Page 284 - Biaxial Multiaxial Fatigue and Fracture

268 A. BLiCZYNSKf AND G. GLINKA

THE NOTCH TIP STRESS-STRAM RELATIONS

The load or any other parameter representing the load is usually given in the form of the nominal
or reference stress being proportional to the remote applied load and the stress concentration
factor ICt. However, the use of the stress concentration factor, K,, is not sufficient in the case of
multiaxial stress states near the notch tip because it supplies information about only one stress
component. Therefore the fictitious “linear elastic” stresses which would exist near the notch tip
in the absence of plasticity are used in the method discussed below. In the case of notched bodies
in plane stress or plane strain state the relationship between the load and the elastic-plastic notch
tip strains and stresses in the localized plastic zone is often approximated by the Neuber rule [l]
or the Equivalent Strain Energy Density (ESED) equation [2]. It was shown later [3,4] that both
methods can be extended for multiaxial proportional and non-proportional modes of loading.
Similar methods were also proposed by Hoffman and Seeger [ 51 and Barkey et al. [6 1. All
methods consist of two parts namely the constitutive equations and the relationships linking the
fictitious linear elastic stress-strain state (oi;,~ij? at the notch tip with the actual elastic-plastic
stress-strain response (G{,Ei;), as shown in Fig. 2.

Ee

Fig. 2. Stress states in geometrically identical elastic and elastic-plastic bodies subjected to
identical boundary conditions.

The Neuber rule [2,3] for proportional loading, where the Hencky stress-strain relationships are
applicable, can be written for the uni-axial and multiaxial stress state in the form of equation (sa)
and (5b) respectively.

t&&i2 = a;&? (uniaxial stress state) (54