Page 224 - Biaxial Multiaxial Fatigue and Fracture

208 A. VARVANI-FARA HANI

uniaxial loading condition is the well-known Ramberg-Osgood relation
( / *yn*
(ql =ol1/E+ crII K ), which is commonly used to present cyclic uniaxial stress-strain
curve.
The range of maximum shear stress and the corresponding normal stress range are
calculated from the largest stress Mohr’s circle during the first reversal (at the angle 81) and the
second reversal (at the angle 82) of a cycle as:

where csl I. ~22 and 033 are the principal stress values calculated using Eq (3).
Similarly, the range of maximum shear strain and the corresponding normal strain range on the
critical plane at which Mohr’s circles are the largest during the first reversal (at the angIe 81)
and the second reversal (at the angle 82) of a cycle are calculated as:

where E~I, ~22, and ~33 are the principal strain values (&11>~22> ~33) which are calculated using
Eq (4).

Proposed fatigue parameter

In this paper for the convenience of presentation, first the proposed parameter and its capability
to take into account the effects of out-of-phase strain hardening and mean stress are discussed
for the load histories with frequency ratio of -1 [17,23,24] and then the damage model is
extended for other ratios of 0(=2 and a=3.
(2)
obtained from the
The range of maximum shear stress and shear strain A ib~
largest stress and strain Mohr’s circles at angles el and 82 during a cycle and the corresponding
normal stress range Ao,, and the normal strain range A&,, on that plane are the components of
the proposed parameter in the present paper.
Multiaxial fatigue energy-based models have been long discussed in terms of normal and
shear energy weights. In Garud’s approach [8] he found that an empirical weighting factor
equal to C=0.5 in the shear energy part of his model (Eq 10) gave a good correlation of
multiaxial fatigue results for 1% Cr Mo V steel for both in-phase and out-of-phase loading
conditions: