Page 470 - Biaxial Multiaxial Fatigue and Fracture

454 M. WEICK AND 1 AKTAA

the microstructural barriers have a noticeably smaller influence on the crack growth rate at high
loading levels.
While the crack propagation in the short cracks regime can be described using the methods of
the elastic-plastic fracture mechanics (EPFM) [9], approaches of the so-called microstructural
fracture mechanics (MFM) are needed for the regime of micro cracks [lo]. In the following, a
model for micro and short crack propagation will be presented, which was developed on the
base of the model by McDowell and Bennet [8] and applied to our multiaxial tests for lifetime
prediction.

Microcrack propagation modelling. TO describe the average crack growth rate in the short
cracks regime, the following elastic-plastic fracture mechanics approach proposed by Hoshide
and Socie for mixed mode loading [9] is used

where the crack growth rate df~ correlates with the range of J-integral AJ. Cj and m,are
material and temperature dependent parametexdl can be calculated in terms of an elastic and
a plastic part.
AJ=AJ,, +NP, (9)

For mixed mode loading the elastic part is based on the normal stress ranges Aon and the shear
stress ranges AT on the plane, where the crack is assumed to nucleate and propagate. This is
usually the plane of maximum shear strains 18,101. Neglecting the influence of plastic
deformation on the effective crack length the elastic part can be phrased as [9]:

For the plastic part is given by the formula derived by Hoshide and Socie [9] generalised here
for the case of multiaxial non-proportional cyclic loading:

AJpl =T(h,n,v)A~; Aoq a (1 1)

1-n
with 7 =s(h)-+t,(h)xn
J;;

and h=- AT
Acll
Aoq denotes the von Mises equivalent stress range. Its calculation is analogous to the
determination of A€;. The dimensionless function 7 takes into account the increased plastic
deformation in front of the crack tip in comparison to the global plastic deformation. The
function s(h) takes into account the mode mixity of the crack loading and decreases as h
increases. For pure Mode I loading ( h = 0) s =3.85. For the pure Mode I1 (h -+ -) s=1,45 [9].
For a mixed mode loading we propose an interpolation in the following form: