Deviatoric Neuber method for stress and strain analysis at notches under multiaxial loadings

Fatigue life prediction of notched components requires accurate local stresses and strains at notch areas. Researchers have developed a number of approximation methods to estimate local elasto-plastic stress and strain responses on the basis of elastic stress/strain results. The most two common methods are known as the Neuber rule and the equivalent strain energy density (ESED) method. It has been presented that the Neuber rule has a tendency to overestimate notch elasto-plastic strains and stresses while the ESED method tends to underestimate notch elasto-plastic strains and stresses. These drawbacks are attributed to the fact that the original Neuber rule was developed for notched bodies under pure shear loading, but the Neuber rule is applied to other multiaxial loadings where the present stress state can significantly vary from the pure shear stress state. Therefore, analytical approximation model based on the deviatoric form of the Neuber rule has been proposed to estimate elasto-plastic stresses and strains at notches. Predicted notch root stresses and strains from the proposed model are compared with non-linear Finite Element Analysis (FEA) results for SAE 1045 and SAE 1070 steel notched-bars. The SAE 1045 and SAE 1070 steel notch-bars are subjected to monotonic and cyclic non-proportional loadings respectively. The model shows very good agreements with the FEA data for both steel materials.