Page 426 - Biaxial Multiaxial Fatigue and Fracture

4 10 K AUBIN. I! QUAEGEBEUR AND S. DEGALLALY

From experimental observations about the cyclic behaviour of an austenitic stainless steel
under non-proportional loading, and particularly about the phenomenon of cross hardening,
Tanaka introduced the notion of a tensor C in the deviatoric space, called "Structural tensor".
-
- = c, [ [ 731 -I" (9)
He linked this tensor to the macroscopic behaviour of the material as well as to observations of
dislocation substructures. This tensor is defined as follows:
c

where p is the plastic strain rate and c, a material parameter.

By using this structural tensor, Tanaka defined a non-proportional parameter A by:

(10)

The author defined a limit surface in the plastic strain space, with a centre and a radius q.
This surface allows to take into account the amplitude effect. 1 and q are expressed by:
I (B'-x)p and q = (IH' -111 (1 1)
ry
Y
=

Table 2. Constitutive equations of model NLK.