Calculation of Notch Strains Under Multiaxial Nominal Loading
by
Mark Edward Barkey
Department of Theoretical and Applied Mechanics
Abstract
An approximate analytical method is developed to calculate strains at stress concentrators in structures of clastic-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, and accounts for varying degrees of constrained plastic flow at the stress concentrator. Plastic strain increments at the stress concentrator and anisotropic work-hardening effects are then related to this yield surface using standard methods of plasticity.
The method is applied to mildly and sharply notched shafts, and a plate with a central through hole subjected to proportional and nonproportional nominal loading. The results of these calculations are compared with experimental results of a mildly notched shaft subjected to combined tensile and torsional load, and with extensive finite element analyses of all of the structures.
The strain calculations agree well with both qualitatively and quantitatively with the experiments and finite element calculations when using an appropriate uniaxial load-notch plastic strain relationship, and are suitable for strain-life fatigue calculations.
Download (5 MB)