Page 206 - Biaxial Multiaxial Fatigue and Fracture

190 I: UGODA ET AL.

where k, is a coefficient, we can easily calculate a random history of stresses .c(t), correspond-
ing to history of the nominal shear stresses under torsion q(t) with the gradient of these
stresses.
Similarly as in the case of Eq. (1 8) we can transform a random history of shear strains.
Applying the equation

where k, is a coefficient, we can also easily calculate the random history of strains y(t), corre-
sponding to history of the nominal shear strains under torsion yt(t) with the gradient of these
strains. In order to assume suitable coefficient k, and k, please remember that under torsion and
tension the exponents (inclinations) of the Wohler's curves are often different (see Fig.3).
Moreover, from Fig.3 it appears that the knees of the considered lines occur at different num-
bers of cycles. Thus, for a number of cycles Nt., less than the limit numbers of cycles under
tension-compression No and torsion Not we can determine ratios of the permissible stresses and
strains. For a high number of cycles we can assume the approximate formulas for calculations
constant coefficient k, and kc, like those in the paper by Lowisch [21 J

where

is a number of cycles for which we convert stresses and strains from torsion to tension.
Let us note that in the range of HCF the coefficient kFCF and kFCF change a little. For ex-
ample, in the case of the considered material kFcF = 0.521 for Nf = IO6 cycles and krCF =
0.663 for Nf= 10' cycles.

FATIGUE LIFE CALCULATION BASED ON THE ENERGY PARAMETER
The parameter of the normal strain energy density in the critical plane is verified in this paper.
Fig. 4 shows the algorithm for fatigue life determination using the energy parameter.
At first (stage 1) we register histories of normal stress oxx(t) from tension and shear stress
Txcxy(t) from torsion on the surfaces of tested specimens. Having histories of the stress state
components, we are able to determine (stage 2) the four strain courses