Improved bounds for the yield stress of a model polycrystalline material

• Published in: Journal of the mechanics and physics of solids 2000-09, Vol.48 (9), p.1799-1825
• Main Authors: Nesi, V., Smyshlyaev, V.P., Willis, J.R.
• Format: Article
• Language: English
• Subjects: B. Constitutive behaviour; B. Ideally plastic material; B. Polycrystalline material; C. Variational calculus; Cross-disciplinary physics: materials science; rheology; Elasticity and anelasticity; Elasticity and anelasticity, stress-strain relations; Exact sciences and technology; Homogenization; Materials science; Physics; Treatment of materials and its effects on microstructure and properties
• ISSN: 0022-5096
• DOI: 10.1016/S0022-5096(99)00100-3

Anti-plane deformation of a model two-dimensional polycrystal composed of rigid-perfectly plastic grains is considered. Each grain has two orthogonal slip planes, with different Schmid stresses M 1 and M 2. New upper bounds for the overall, or effective, yield stress are derived, in the case that the microgeometry of the polycrystal is isotropic. One is obtained by application of the translation method, and this is further refined by use of a method that combines the Talbot–Willis variational approach with the translation method. The new bounds always improve on the Taylor–Bishop–Hill bound and also improve on a bound recently established by R.V. Kohn and T.D. Little for a range of values of M 1/ M 2. The “refined” bound also improves on the bound obtained by direct use of the Talbot–Willis machinery, but it was obtained only after a relatively difficult computation.