Page 297 - Biaxial Multiaxial Fatigue and Fracture

An Analysis of Elasto-Plastic Strains and Stresses in Notched Bodies Subjected to Cyclic ... 281

Load Path #2

120 1

80

p" 40
E
ln
$ 0
ln
L
m
5 -40

-80

-120 J
Shear strain
Fig. 12b. Evolution of the elastic-plastic shear strain and shear stress at the notch tip induced by
the Stress Path #1

Just above the onset of yielding at the notch tip, the strains predicted using the proposed model
and the finite element data gradually deviate form the linear elastic behavior. Both sets of results
reveal some ratcheting of the axial strain (Fig. 1 la); however it appears that the proposed model
stabilizes quicker than the FEM data based on the ABAQUS software package plasticity model.
The data obtained for the Stress Path #2 are shown in Figs. 12a and 12b. The proposed model
overestimates the notch tip strains in comparison with the FEM data similarly to the classical
uniaxial Neuber rule. However, this overestimation is not significant and it could be acceptable
in many practical applications.

CONCLUSIONS

A method for calculating elastic-plastic strains and stresses near notches induced by multiaxial
loading paths has been proposed. The method has been formulated using the equivalence of the
total distortional strain energy density. The generalized equations of the total equivalent strain
energy density yielded a conservative solution for the notch tip strains and stresses in the case of
cyclic non-proportional loading paths. The method has been verified by comparison with finite
element data obtained for identical notched components subjected to non-proportional loading
paths.
The notch tip strains and stresses calculated for cyclic load paths can be used for the estimation
of fatigue lives for multiaxial cyclic loading histories. The calculated from equation (12) and the
2
FEM determined axial and shear strain components, ~ 2 and ~E23a, and the axial and shear stress
components, (~22~and (~23~, respectively are shown in Figures 11 and 12.