Page 422 - Biaxial Multiaxial Fatigue and Fracture

406 c! AUBIN, R QUXEGEBEUR AND S. DEGAUALY

700
650
600
550
500
-Monotonic tension
450
+ Tensioncompression
400
350 + Torsion
300 0 Proportiona145°

0 0.002 0.004 0.006 0.008

Fig. 5. Cyclic stress-strain responses at the stabilized or quasi-stabilized cycles for proportional
loading paths.

Cyclic hardening-softening behaviour under non-proportional loading
A series of tests using four non-proportional loading paths were performed (see Fig, 3). An
y')
example of the response obtained in the different planes, (CJ, & 7) , (E', y'/&), ' (7, ,
(a,&'), is given in Fig. 6 for the hourglass path. At each cycle, the radii and the centre
positions of the smallest circles circumscribed around the responses in the plane (c, & 7) and
( 4
in the plane E', y' & are calculated. These radii are called equivalent stress amplitude and

equivalent plastic strain amplitude respectively.
Cyclic hardening-softening curves at a strain amplitude of 0.5 % for the seven loading paths
tested, proportional and non-proportional, are given in Fig. 7. Whatever the loading path, the
cycling leads to quasi-stabilization after a phase of hardening followed by a low softening.
Figure 8 shows the cyclic stress-strain responses in terms of equivalent stress amplitude versus
equivalent plastic strain amplitude at the stabilized cycles. At a same strain amplitude, for non-
proportional loading paths, the duplex stainless steel hardens much more than for proportional
paths. This cyclic hardening, called extra-hardening, depends on the strain amplitude and on
the loading path. For a circle path, at the strain amplitude 0.2 %, there is no extra-hardening,
because the plastic strain is about zero. On the contrary, at the strain amplitude 0.5 %, the
stabilized stress is 20 % higher (or 120 MPa higher) than the one for the proportional path. In
comparison, on an austenitic stainless steel type AIS1 316L at the same strain amplitude, the
circle path induces an extra-hardening of 70 % (or 225 MPa) [lo-141. The hardening effect due
to loading path, in absolute and in relative values, is lower for duplex stainless steel than for
austenitic stainless steel. For the duplex stainless steel, three groups can be defined among the
tested loading paths according to the increasing degree of hardening: (i) tension-compression,
torsion and proportional 45' paths; (ii) clover path, (iii) circle, square and hourglass paths.