Citation: Elkin, A.; Gaibel, V.;
Dzhurinskiy, D.; Sergeichev, I. A
Multiaxial Fatigue Damage Model
Based on Constant Life Diagrams for
Polymer Fiber-Reinforced Laminates.
Polymers 2022, 14, 4985. https://
doi.org/10.3390/polym14224985
Academic Editor:
Alberto Campagnolo
Received: 25 October 2022
Accepted: 15 November 2022
Published: 17 November 2022
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Article
A Multiaxial Fatigue Damage Model Based on Constant Life
Diagrams for Polymer Fiber-Reinforced Laminates
Aleksandr Elkin * , Viktor Gaibel, Dmitry Dzhurinskiy and Ivan Sergeichev
Center for Materials Technologies, Skolkovo Institute of Science and Technology, Bolshoy Boulevard 30, Bld. 1,
Moscow 121205, Russia
* Correspondence: aleksandr.elkin@skoltech.ru; Tel.: +7-968-573-4754
Abstract:
In the last decade, fatigue damage models for fiber-reinforced polymer composites have
been developed assuming the fracture energy equivalence hypothesis. These models are able to
predict a fatigue life of composite laminates, but their identification requires a significant number
of off-axial tests for various stress ratios. The present study proposes the stress ratio dependent
model, which phenomenologically adopts a decrease in stiffness and residual strength of a unique ply
according to experimental constant life diagrams. Hashin, Tsai–Hill, and the maximum stress failure
criteria are utilized for damage initiation considering the residual strength of the ply. The obtained
results indicate a sufficiency of using S-N curves for UD 0
◦
, UD 45
◦
, and UD 90
◦
for identification of
the model. The model was verified by S-N curves for UD 10
◦
, UD 15
◦
, and UD 30
◦
and its applicability
was demonstrated for prediction of a fatigue life of composite laminates with an arbitrary lay-up.
The model is implemented into ABAQUS finite element software as a user subroutine.
Keywords:
fiber-reinforced polymer composites; fatigue; damage initiation; residual strength; finite
element analysis
1. Introduction
In recent decades, metallic components have been replaced by fiber-reinforced plastics
(FRPs) in industry and infrastructure, e.g., glass FRPs are widely used in wind turbine
blades [
1
] and pressurized vessels [
2
]. FRPs demonstrate better fatigue performance relative
to metals, and, in earlier engineering analysis, composite structures were treated even as
fatigue free [
3
]. However, recent studies show that cyclic loads significantly reduce stiffness
and strength of FRPs, and these effects cannot be neglected.
Nowadays, a variety of approaches were proposed for prediction of fatigue life of
materials and structures under multiaxial stress state. For example, the critical plane-based
criteria have been developed to assess fatigue performance of notched and unnotched
metal components [
4
–
7
]. Zhu et al. [
7
] concluded that the modified Smith–Watson–Topper
criterion [
8
] is more suitable for brittle materials, and the modified generalized strain energy
criterion [
7
] provides better results for ductile materials. Nassiraei et al. [
9
,
10
] improved
fatigue life of composite structures by lay-up optimization for various FRPs to reduce stress
concentration factors under bending and axial loads in tubular X-connections utilizing
finite element analysis (FEA).
The fatigue phenomenon in FRPs is divided into three main stages [
3
,
11
–
13
], as pre-
sented in Figure 1. The first stage characterizes the initiation of small unconnected matrix
cracks, causing inter-fiber failure (IFF). The second stage begins when the accumulated
cracks form macro damage, so-called characteristic damage state (CDS), such as delamina-
tion (DEL) or large inter-layer cracks. The final stage occurs when fibers begin to fail (FF)
that causes the failure of the multilayered composite.
Polymers 2022, 14, 4985. https://doi.org/10.3390/polym14224985 https://www.mdpi.com/journal/polymers
