Page 483 - Biaxial Multiaxial Fatigue and Fracture

Fatigue Assessment of Mechanical Components Under Complex Multiaxial hading 467

In order to handle non-proportional loading effect on fatigue resistance, many new
methodologies have been developed and are based on various concepts such as the critical
plane approach [5], integral approach [6], mesoscopic scale approach [7], etc.
A common feature of many high-cycle multiaxial fatigue criteria is that they are expressed
as a general form and include both shear stress amplitude r, and normal stress u during a
loading cycle:
T, + k(N)o= R(N) (1)

where k(N) and h(N) are material parameters for a given cyclic life N. Multiaxial fatigue
models differ in the interpretation of how shear stress and normal stress terms in Eq. (1) are
defined.
For non-proportional cases, a stress-based version of the ASME boiler and pressure vessel
code, case N-47-23 [8], may be used as an extension of the von Mises criterion, in which an
equivalent stress amplitude parameter, SEQA, is defined from stress ranges Abx, Aby, Abz, Arxy,
Azyz. AT^,, in the form

I
ScQa =xJAc, -Ae,)2 +(ACT, -Aci)2 +(Aci -Ac,)' +6(Arm2 AT,:^ +AT,') (2)
where Ao,=o,(t,)-o,(tz), Ao,=o,(t,)-o,(tz), etc. SEQA is maximized with respect to two time
instants, 11 and t2, during a fatigue loading cycle.
For constant amplitude bending and torsional stresses such as

Eq.(2) becomes

9
3
+:
S, =%/I + K2 +,/I I( cos(2Sx,) + - K . (4)
16
where K=2ztla,.
When r,/ob=0.5 and 6,,=0 (proportional loading case), Eq. (4) gives S,, = 1.3230,. When
z,/ob=0.5 and F,,=90" (out-of-phase loading case), Eq. (4) gives S,, = bh, which means that
out-of-phase load case is predicted to be less damaging than the proportional load case with the
Same stress amplitudes.
However, experimental results showed that the prediction by Eq. (4) for out-of-phase load
case is inconsistent and non-conservative. Hitherto, many approaches have been proposed for
treating the non-proportional effects, among them the critical plane approach and the integral
approach are two important concepts.

Critical Plane Approaches

Critical plane approaches are based upon the physical observation that fatigue cracks initiate
and grow on certain material planes. The orientation of the critical plane is commonly defined
as the plane with maximum shear stress amplitude. The linear combination of the shear stress