A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot’s incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J2deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.

Instabilities and near tip crack fields in elastic, incompressible solids / D., Bigoni; Radi, Enrico; D., Capuani. - STAMPA. - 1:(2002), pp. 1-8. ((Intervento presentato al convegno IUTAM Symposium 02/4 on Asymptotics, Singularities and Homogeneization in Problems of Mechanics tenutosi a Liverpool UK nel 8-11 Luglio 2002.

Instabilities and near tip crack fields in elastic, incompressible solids

RADI, Enrico;
2002

Abstract

A closed-form asymptotic solution is provided for velocity fields and the nominal stress rates near the tip of a stationary crack in a homogeneously pre-stressed configuration of a nonlinear elastic, incompressible material. In particular, a biaxial pre-stress is assumed with stress axes parallel and orthogonal to the crack faces. Two boundary conditions are considered on the crack faces, namely a constant pressure or a constant dead loading, both preserving an homogeneous ground state. Starting from this configuration, small superimposed Mode I or Mode II deformations are solved, in the framework of Biot’s incremental theory of elasticity. In this way a definition of an incremental stress intensity factor is introduced, slightly different for pressure or dead loading conditions on crack faces. Specific examples are finally developed for various hyperelastic materials, including the J2deformation theory of plasticity. The presence of pre-stress is shown to strongly influence the angular variation of the asymptotic crack-tip fields, even if the nominal stress rate displays a square root singularity as in the infinitesimal theory. Relationships between the solution with shear band formation at the crack tip and instability of the crack surfaces are given in evidence.
IUTAM Symposium 02/4 on Asymptotics, Singularities and Homogeneization in Problems of Mechanics
Liverpool UK
8-11 Luglio 2002
1
1
8
D., Bigoni; Radi, Enrico; D., Capuani
Instabilities and near tip crack fields in elastic, incompressible solids / D., Bigoni; Radi, Enrico; D., Capuani. - STAMPA. - 1:(2002), pp. 1-8. ((Intervento presentato al convegno IUTAM Symposium 02/4 on Asymptotics, Singularities and Homogeneization in Problems of Mechanics tenutosi a Liverpool UK nel 8-11 Luglio 2002.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11380/466506
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