in strain gradient plasticity does not go through the HRR field, but via a plastic zone.
Original language | English (US) |
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Pages (from-to) | 1-27 |
Number of pages | 27 |
Journal | International Journal of Fracture |
Volume | 100 |
Issue number | 1 |
DOIs | |
State | Published - 1999 |
Funding
Y.H. acknowledges the support from US National Science Foundation (Grant #INT-94-23964 and #CMS-96-10491). T.F.G. and K.C.H. acknowledge the support from China National Natural Science Foundation and China State Commission of Education.
Keywords
- Fracture
- Strain gradient effects
ASJC Scopus subject areas
- Computational Mechanics
- Modeling and Simulation
- Mechanics of Materials