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BiaxiaVMultiaxial Fatigue and Fracture
Andrea Carpinteri, Manuel de Freitas and Andrea Spagnoli (Eds.)
0 Elsevier Science Ltd. and ESIS. All rights reserved. 203
CRITICAL PLANE-ENERGY BASED APPROACH FOR ASSESSMENT OF BIAXIAL
FATIGUE DAMAGE WHERE THE STRESS-TIME AXES ARE AT DIFFERENT
FREQUENCIES
A. Varvani-Farahani
Department of Mechanical, Aerospace and Industrial Engineering, Ryerson University, 350
Victoria Street, Toronto, Ontario, MSB 2K3, Canada
ABSTRACT
A new fatigue parameter has been developed to assess the fatigue lives under in-phase and out-
of-phase biaxial constant amplitude fatigue stressing where the stresses are at different
frequencies. In this parameter, the normal and shear stress and strain ranges have been
calculated from the largest stress and strain Mohr’s circles. The total damage accumulation in a
block loading history has been calculated from the summation of the normal and shear energies
on the basis of a cycle-by-cycle analysis. The normal and shear energies used in this parameter
are divided by the tensile and shear fatigue properties, respectively, and the proposed
parameter, unlike many other parameters, does not use an empirical fitting factor. The
proposed fatigue parameter has successfully correlated biaxial fatigue lives of thin-walled
EN24 steel tubular specimens tested under in-phase and out-of-phase biaxial fatigue stressing
where stresses were at different frequencies and included mean values.
KEYWORDS
Fatigue damage parameter, loading frequency ratio, block loading history, critical plane, shear
and normal energies
INTRODUCTION
Many engineering components that undergo fatigue loading experience multiaxial stresses, in
which two or three principal stresses fluctuate with time, i.e. the corresponding principal
stresses are out-of-phase or the principal directions change during a cycle of loading. These
components include car axles, helicopter propeller shafts, and airplane wings subjected to
bending and torsion, which can be out-of-phase, and at different frequencies. To assess fatigue
life of the components, many attempts have been made to derive theories based on equivalent
stressktrain, elastic-plastic work/energy and critical plane approaches. General reviews of
multiaxial fatigue life prediction methods are presented by Garud [l], Brown and Miller [2],
and You and Lee [3]. As yet there is no universally accepted approach. It was shown that the
von Mises criterion was limited to correlating multiaxial life data under proportional loading in
the high cycle fatigue regime [4-51. Energy approach has been applied in conjunction with