In this paper we focus on the analysis of the partial differential equations arising from a new approach to modeling brittle fracture based on an extension of continuum mechanics to the nanoscale. It is shown that ascribing constant surface tension to the fracture surfaces and using the appropriate crack surface boundary condition given by the jump momentum balance leads to a sharp crack opening profile at the crack tip but predicts logarithmically singular crack tip stress. However, a modified model, where the surface excess property is responsive to the curvature of the fracture surfaces, yields bounded stresses and a cusp-like opening profile at the crack tip. Further, two possible fracture criteria in the context of the new theory are discussed. The first is an energy-based crack growth condition, while the second employs the finite crack tip stress the model predicts. The classical notion of energy release rate is based upon the singular solution, whereas for the modeling approach adopted here, a notion analogous to the energy release rate arises through a different mechanism associated with the rate of working of the surface excess properties at the crack tip. © The Author(s), 2010.
|Original language||English (US)|
|Number of pages||46|
|Journal||Mathematics and Mechanics of Solids|
|State||Published - Feb 15 2010|
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-C1-016-04
Acknowledgements: The authors would like to thank Dr John Slattery and Dr Kaibin Fu for the numerous fruitful discussions. This work was supported in part by the Air Force Office of Scientific Research through Grant FA9550-06-0242 and in part by award number KUS-C1-016-04 made by King Abdullah University of Science and Technology (KAUST).
This publication acknowledges KAUST support, but has no KAUST affiliated authors.