TY - JOUR

T1 - Nonsymmetric cavity formation at a circular inclusion under remote equibiaxial load

AU - Levy, Alan J.

N1 - Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1995/7

Y1 - 1995/7

N2 - This paper examines the phenomenon of cavity formation through an analysis of the problem of a plane circular elastic inclusion embedded in an unbounded elastic matrix subject to a remote equibiaxial load. Consistent with infinitesimal strain kinematics, nonlinear behavior is confined to a cohesive zone so that inclusion-matrix interaction is characterized by a nonlinear interface force-interface separation law requiring a characteristic length for its prescription. Equilibrium solutions for both rotationally symmetric and nonsymmetric cavity shapes are sought based on an integral equation formulation together with known elasticity solutions for circular domains. For values of remote load, interface strength and elastic moduli within certain bounds only rotationally symmetric cavities occur under decreasing characteristic length-inclusion radius ratio. At other parameter values the existence of nonsymmetric cavities is studied by performing a linearized bifurcation analysis about the rotationally symmetric equilibrium state. A post bifurcation analysis is carried out by reducing the governing integral equations to a truncated set of nonlinear algebraic equations and analysing those. Stability of equilibrium states is assessed with the Hadamard stability definition. Calculations for the interfacial tractions are carried out as well. The study reveals that rotationally symmetric cavities must give way to the abrupt formation of stable nonsymmetric cavities when the interface force attains its maximum value. Thus, the phenomenon of ductile decohesion, or the gradual opening of a cavity coincident with an unloading of the interface, cannot occur (for the system being studied) without artificially constraining the inclusion against rigid displacement.

AB - This paper examines the phenomenon of cavity formation through an analysis of the problem of a plane circular elastic inclusion embedded in an unbounded elastic matrix subject to a remote equibiaxial load. Consistent with infinitesimal strain kinematics, nonlinear behavior is confined to a cohesive zone so that inclusion-matrix interaction is characterized by a nonlinear interface force-interface separation law requiring a characteristic length for its prescription. Equilibrium solutions for both rotationally symmetric and nonsymmetric cavity shapes are sought based on an integral equation formulation together with known elasticity solutions for circular domains. For values of remote load, interface strength and elastic moduli within certain bounds only rotationally symmetric cavities occur under decreasing characteristic length-inclusion radius ratio. At other parameter values the existence of nonsymmetric cavities is studied by performing a linearized bifurcation analysis about the rotationally symmetric equilibrium state. A post bifurcation analysis is carried out by reducing the governing integral equations to a truncated set of nonlinear algebraic equations and analysing those. Stability of equilibrium states is assessed with the Hadamard stability definition. Calculations for the interfacial tractions are carried out as well. The study reveals that rotationally symmetric cavities must give way to the abrupt formation of stable nonsymmetric cavities when the interface force attains its maximum value. Thus, the phenomenon of ductile decohesion, or the gradual opening of a cavity coincident with an unloading of the interface, cannot occur (for the system being studied) without artificially constraining the inclusion against rigid displacement.

UR - http://www.scopus.com/inward/record.url?scp=0029341978&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029341978&partnerID=8YFLogxK

U2 - 10.1016/0022-5096(95)00021-A

DO - 10.1016/0022-5096(95)00021-A

M3 - Article

AN - SCOPUS:0029341978

VL - 43

SP - 1003

EP - 1024

JO - Journal of the Mechanics and Physics of Solids

JF - Journal of the Mechanics and Physics of Solids

SN - 0022-5096

IS - 7

ER -