Mirzaei fatigue composite SMA 1-s2 0-S0263822322005293-main

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Composite Structures 293 (2022) 115753
Available online 14 May 2022
0263-8223/© 2022 Elsevier Ltd. All rights reserved.
Fatigue behavior of laminated composites with embedded SMA wires 
A.H. Mirzaei, M.M. Shokrieh *, A. Saeedi 
Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and 
Technology, Tehran 16846-13114, Iran 
A R T I C L E I N F O 
Keywords: 
Laminated composites 
Shape memory alloy wires 
Progressive fatigue damage 
Self-heating 
Thermomechanical constitutive modeling 
A B S T R A C T 
Embedding pre-strained shape memory alloy (SMA) wires within laminated composites can enhance their fatigue 
performance due to pseudoelastic and shape memory effects. In the present research, an experimental program 
was conducted to investigate the fatigue behavior of carbon/epoxy laminated composites with/without 
embedded SMA wires. Moreover, a novel fatigue model was proposed to predict the behavior of laminated 
composites with embedded SMA wires. The model is an integration of three parts. The first part is the progressive 
fatigue damage model to simulate the fatigue behavior of composites. The second part is the self-heating model 
for the prediction of the self-temperature rise in laminated composites subjected to cyclic loading. The third part 
is the thermomechanical constitutive model of the mechanical behavior of the SMA wire. Effects of the stacking 
sequence, the applied stress level, and the pre-strain level of SMA on fatigue behavior of laminated composites 
were studied. Good agreement between theoretical and experimental results revealed the ability of the present 
model. 
1. Introduction 
The shape memory alloys (SMAs), due to their unique thermo-
mechanical properties, i.e., the pseudo-elastic (PS) effect and the shape 
memory (SM) effect, have been vastly utilized in engineering applica-
tions [1,2]. The PS behavior of SMAs is defined by their large recover-
able strain upon loading. Unlike the conventional alloys, which show 
plastic behavior under large deformation after a few cycles of loading, 
SMAs can preserve their elastic behavior and create a large hysteresis 
loop under cyclic loadings [3]. Moreover, the pre-strained SMAs can 
produce a compressive recovery force after activation of the system due 
to their SM effect [4,5]. The generated compressive force can result in 
crack closure effect [6,7], resistance against damage propagation [8,9], 
and postponing the final failure in composite laminates [10–12]. 
Regarding the great reinforcing potential of the SMA wires, they can 
also be employed in fiber-reinforced composite laminates to improve the 
fatigue life of the composite structures. So far, a few experimental in-
vestigations were conducted to examine improving the fatigue life of the 
composite materials by SMA wires. Wang et al. [13] studied the fatigue 
behavior of glass/epoxy composite laminates with embedded SMA 
wires. They reported that by using SMA wires, the fatigue life of the 
composite specimens increased by more than two times. Moreover, they 
found that for unidirectional plies, the position of the wire did not 
significantly affect the fatigue life enhancement. In another study, 
Daghash and Ozbulut [14,15] employed SMA wires as reinforcements in 
a thermoset polymer matrix and studied the tensile and fatigue behavior 
of the SMA/epoxy composites. They showed that by using SMA wires, 
the recoverable strain of their polymer upon unloading was improved, 
and fatigue life enhancement was observed. Shimamoto et al. [16] 
studied fatigue crack propagation behavior in epoxy matrix composite 
reinforced with embedded SMA wires. Their results revealed that the 
generated recovery compressive force in the SMA wires decreased the 
matrix crack-tip stress intensity, and as a consequence, led to resistance 
against fatigue crack propagation. Experimental studies are also per-
formed on SMA wires reinforced carbon-fiber-reinforced-polymer 
(CFRP) patches for enhancement of the fatigue life of the composite 
samples [17–20]. It was demonstrated that CFRP/SMA hybrid patches 
can enhance the fatigue life of cracked specimens. 
In the present research, the fatigue behavior of carbon/epoxy lami-
nated composites with/without embedded SMA wires was investigated. 
To the best knowledge of the present authors, there is no model for 
simulating the fatigue behavior of laminated composites with embedded 
SMA wires. By integrating three submodels, a novel fatigue model was 
developed for the simulation of the fatigue behavior of SMA-embedded 
reinforced laminated composites. The first submodel is the progressive 
fatigue damage (PFD) model of laminated composites, developed by 
* Corresponding author. 
E-mail address: shokrieh@iust.ac.ir (M.M. Shokrieh). 
Contents lists available at ScienceDirect 
Composite Structures 
journal homepage: www.elsevier.com/locate/compstruct 
https://doi.org/10.1016/j.compstruct.2022.115753 
Received 20 August 2021; Received in revised form 21 March 2022; Accepted 8 May 2022 
mailto:shokrieh@iust.ac.ir
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Composite Structures 293 (2022) 115753
2
Shokrieh and Lessard [21]. The second submodel is the self-heating 
model for the prediction of the self-temperature rise in laminated 
composites subjected to cyclic loading, recently developed by the pre-
sent authors [22]. The third submodel is the thermomechanical consti-
tutive model of the mechanical behavior of the SMA wire, developed by 
Liang and Rogers [23]. The SMA wires are embedded into the host 
laminated composites to investigate their effect on the static strength. 
