Page 100 - Biaxial Multiaxial Fatigue and Fracture

Multiaxial Fatigue Life Estimations for 6082-T6 Cylindrical Specimens Under ... 85

Several criteria were subsequently proposed by other researchers adopting the critical plane
approach. Among the most employed in the case of out-of-phase loadings, it is worth mentioning
the criteria proposed by Findley [12], by Matake [13] and by McDiarmid [14]. The first method
considers as critical plane the one where a linear combination of the shear and the normal stresses
reaches its maximum value. The other two are based on the assumption that the critical plane is the
one experiencing the maximum shear stress amplitude and the fatigue damage depends even on the
stress normal to this plane. These criteria allow the evaluation in a component of “non-failure”
conditions, but they are not suitable for the fatigue lifetime calculation.
By starting from a mesoscopic approach, Dang Van [15] proposed an original criterion
completely different if compared to the methodologies above discussed. In particular, the simplest
version of this method is formalised as a linear combination of the shear and the hydrostatic
stresses. This criterion postulates that the fatigue failure is avoided if, in each instant of the load
history, the critical stress parameter is lower than a reference value depending on two fatigue
limits experimentally determined in simple loading conditions (typically, the use of the uniaxial
and the torsional fatigue limits is suggested).
Papadopoulos [16] as well formulated a criterion founded on the mesoscopic approach
fundamentals. By using rigorous mathematical procedures applied to the elastic shakedown state
concept, he introduced two different formulations valid for brittle and ductile materials, which
gave satisfactory results in the fatigue limit estimation of plane components subjected to in-phase
and out-of-phase loadings [ 171. Recently, Papadopoulos proposed a new development of this
method for the fatigue life calculation in the medium-high cycle fatigue field [18].
Carpinten and Spagnoli [19, 201 formulated a new method founded on an original
reinterpretation of the classical critical plane approach. Their new criterion correlates the critical
plane orientation with the weighted mean principal stress directions and the multiaxial fatigue
assessment is performed by using a non-linear combination of the maximum normal stress and the
shear stress amplitude acting on the critical plane.
By using the theory of cyclic deformation in single crystal, Susmel and Lazzarin [21] presented
a medium-high cycle multiaxial fatigue life prediction method developed under the hypothesis of
homogeneous and isotropic material and based on the combination of a modified Wohler curve
and a critical plane approach. This criterion correlated very well with the experimental results
referred both to smooth and blunt notched specimens subjected to either in-phase or out-of-phase
loads [21,22].
All the approaches discussed above can be employed for the multiaxial fatigue assessment of
mechanical components of homogeneous and isotropic materials, but they do not give satisfactory
results in the presence of anisotropy, as it happens with composites. For this reason different
theories have been formulated to predict the fatigue endurance of this kind of materials.
Initially, it is important to highlight that the fatigue damage of composites under multiaxial
loadings is mainly influenced by the biaxiality ratios [23]; in particular it depends on the shear
stress components and it holds true both for plane and notched components. Another important
role is played by the off-axis angle (lay-up), whereas the influence on the fatigue strength of the
out-of-phase angle between load components seems to be negligible, at least for the glass/polyester
laminates [23].
By reanalysing about 700 experimental data take from the literature Susmel and Quaresimin
[24] showed that the best accuracy in the multiaxial fatigue prediction of composite materials can
be obtained by using the criteria proposed by Tsai-Hill [25], by Fawaz & Ellyin [26] and by Smith
& Pascoe [27]. In particular, the first one is founded on the application of the classical polynomial
failure criterion due to Tsai-Hill to the multiaxial fatigue assessment. The second one is based on