Page 102 - Biaxial Multiaxial Fatigue and Fracture

Multiaxial Fatigue Life Estimations for 6082-T6 Cylindrical Specimens Under ._.

where in Eq. 1 the maximum value of normal stress is able to include the influence of mean stress
on the fatigue strength, according to the Socie’s fatigue damage model [6].
Consider now a log-log Wohler diagram where in the abscissa there are the number of cycles to
failure Nf and in the ordinate the shear stress amplitude ta(+*, e*) calculated on the initiation plane
(Figure 2).
It can be demonstrated [21] that different fatigue curves are generated in the modified Wohler
diagram by changing the p values. Each single curve is identified by the inverse slope k,(p) and
by the reference shear stress amplitude %&Ref (p) corresponding to NRef cycles (usually 2.106 cycles
in several design codes). Moreover, experimental results showed [21, 221 that as the p ratio
increases the fatigue curve moves downwards in the modified Wohler diagram (Figure 2).
On the basis of this observation and by evaluating the functions t&Ref(p) and k, (p) by a best fit
procedure performed using experimental data, it is possible to predict the fatigue life for a
multiaxial cyclic stress state by applying the following expression:

By reanalysing systematically experimental data taken from the literature [21, 221, it has been
observed that a good correlation with experimental results can be obtained just by expressing
qRef (p) and k,(p) as linear functions and by using uniaxial and torsional fatigue data for their
calibration. In particular, under this assumption ThRef(p) and kr (p) can be expressed as follows:

The presented method can also be used to estimate the fatigue life of notched components by
applying the correction based on the fatigue notch factor Kf to the fatigue curves used in the model
calibration, and by performing the assessment in terms of nominal stresses [21,22].
Given that the multiaxial fatigue behaviour can be described by a single modified Wohler curve
as the p value changes, it can be highlighted that a multiaxial notch factor can be always defined
as function of the p ratio. By applying this idea, it has been demonstrated that the multiaxial &
factor is always a linear function of the stress ratio p [22].
Finally, it is interesting to mention the fact that this method can be reinterpreted even in terms
of critical distance approach [31]. In particular, by using as critical distance a length depending on
the El’Haddad short crack constant [32], it has been shown that this method is capable of
predictions within an error of about 15%, when employed to estimate the fatigue limit of
V-notched specimens of low carbon steel subjected to in-phase MODE I and MODE I1 loads [31].