Geng, YN and Cai, ZX and Fu, YB (2017) On the near-critical behavior of cavitation in elastic plane membranes. International Journal of Non-Linear Mechanics. ISSN 0020-7462

[img] Text
FU_maths_2017.pdf - Accepted Version
Restricted to Repository staff only until 12 April 2018.
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (592kB)

Abstract

Abstract Material cavitation under tensile loading is often studied by assuming the pre-existence of a small void. In this case the void would initially grow but without significant change in its size, and cavitation is said to take place if this slow growth is followed by rapid growth at higher load values. In the limit when the original void radius δ tends to zero, there will be no growth until a load or stretch measure, λ say, reaches a well-defined critical value λ cr at which a cavity appears suddenly. In this paper we study the near-critical asymptotic behavior of cavitation in plane membranes when δ is not zero but small, and show that the near-critical behavior is governed by a scaling law in the form λ − λ cr = C ( δ / L ) m , where L is the undeformed outer radius of the plane membrane, and C and m are non-dimensional constants. The positive power m in general depends on the material model used, but for the three classes of material models considered, it happens to be equal to 2 ( 1 + ν ) / ( 3 + ν ) in each case, where ν is Poisson’s ratio for infinitesimal deformations. If a pre-existing void is viewed as an imperfection, then this scaling law describes the imperfection sensitivity of cavitation: it states that in the presence of imperfections significant void growth would occur when λ were increased to within an order ( δ / L ) m interval around λ cr .

Item Type: Article
Additional Information: This is the accepted author manuscript (AAM). The final published version (version of record) is available online via Elsevier at http://doi.org/10.1016/j.ijnonlinmec.2017.04.012 - please refer to the terms of use of the publisher.
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Maths
Depositing User: Symplectic
Date Deposited: 20 Apr 2017 15:30
Last Modified: 20 Apr 2017 15:31
URI: http://eprints.keele.ac.uk/id/eprint/3290

Actions (login required)

View Item View Item