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| Evaluation of plastic stress singularities of anti-plane V-notches in hardening materials |
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Abstract Abstract: The interpolating matrix method for the determination of higher order stress and displacement fields for antiplane shear loading of power-law hardening materials is presented. First the asymptotic displacement field in terms of radial coordinates at the notch tip is adopted. When the material near the notch tips arises in plastic deformation, the Von Mises yield criterion and the plastic ‘total strain’ theory are used. By introducing the displacement expressions into the governing differential equations of the plastic theory, it results in a set of the eigenvalue problem of nonlinear ordinary differential equations with the stress singularity orders and the associated eigenfunctions. Then the interpolating matrix method is used to solve the eigenvalue problem by an iteration process. The several leading plastic stress singularity orders of antiplane V-notches and cracks have been obtained. Simultaneously the associated eigenvectors of the displacement and stress fields in the notch tip region have been determined with the same degree of accuracy. The validity of the present method is confirmed by comparing with the existed results in the numerical examinations.
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Received: 14 May 2014
Published: 28 February 2014
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2015, Vol. 36 
