Page 400 - Biaxial Multiaxial Fatigue and Fracture

3 84 M. FILIPPINI ET At.

disadvantage of these criteria is that their application is limited to the case of fixed principal
stress or strain directions during the loading cycle. Modified versions of such criteria, so that
application to out-of-phase loadings is made possible, have been also proposed [ 13.
In the so-called critical plane approaches, quantities related to the mechanism of formation
of fatigue cracks under multiaxial loading are inserted explicitly in the formulation of the
criteria: a combination of normal and shear stresses or strains acting on particularly oriented
planes, on which fatigue cracks are likely to nucleate, is chosen as the critical parameter for
assessing the fatigue life of components submitted to multiaxial cyclic loading. Among critical
plane approaches, a distinction between criteria formulated in terms of strain or in terms of
both stress and strain is also possible. Following the proposal of Brown and Miller [23 (r-
plane) and successive contributions [3f, the shear and the normal strain acting on the plane of
maximum alternating shear strain are used. Though these criteria employ exclusively strain-
related quantities, they should be classified in the category of critical plane approaches, rather
than in the strain based criteria (see Socie and Marquis [5]). The proposals of Socie [6], where
combinations of stress and strain acting on critical planes are used to predict fatigue life, have
been applied for predicting fatigue behaviour in the intermediate life region. The critical plane
approach is given a physical justification based on the observations of nucleation and early
growth of fatigue cracks but, in most cases, its adoption is limited by the need of developing
complex multiaxial material models.
The observation of hysteresis loops in low-cycle fatigue testing have suggested many
authors the formulation of criteria based on the relationship between the total or the plastic
energy in a loading cycle and the fatigue life. These criteria are usually grouped under the
name of energy criteria: among many others, the proposals [7,8,9] may be considered.
However, the major obstacle to the application of criteria based on strain energy is either the
necessity of the complete loading histories of all the components of stress and strain tensors or
the availability of a material model able to reproduce the stress-strain loading paths
experienced by the material. More detailed review of multiaxial fatigue criteria can be found in
references [5,10,11,12].
In this paper a new approach based on a space average of the tensor of total strains reducing
the complex loading history to an effective equivalent strain is presented. The proposed
approach, based on an extension of the Sonsino-Grubisic methodology [13], takes into account
the effect of shear strains on crack initiation, expanding the investigation of the interaction of
shear strains on all different interference planes. This new approach makes possible to link the
advantages of a strain based criterion with the possibility of taking into account the different
material behaviour due to out-of-phase loads and the modifying effect of superimposed mean
strains. In general, the advantage of criteria based on total strain is that they may be easily
applied without making use of an elasto-plastic multiaxial model, at least in the case of simple
components or specimens. In the case of complex geometry structures, the strains at the critical
points have still to be calculated by means of finite element method in combination with a
suitable material model. Alternatively, measured strains by means of strain gauges may be
employed in combination with the criterion presented in this paper for predicting the fatigue
life of a component.
Moreover, the possibility of taking into account the effect of a mean strain allows extending
the use of the new criterion to the range of intermediate fatigue life (about lo5 cycles). The
effect of mean strains on the fatigue life may be neglected in the low-cycle fatigue range;
nevertheless it may seriously affect fatigue life in the intermediate life range up to the high-
cycle fatigue regime. This effect is more evident in the case of superalloys and hard metals,
where the mean strains are closely related to the mean stresses, even at shorter lives.