Page 254 - Biaxial Multiaxial Fatigue and Fracture

238 C. GAIER AND H. DANNBAUER

The result quality for combined in phase loading has been moved in the right direction, but
still it has not reached the test result. Additional improvements are not possible anymore,
because a further increase of the fatigue limit at B = 0’ would also change the result for pure
bending. But the result for bending should not be affected, because it has been already adapted
to the test result.

SUMMARY AND OUTLOOK

The critical plane criterion is proved to deliver good results for brittle materials, but it is shown
that it has some drawbacks when applying it to ductile ones in combination with out of phase
loading. A method, where a new material parameter has been introduced, is proposed to
overcome these problems. This method can be applied also for stochastic load combinations.
Additionally a method has been introduced for the assessment of both normal and shear
stress for stochastic nonproportional loadings. Advantages of the proposed “critical plane -
critical component” method are:
- Independency from coordinate system
- Normal and shear stress and all possible combinations are taken into account.
- rainflow-counting can be applied for lifetime evaluation without any problems.
- Applicable for both brittle and ductile materials by specifying cyclic data in dependence on
the polar angle 8 (S/N-curves, Haigh-diagrams, etc.)
- The interpolation function between tensiodcompression and torsional load can be adapted
to test results.
- Generally applicable for biaxial and triaxial stress (or strain) states
- Physical interpretation possible as ,,critical component“ of stress vector
Disadvantages are:
- High computational effort
- Sometimes additional corrections are necessary for out-of-phase loading (e.g. for
tempering steel).
Alternatively, integral methods can be applied instead of a maximum search, to obtain an
averaged value for the lifetime. This has been already proved for infinite lifetime evaluation
(safety against fatigue limit) of hard metals, e.g. by Zenner et al. [9-10] and Papadopoulos et al.
[ 121. For lifetime prediction till crack initiation, further investigations are necessary. Future
efforts take aim to extend the proposed method by integral solution algorithms.
The methods, as presented here, are based merely on stresses and therefore applicable only
to the high cycle fatigue domain (HCF) for lifetimes 2 -5000. Nevertheless, in principle these
methods could be extended for low cycle fatigue (LCF) too by exchanging stresses for strains
and introducing suitable damage parameters. Such strain based fatigue evaluations need to be
combined with usually extensive non-linear elastic-plastic stress-strain analyses. Experiences in
this direction are still outstanding.