Page 185 - Biaxial Multiaxial Fatigue and Fracture

Sequenced Axial and Torsional Cumulative Fatigue: .. , 169

CUMULATIVE DAMAGE MODELS

The results of the cumulative fatigue experiments performed for this study were compared with
predictions of two load interaction models: the LDR (Eq. 1) [23, and the DCA (Eq. 2) [7].
($1 = I - ($1

The LDR assumes that damage accumulated during each load excursion can be simply
added to the already accumulated damage in the material. Load sequence and changes in the
properties of the material are not taken into account. The LDR has the distinct advantage of
being straight forward to implement for virtually all loading histories, provided sufficient
baseline fatigue data are available and an adequate cycle counting method is employed.
The DCA attempts to model the observed non-linear interactions between two load-level
experiments. The underlying assumption of the DCA is that high amplitude loading initiates
cracking early in life whereas under lower amplitude loading measurable cracking does not
occur until late in life. In the case of the experiments performed in this study, the implication is
that the initially imposed lower amplitude loading might not initiate cracks. In the subsequent
higher amplitude loading the material might then ‘ignore’ the previous cycling or even derive a
benefit from it, allowing the sum of life fractions to be greater than unity.

RESULTS AND DISCUSSION
The initially imposed lower amplitude cyclic loading (0.65% axial and 1.24% torsional
nominal strain ranges) had sufficient plasticity to cause this solution-annealed material to
isotropically harden. The magnitude of the hardening in the first load level was proportional to
the number of imposed cycles. The cyclic hardening behavior for the lower amplitude, first
load level, loading is presented in Fig. 1. The horizontal lines in each of these figures
correspond to stress range for the last cycle of the lower amplitude loading. The vertical drop
lines indicate the last cycle of the first load level for each experiment.
There was some variation in the first cycle stress range for both the axial and torsional
loading. In the first load levels, the average axial first cycle stress range (the left most data
point in each of the curves in Fig. I (a) and (c)) was 646 MPa with a standard deviation of 15
MPa, while the torsional first cycle average stress range (the left most data point in each of the
curves in Fig. 1 (b) and (d)) was 382 MPa with a standard deviation of 14 MPa. The most likely
explanations for these variations include the natural variability in the material properties and
discrepancies in the machining andlor measurement of the specimen gage section. A 0.1%
error in the measurement of a gage section dimension (inner or outer radius), which is the
approximate precision of the micrometers employed, would lead to a 0.2% error in the axial
stress and a 0.4% error in the shear stress calculations. This dimensional measurement error
would account for only about 10% of the variability observed. The specimen to specimen
variation in the hardening rate, however, in all the axial and torsional experiments was small.