Page 162 - Biaxial Multiaxial Fatigue and Fracture

BiaxiaYMultiaxial Fatigue and Fracture
Andrea Carpinten, Manuel de Freitas and Andrea Spagnoli (Eds.)
Q Elsevier Science Ltd. and ESIS. All rights reserved. 147

FATIGUE LIMIT OF DUCTILE METALS UNDER MULTIAXIAL LOADING

Jiping LIU' and Harald 2J3NNER2

1 Volkswagen AG, 38436 WoEfsburg, Germany
2 TU Clausthal, 38678 Clausthal-Zellerfeld, Germany

ABSTRACT

The further-developed Shear Stress Intensity Hypothesis (SM) is presented for the calculation
of the fatigue limit of ductile materials under multiaxial loading. The fatigue limit behaviour
for different cases of multiaxial loading is analysed with SM and experimental results,
especially with the effect of mean stresses, phase difference, frequency difference, and wave
form. In a statistical evaluation, the further-developed SM provides a good agreement with the
experimental results.
KEYWORDS

Fatigue limit, multiaxial loading, multiaxial criteria, weakest link theory

INTRODUCTION

A multiaxial stress state which varies with time is generally present at the most severely
stressed point in a structural component. The stress state is usually of complex nature. The
individual stress components may vary in a mutually independent manner or at different
frequencies, for instance, if the flexural and torsional stresses on a shaft are derived from two
vibrational systems with different natural frequencies.
For assessing this multiaxial stress state, the classical multiaxial criteria, such as the von
Mjses criterion or the maximum shear stress criterion, are not directly applicable. This is
illustrated in Fig. 1 for two load cases. In the first case, an alternating normal stress occurs in
combination with an alternating shear stress with a phase shift of 90°, Fig. la. The second case
involves a normal pulsating tensile normal stress cr, and a compressively pulsating normal
stress oy, Fig. Ib. In both load cases, the principal stresses exhibit the same variation with time.
In accordance with the classical multiaxial criteria, the same equivalent stresses are calculated
in both cases. The endurance limits are very different, however, as is shown by experiments.
This is explained by the fact that the principal direction can vary in the case of multiaxial
stress. A variable principal direction is not taken into account by the classical multiaxial
criteria.