Page 164 - Biaxial Multiaxial Fatigue and Fracture
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Fatigue Limit of Ductile Metals Under Multiaxial Loading 149
In the present paper, the further-developed shear stress intensity hypothesis (SIH) is
described. The fatigue limit behaviour of ductile metallic materials is explained with special
attention to the effects of the mean stresses, the phase difference, the frequency difference, and
the wave form.
SHEAR STRESS INTENSITY HYPOTHESIS
The development of the shear stress intensity hypothesis (SLH) can be retraced to the
interpretation of the von Mises criterion in accordance with Novoshilov [20]. In the past, the
von Mises criterion has been interpreted differently:
- Distortion energy (Maxwell 1856, Huber 1904, Hencky 1924)
- Octahedral shear stress (Nadaj 1939)
- Root mean square of the principal shear stresses (Paul 1968)
- Root mean square of the shear stresses for all intersection planes (Novoshilov 1952)
Novoshilov proved that the mean square value of the shear stresses over all cutting planes is
identical to the von Mises stress:
Simbuerger [ 161 applied this new interpretation according to Novoshilov to cyclic
multiaxial loading and developed the hypothesis of the effective shear stresses. Zenner [17,21-
231 has further developed this multiaxial criterion and designated the result as the shear stress
intensity hypothesis (SM).
In [24] the classical multiaxial criteria, the maximum shear stress criterion and the von
Mises criterion, have been derived as special cases of the weakest link theory. On the basis of
this analysis, a general fatigue criterion has been formulated for multiaxial stresses. The
existing multiaxial criteria of integral approach and of the critical plane approach can be
derived as special cases from the general fatigue criterion.
On the basis of this analysis of the weakest link theory in 1241, the shear stress intensity
hypothesis SIH is newly formulated and further developed.
In the newly developed SM, the equivalent shear stress amplitude and the equivalent
normal stress amplitude are evaluated as an integral of the stresses over all cutting planes, Fig.
2:
