Page 404 - Biaxial Multiaxial Fatigue and Fracture

388 M. FILIPPINI ET AL.

An instantaneous effective shear strain may be calculated at every time t by averaging the
(scalar) squared shear strain intensity ( y,, (q, 29,t))* in the following way:

Taking into account a full loading cycle, an effective shear strain amplitude is defined as
follows:

Since the procedure adopted to derive the effective shear strain does not depend on the
particular shape of the loading cycle, the criterion may be also applied to non-sinusoidal,
proportional and/or non-proportional multiaxial loading histories.

Fully reversed loading

Let us consider a multiaxial loading the mean strains of which are zero. We seek to establish an
axial equivalent strain amplitude, based on the effective shear strain amplitude introduced
before, such as to be able to use directly the Mansotdoffin relationship to make fatigue life
predictions. Formally, we write:

where K is a material function, which depends on the relative amount of plastic and elastic
strains present in a load cycle. It is determined by imposing the E~ to reduce to the in the
case of axial strain loading, i.e.:

If a sinusoidal axial strain E, sin(mt), which remains within the elastic range of the
behaviour of the material, i.e. E? =E= = -v,,E, , is considered, the effective shear strain
amplitude calculated according to Eqs (9) and (10) is:

Therefore, the material function K reduces to a constant for the elastic case, denoted as K,, :