Page 450 - Biaxial Multiaxial Fatigue and Fracture

434 Z ITOH AND Z MIYAZQKI

On the other hand, in the tests of Case 3 and 4, dl and dll have the same value but the strain waves
on I and 11-planes have not only the main large strain amplitude but also a small one, since the
strain paths are crossing at angles which are not right angles in the El(t)-C(t) diagram (81.6
degrees in Case 3 and 4). In this case, d1 and drr can be expressed by

Here, in the tests of Case 1, 2 and Case 3,4, taking into account that the relationship between dl
and d11 can be expressed by

(for Case 1, 2)
(12)
(for Case 3.4)

the total damage for cruciform straining can be rewritten as

(for Case 1 - 4) (13)

Box and circular loading. In tests with box (Case 10-12) and circular (Case 14) straining, dl and
dll are given by Eq.( IO) as in the cruciform straining tests. In addition, the relationship between
d1 and dI1 is expressed in Case 10, 12 and 14 by Eq.( 12), so that the total damage is given by
Eq.(13). In these cases, however, the value of the nonproportional intensity factor, f~p, is
approximately doubled in comparison with those of the cruciform straining tests as listed in
Table 2, resulting in the larger total damage.

Step loading. In the step straining tests (Case 6-9), the strain path is basically composed by one
main strain range with large amplitude on the I-plane and several strain ranges with small
amplitudes on the 11-plane. As for example shown in Fig.6, the strain path of Case 7 consists of
the maximum strain amplitude with one cycle on the I-plane, and the medium strain amplitude
with three cycles, and further small strain amplitudes with two cycles on the 11-plane. In this
case, the damages on I and II-planes can be expressed by,