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On the near-critical behavior of cavitation in elastic plane membranes

On the near-critical behavior of cavitation in elastic plane membranes Thumbnail


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 d tends to zero, there will be no growth until a load or stretch measure, ? say, reaches a well-defined critical value ? cr at which a cavity appears suddenly. In this paper we study the near-critical asymptotic behavior of cavitation in plane membranes when d is not zero but small, and show that the near-critical behavior is governed by a scaling law in the form ? - ? cr = C ( d / 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 + ? ) / ( 3 + ? ) in each case, where ? 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 ? were increased to within an order ( d / L ) m interval around ? cr .

Acceptance Date Apr 12, 2017
Publication Date Apr 15, 2017
Journal International Journal of Non-Linear Mechanics
Print ISSN 0020-7462
Publisher Elsevier
DOI https://doi.org/10.1016/j.ijnonlinmec.2017.04.012
Keywords Cavitation, Imperfection sensitivity, Void growth, Membrane
Publisher URL http://doi.org/10.1016/j.ijnonlinmec.2017.04.012

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