A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale

Handle URI:
http://hdl.handle.net/10754/597334
Title:
A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale
Authors:
Sendova, T.; Walton, J. R.
Abstract:
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.
Citation:
Sendova T, Walton JR (2010) A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale. Mathematics and Mechanics of Solids 15: 368–413. Available: http://dx.doi.org/10.1177/1081286510362457.
Publisher:
SAGE Publications
Journal:
Mathematics and Mechanics of Solids
KAUST Grant Number:
KUS-C1-016-04
Issue Date:
15-Feb-2010
DOI:
10.1177/1081286510362457
Type:
Article
ISSN:
1081-2865; 1741-3028
Sponsors:
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).
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Publications Acknowledging KAUST Support

Full metadata record

DC FieldValue Language
dc.contributor.authorSendova, T.en
dc.contributor.authorWalton, J. R.en
dc.date.accessioned2016-02-25T12:30:55Zen
dc.date.available2016-02-25T12:30:55Zen
dc.date.issued2010-02-15en
dc.identifier.citationSendova T, Walton JR (2010) A New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscale. Mathematics and Mechanics of Solids 15: 368–413. Available: http://dx.doi.org/10.1177/1081286510362457.en
dc.identifier.issn1081-2865en
dc.identifier.issn1741-3028en
dc.identifier.doi10.1177/1081286510362457en
dc.identifier.urihttp://hdl.handle.net/10754/597334en
dc.description.abstractIn 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.en
dc.description.sponsorshipThe 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).en
dc.publisherSAGE Publicationsen
dc.subjectFractureen
dc.subjectFracture criteriaen
dc.subjectSurface excess propertiesen
dc.titleA New Approach to the Modeling and Analysis of Fracture through Extension of Continuum Mechanics to the Nanoscaleen
dc.typeArticleen
dc.identifier.journalMathematics and Mechanics of Solidsen
dc.contributor.institutionUniversity of Minnesota Twin Cities, Minneapolis, United Statesen
dc.contributor.institutionTexas A and M University, College Station, United Statesen
kaust.grant.numberKUS-C1-016-04en
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