Page 121 - Biaxial Multiaxial Fatigue and Fracture

106 G.B. MARQUIS AND 2 K4MAUIIVEN-ROIKOMEN

features which lead to fatigue damage. Small cracks grow in a complicated manner that is
affected by crack closure, microstructure and crack size. Linear elastic fracture mechanics
assumes that the stress and strain fields surrounding a crack are uniquely determined by the
stress intensity factor. However, continuum mechanics assumptions are not valid for cracks of
the size of the microstructure because, on this scale, a polycrystalline material does not
resemble the ideal homogeneous solid. Closure conditions for small cracks are also different
since the crack wake is small. These factors prevent direct modeling with linear elastic or
elastic-plastic fracture mechanics.
Critical plane models

The so-called critical plane approaches to multiaxial fatigue have evolved from experimental
observations of the nucleation and growth of cracks during cyclic loading. Models in this class
attempt. to compute fatigue damage on specific planes within a test specimen or component. A
critical plane can, therefore, be defined as one or more planes within a solid subject to a
limiting value of some damage parameter. For example, in some models the limiting damage
parameter value is associated with the maximum alternating shear strain on a specific plane
while other models define as critical the plane experiencing the maximum value of some
combination of stress and strain components during a load history. The common element in all
critical plane approaches is that fatigue life is considered to be controlled by the combination
of stresses and strains acting on a specific critical plane or on a set of critical planes. Socie and
Marquis have published a review on critical plane and other approaches to multiaxial fatigue
[I].
It has been observed that fatigue life will usually be dominated either by crack gowth along
shear planes or along tensile planes. Crack growth mode will depend on material, stress state,
environment and strain amplitude. A critical plane model will incorporate the dominant
parameters governing either type of crack growth. Due to the different possible cracking
modes, shear or tensile dominant, no single damage model should be expected to correlate test
data for all materials in all life regimes.
While critical plane models underscore the important role of crack nucleation and
propagation on fatigue, they do not specifically model crack propagation. Normally they
describe the complex crack nucleation and microcrack growth mechanisms in a general sense
using load or strain values available in most engineering applications. These stress or strain
terms are normally those values that are obtained directly from strain gage measurements or
finite element analysis. Crack growth from an initial size to faiIure is assumed, but for the sake
of simplicity most models avoid the integration of crack a propagation equation. Successful
models are able to predict both the fatigue life and the dominant failure plane(s).
Among the early critical plane fatigue damage criteria, the Findley model [2-4] is one of the
most refined. Findley suggested that the normal stress, On, on a shear plane might have a linear
influence on the allowable alternating shear stress, A212.

This model differs from earlier empirical methods [5-71 and methods based on extensions of
static yield criteria in that it identifies the stress components acting on a specific plane within