Page 99 - Biaxial Multiaxial Fatigue and Fracture

84 L. SUSMEL AND N. PETRONE

due to the plasticity cannot be disregarded), strain based methodologies are always suggested,
whereas in the high cycle fatigue field, stress based techniques have to be employed to predict the
multiaxial fatigue limit.
Criteria valid for the fatigue liietime calculation can be classified in three different categories:
strain based methods, straidstress based methods and energy based approaches.
Brown and Miller [3] observed that the fatigue life prediction could be performed by
considering the strain components normal and tangential to the crack initiation plane. Moreover,
the multiaxial fatigue damage depends on the crack growth direction: different criteria are required
if the crack grows on the component surface or inside the material. In the first case they proposed
a relationship based on a combined use of a critical plane approach and a modified Manson-Coffin
equation, where the critical plane is the one of maximum shear strain amplitude. Subsequently,
Wang and Brown [4] introduced in the criterion formulation the mean stress normal to the critical
plane in order to account for the mean stress influence.
Socie [5,6] observed that the Brown and Miller’s idea could be successfully employed even by
using the maximum stress normal to the critical plane, because the growth rate mainly depends on
the stress component normal to the fatigue crack. Starting from this assumption, he proposed two
different formulations according to the crack growth mechanism: when the crack propagation is
mainly MODE I dominated, then the critical plane is the one that experiences the maximum
normal stress amplitude and the fatigue lifetime can be calculated by means of the uniaxial
Manson-Coffin curve [5]; on the other hand, when the growth is mainly MODE I1 governed, the
critical plane is that of maximum shear stress amplitude and the fatigue life can be estimated by
using the torsional Manson-Coffin curve [6].
Criteria based on energetic parameters calculation are founded on the assumption that the
energy density is the unique parameter really significant of the fatigue damage. The employment
of this quantity has a crucial advantage over the methodologies discussed above: theoretically, the
amount of energy required for the fatigue failure is independent from the complexity of the stress
state present at the critical point, therefore just a uniaxial fatigue curve is enough to predict fatigue
lives even in the presence of complex loadings.
Garud [7] suggested that the multiaxial fatigue assessment could be performed by using only
the energy due to the plastic deformation. Subsequently, Ellyin [8, 91 stated that not only the
plastic energy but also the positive elastic energy is crucial to estimate properly the fatigue
damage. In particular, fatigue depends on the elastic energy due to the tensile stress components,
because experimental investigations clearly showed that fatigue failures can occur in the high
cycle fatigue field, where the plastic contribution is negligible. Moreover, it is well known that a
positive mean stress component reduces the fatigue life more than a negative one. For these two
reasons an energy based approach can give satisfactory results only when it can account for both
the plastic and the positive elastic contribution.
Recently, Lazzarin and Zambardi [lo] employed successfully a linear-elastic energy method
together with a critical distance approach for the static and fatigue assessment of sharply notched
components under mixed mode loadings.
In the ambit of high cycle fatigue most of the established theories are based on the use of stress
components. The oldest high-cycle fatigue assessment method has been proposed by Gough [ll]
and it is based on an extensive experimental investigation conduced on smooth and notched
specimens of different materials subjected to in-phase bending and torsion loadings. By
reanalysing these results Gough proposed two empirical formulations valid for brittle and ductile
materials.