Page 285 - Biaxial Multiaxial Fatigue and Fracture

An Analysis of Elasto-Plastic Strains and Stresses in Notched Bodies Subjected to Cyclic _.. 269

oe = 0'8 (multiaxial stress state) (5b)
!!!I !!!I
The Neuber rule (5a) represents the equality of the total strain energy (the strain energy and the
complimentary strain energy density) at the notch tip, represented by the rectangles A and B in
Fig.3.

Fig. 3. Graphical interpretation of the Neuber rule.

The total strain energy density equation written in engineering notation takes the form of
expression (6).

The overall strain energy density equivalence represented by eq.(6) relating the pseudo-elastic
and the actual elastic-plastic notch tip strains and stresses at the notch tip has been generally
accepted as a good approximation rule but the additional conditions, necessary for the complete
formulation of a multiaxial stress state problem, are still the subject of discussion. Hoffman and
Seeger [SI assumed that the ratio of the actual principal strains at the notch tip is to be equal to
the ratio of the fictitious elastic principal strain components while Barkey et al. [6] suggested
using the ratio of principal stresses. The data presented by Moftakhar [7] indicate that the
accuracy of the stress or strain ratio based analysis depends on the degree of constraint at the
notch tip. Therefore, Moftakhar et al. [7] have proposed to use the ratio of the strain energy