Page 283 - Biaxial Multiaxial Fatigue and Fracture
P. 283
An Analysis of Elasto-Plastic Sirains and Shasses in Notched Bodies Subjected to Cyclic ... 267
1
where: 8,; ai - ;
=
/
t s2"
+
J
a,,"
7
Fig. 1. Stress state at a notch tip (notation).
Non-proportional load histories require the application of the theory of incremental plasticity.
The Hooke law and the Prandtl-Reuss flow rule are the most frequently used models. For an
isotropic body, the two models together give the basic incremental stress-strain relationship.
The multiaxial incremental stress-strain relation (3) is obtained from the uniaxial stress-strain
curve by relating the equivalent plastic strain increment to the equivalent stress increment such
that:
The function, f(o,), is identical to the plastic strain - stress relationship obtained
experimentally from an uni-axial cyclic tension-compression test.
