Page 181 - Biaxial Multiaxial Fatigue and Fracture

166 P BONACUSE AND S. MLLURI

INTRODUCTION

Many multiaxial fatigue damage models are based on the premise that damage is a tensor, Le.,
it has both magnitude and direction. These ‘tensorial’ approaches imply that damage imposed
by loading in one direction does not readily interact with subsequent damage imposed by
loading in another direction. By subjecting thin-walled tubular specimens to fatigue in
different loading directions, in sequence, this hypothesis can be tested. In this study, a block of
lower amplitude loading, at a given fraction of the estimated life, preceded a second block of
higher amplitude loading to failure. This work is a complement to a previous study [I] where
higher amplitude cycles were imposed initially, followed by lower amplitude loading to failure.
Various combinations of axial and torsional load-type and load-sequence interactions have
been explored in both studies.
The most common method of accounting for the fatigue damage accumulated in a material
subject to variable amplitude loading is to estimate the fraction of the fatigue life expended for
each cycle of a given amplitude and then sum up all the fractions for each of the load
excursions. When this sum reaches unity, the material is said to have used up its available life.
This model is commonly referred to as the linear damage or Palmgren-Miner rule (LDR) [2].
However, many studies have shown LDR to be inaccurate by as much as an order of magnitude
for certain combinations of variable amplitude loading [3-61. Halford [3] outlines the uniaxial
loading combinations where the LDR is likely to break down and where alternative approaches
may prove useful.
In the present study, two cumulative fatigue damage models are assessed for their ability to
predict the remaining cyclic life after prior loading at both different amplitudes and different
loading directions. The first model is the LDR [2]. The second is the damage curve approach
(DCA) of Manson and Halford [7]. In the previous study (high amplitude loading followed by
low amplitude loading), the damage curve approach (DCA) was found to model the load
interaction behavior remarkably well for all the cases investigated including the mixed load
experiments (axial followed by torsional and torsional followed by axial). This seemed to
indicate that the fatigue damage was most likely isotropic, at least when the loading sequence
was high amplitude followed by low amplitude.
A possible explanation for apparent isotropic nature of damage accumulation under fulIy
reversed fatigue loading is that the cyclic hardening behavior of superalloys is, at least to some
extent, isotropic in nature. This hardening should influence damage accumulation even when
loading is imposed in another direction. The magnitude of plastic deformation is often used as
a measure of the accumulated damage in a loading cycle. If the material is in a work hardened
state from previous mechanical cycling it should be able to absorb a larger portion of ensuing
deformations elastically, resulting in lower plastic strains. Thus, a smaller increment of
damage wouId then be accrued in each subsequent cycle. This mechanism would be in
competition with propagating cracks that may have initiated in the prior cycling; higher stresses
due to work hardening would increase the crack propagation rate in the subsequent loading.

MATERIAL, SPECIMENS, AND TEST PARAMETERS

Specimens used in this study were fabricated from hot rolled, solution annealed, Haynes 188
superalloy, 50.8 mm diameter bar stock (heat number: 1-1880-6-1714). This is the same heat
of material used to perform the experiments described in Ref. [I]. The measured weight