Page 21 - Biaxial Multiaxial Fatigue and Fracture

6 K. DANG VAN, A. BIGNONNET AND JL. FAYARD

Once the local stress cycle in the critical locus is characterised, one has to choose a
criterion. Local shear .r(t) and hydrostatic tension p(t) were chosen as pertinent parameters; the
fatigue criterion is a linear relation between these quantities:

F(o)= + a.p -b 2 0 (2)
z
where a and b are material constants that can be determined by two simple types of fatigue
experiments; b for instance corresponds to the fatigue limit in simple shear.
General application of this criterion requires the consideration of the plane on which the set
(.r(t),p(t)) is a ccmaximums relative to the criterion. This computation can be done as following:
the maximum local shear at any time t is given by

The stresses oI (t), o, (t) are the principal stresses at time t. The quantity that determines the
risk of fatigue occurrence is defined by the parameter d, calculated over a period such that:

It is also frequent in some applications to use the concept of local equivalent stress for a life
duration Ni defined by

It is observed however that for high cycle fatigue (N> 5.10') ai depends weakly on Ni so
that, taking ai = a, we define the local equivalent stress by

As a final remark, it must be noticed that the local stress in the stabilized state is chosen in
preference to plastic strain or dissipative energy, which is also contained in the elastic
shakedown hypothesis. The main reasons are that these latter quantities are not easy to evaluate
since, in high cycle fatigue, plastic deformations are heterogeneous and occur only in some
misoriented grains. Moreover, the increases per cycle of theses quantities are so tiny that such
ways of estimating them lead to large errors and great uncertainties in predicting the fatigue
resistance.

FATIGUE ASSESSMENT OF WELDED STRUCTURES

A structural approach
Current practice in welded structure design is based on the use S-N curves, hot spot stress or
structural stress. These approaches are useful to industrial applications in many cases.
However, they are difficult to handle in order to take into account multiaxial loadings, which
strongly influence the fatigue strength of welded structures. Engineers in design offices do not