Page 122 - Biaxial Multiaxial Fatigue and Fracture

Long-Lije Multiaxial Fatigue of a Nodular Gmphite Cast Iron 107

the material. Findley identified a critical plane for fatigue crack initiation and growth that is
dependent on both alternating shear stress and maximum normal stress. The combined action
of shear and normal stresses is responsible for fatigue damage and the maximum value of the
quantity in parentheses is used rather than the maximum value of shear stress.
Other successful long-life shear stress based models for multiaxial fatigue have the same
general form as Eq. (1) and include both a shear stress and a normal stress terms to account for
observed mean stress and combined loading effects. Several examples long-life shear stress
based models and the shear and normal stress terms employed in these models are listed in
Table 1. Of these examples, all except the Sines model fall into the critical plane category
because Tresca shear stress is associated with a specific plane.

Table 1. Examples of long-life shear stress based models
Model Shear stress term Normal stress term
Findley [2-41 Tresca Normal stress, On
Sines [6-71 Von Mises Hydrostatic stress
McDiarmid [8] Tresca Normal stress, On (on maximum shear plane)
Dang Van [9] Tresca (microscopic value) Hydrostatic stress

Critical plane models for tension

Numerous researchers [ 1,10,11] have emphasised the need for alternate fatigue damage models
depending on whether a material fails predominately due to shear crack growth or due to
tensile crack growth. Shear stress based criteria characterised by Eq. (1) have been developed
based on observations of crack nucleation and growth in ductile materials. It is commonly
found that crack nucleation and early growth occurs along planes of maximum shear stress and
that tensile stresses along the plane of maximum shear stress accelerate fatigue damage while
compressive stresses along this plane increases fatigue life.
In contrast, cast iron and stainless steel under some loading conditions have been shown to
be normal stress dominated and, therefore, require different parameters to correlate torsion and
tension fatigue data [IO, 12-15]. In these materials, micro-cracks may nucleate in shear, but
fatigue life is dominated by early crack growth on planes perpendicular to the maximum
principal stress or strain. Long-life fatigue of high strength steels may also be dominated by the
propagation / nonpropagation of Mode I cracks from non-metallic inclusions of other defects.
Smith et al. [ 161 proposed a suitable relationship that includes both the cyclic strain range
and the maximum stress. This model, commonly referred to as the SWT model, was originally
developed as a correction for mean stresses in uniaxial loading situations. The model is still
widely used and is a common feature in most commercial fatigue analysis software. The SWT
model can also be used in the analysis of both proportionally and non-proportionally loaded
components fabricated from materials that fail primarily due to Mode I tensile cracking [ 171.
The SWT model for multiaxial loading is based on the principal strain range, AEI and
maximum stress on the principal strain range plane, On,max:

On,max -=- *" Of (2Nf)2b+~;~;(2Nf)b+c
2 E