Citation: Neto, D.M.; Sérgio, E.R.;
Jesus, F.; Newman, J.C., Jr.; Antunes,
F.V. Fatigue Crack Propagation under
Christmas Tree Load Pattern. Appl.
Sci. 2023, 13, 1284. https://doi.org/
10.3390/app13031284
Academic Editor: José António
Correia
Received: 31 December 2022
Revised: 13 January 2023
Accepted: 14 January 2023
Published: 18 January 2023
Copyright: © 2023 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Fatigue Crack Propagation under Christmas Tree Load Pattern
Diogo M. Neto * , Edmundo R. Sérgio , Francisco Jesus, James C. Newman, Jr. and Fernando V. Antunes
Centre for Mechanical Engineering, Materials and Processes (CEMMPRE), Department of Mechanical
Engineering, Univ Coimbra, 3030-788 Coimbra, Portugal
* Correspondence: diogo.neto@dem.uc.pt
Abstract:
Most mechanical components are subject to dynamic loads, which can cause failure in
service. This study aims to evaluate the effect of variable amplitude loadings on fatigue crack
growth (FCG) in CT specimens produced with the AA2024-T351 aluminum alloy. Specifically, it
is intended to predict the FCG rate when the specimen is subjected to a complex loading pattern,
named the “Christmas Tree Spectrum”. Crack growth is simulated by node release, which occurs
when the cumulative plastic strain at the crack tip reaches a critical value (110%) that is supposed to
be a material property. It is therefore assumed that cyclic plastic deformation is the main damage
mechanism. The specimen was subjected to four different load patterns: the 6–60 N low-frequency
constant amplitude load (CAL); the 6–21 N high-frequency CAL; the Christmas Tree (15–9) and the
Christmas Tree (9–3) patterns. The Christmas Tree 15–9 load pattern is defined by nine increments
of +15 N and
−
9 N followed by eight increments of +9 N and
−
15 N. The results indicate that the
Christmas Tree (15–9) pattern increases crack tip damage relative to the constant amplitude loading.
This is attributed to small variations in material hardening, particularly during the unloading phase
of the load block. On the other hand, the Christmas Tree (9–3) pattern did not show a significant effect,
indicating the importance of the range of small-amplitude cycles. The crack closure phenomenon is
usually used explain the effect of loading parameters, but this is an exception.
Keywords:
fatigue crack growth; 2024-T351 aluminum alloy; Christmas Tree spectrum; cumulative
plastic strain; material hardening; crack closure
1. Introduction
Components and structures are typically submitted to cyclic loads and therefore must
be designed against fatigue. In the damage tolerance approach, initial cracks are assumed
to exist, with a size equal to the limit of detection techniques. The time between inspections
is defined from the number of load cycles required to propagate the crack up to a critical
length. The accuracy of the fatigue crack growth (FCG) rate is therefore crucial in this
design approach.
The FCG is a complex phenomenon, which is affected by different parameters, namely,
material, geometry, environment and loading conditions. The effect of loading parameters,
in particular, has been widely studied but is not completely understood. In practice, the
loads applied to components and structures are usually complex, with variable frequency
and amplitude. Standard load patterns were defined, for different practical applications,
which facilitate the comparison of results [
1
]. The CARLOS load pattern was defined for
automotive applications, WISPER was the loading sequence suggested for wind turbines,
while TWIST and FALSTAFF sequences were proposed for transport and fighter aircraft [
2
].
The TWIST load spectrum, for example, has an average of a thousand small gust cycles
per flight with a major cycle associated with the ground–air–ground sequence and a few
overloads associated with more severe atmospheric turbulence.
However, to understand the mechanisms that explain the effect of these complex load-
ing patterns, it is recommended to follow a strategy of increasing complexity. Accordingly,
the most studied loading pattern is the constant amplitude loading with different stress
Appl. Sci. 2023, 13, 1284. https://doi.org/10.3390/app13031284 https://www.mdpi.com/journal/applsci
