An analytical method is developed to estimate notch root strains in a notched bar of elastic-plastic, isotropic material subjected to proportional and nonproportional multiaxial nominal loading. The method uses anisotropic plasticity theory to define a structural yield surface in nominal stress space that incorporates both the isotropic material properties and the anisotropic geometry factors of the notch. Notch root plastic strain increments and anisotropic work-hardening effects are then related to this yield surface using standard methods of plasticity. Comparisons of the proposed method with previously published strain estimates using the finite element method for a notched shaft under proportional nominal bending and torsion, and with strain gage measurements of a circumferentially notched solid steel shaft subjected to a series of box-shaped nonproportional loading paths in tension-torsion nominal stress space are presented. The strain calculations agree well both qualitatively and quantitatively using an appropriate nominal load-notch plastic strain relationship, and are suitable for strain-life fatigue calculations.

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