Then, the results of the present model were verified by a set of fatigue 
experiments on carbon/epoxy laminates with different layups and stress 
levels. 
2. Theoretical model 
The idea of fatigue life enhancement of the laminated composites by 
using embedded SMA wires is based on employing both pseudoelastic 
(PS) effect and shape memory (SM) effect of SMA wires. During cyclic 
loading, the temperature in the laminate is increased due to the self- 
heating phenomenon. The temperature elevation activates SMA wires 
and the SM effect generates the recovery force, leading to crack closure 
behavior, and consequently fatigue life enhancement of the specimen. 
Also, the PS effect of SMA wires causes a relatively large energy dissi-
pation in the specimen, and fatigue life enhancement can be expected. 
Fig. 1 schematically depicts the procedure of fatigue life improvement 
by embedding SMA wires in laminated composites due to the SM and PS 
effects of SMA wires. 
In the present study, a theoretical model is developed to simulate the 
fatigue behavior of polymeric laminated composites with embedded 
SMA wires. The present model consists of three major submodels as 
follows: 
1. The progressive fatigue damage (PFD) model, developed by Shokrieh 
and Lessard [21] for predicting the fatigue behavior of the host 
laminated composites, 
2. The self-heating model, called the generated-dissipated energy 
(GDE) model, developed by Mirzaei and Shokrieh [22], for predic-
tion of the self-temperature rise in the host laminated composites 
during the cyclic loading, 
3. The nonlinear thermomechanical constitutive model of the me-
chanical behavior of the SMA wire during the cyclic loading, 
developed by Liang and Rogers [23]. 
Using the PFD submodel, the cycle-by-cycle fatigue behavior of the 
host laminated composites with arbitrary geometry and layup under 
complex fatigue loading conditions with/without stress concentration 
can be analyzed. 
The second submodel predicts thetemperature rise in composite 
specimens during the fatigue loading. In this submodel, viscoelastic 
energy is calculated as the reason for heat generation in the specimen 
due to the viscoelastic behavior of the polymeric matrix. Then, by 
applying the heat transfer equations, energy dissipation due to con-
duction and convection mechanisms are calculated. Finally, by applying 
the first law of thermodynamics to these dissipated energies in each 
cycle of life, the temperature rise is computed. 
The third submodel simulates the embedded SMA mechanical 
behavior in laminated composites. The model is capable of calculating 
the martensite volume fraction, mechanical properties, and generated 
recovery force in the wires during cyclic loadings. 
By integration of these three submodels, the behavior of the SMA 
reinforced composite specimens subjected to cyclic loading was simu-
lated. Fig. 2 shows the flowchart of the present model by the integration 
of three submodels. In the following sections, each modeling step is 
Fig. 1. The procedure of fatigue life improvement by embedding SMA wires in laminated composites due to the PS and SM effects. 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
3
described in more detail. 
2.1. The progressive fatigue damage model 
In this section, a short explanation of the PFD model for predicting 
the fatigue behavior of the host laminated composites is presented. For a 
more detailed explanation of the PFD model, it is recommended that 
interested readers refer to Refs. [21,24]. The PFD model contains three 
subsections as the stress calculation, failure analysis, and material 
degradation that are explained as follows. 
2.1.1. Stress calculation 
To model the fatigue behavior of laminated composites, it is neces-
sary to calculate the stresses and strains in the composites precisely [25]. 
In terms of the simple or complex geometry, loading conditions, and 
boundary conditions of the specimen, the classical lamination theory 
(CLT) or the finite element method can be used. In the present study, 
simple laminated composites with simple loading and boundary condi-
tions were studied, therefore CLT was used for the stress analysis. The 
nonlinear shear stress–strain behavior of the unidirectional ply was 
considered. 
2.1.2. Failure analysis 
Different failure criteria of composite materials can be used for 
failure analysis. However, failure criteria capable of detecting the failure 
modes, such as the modified Hashin failure criteria, are recommended to 
be used in the PFD model [26]. Five different failure modes, including 
the fiber in tension or compression, the matrix in tension or compres-
sion, and the fiber–matrix shearing failure modes are considered. It must 
be mentioned that the out-of-plane stresses are not taken into account. 
2.1.3. Material properties degradation 
Material property degradation consists of sudden death and gradual 
degradation rules, which are considered for both stiffness and strength 
of each lamina within the composite specimens. In the model, based on 
failure modes detected by the failure criteria, the relevant mechanical 
properties of the composite ply should be decreased to a very low value 
but non-zero to prevent numerical errors, as shown in Table 1. More-
over, according to the magnitude of the applied stress as well as the 
stress ratio in each cycle of loading, the material properties are gradually 
degraded due to repetitive loading. Eqs. (1) and (2) are proposed for 
Fig. 2. The flowchart of the present model. 
Table 1 
Sudden death rules for stiffnesses and Poisson’s ratio of composite ply. 
Modes of failure Stiffnesses and Poisson’s ratio 
Fiber Tension or 
Compression 
[Exx, Eyy, Exy, νxy] → [0.001*Exx, 0.001* Eyy, 0.001*Exy, 
0.001*νxy] 
Fiber-Matrix Shearing [Exx, Eyy, Exy, νxy] → [Exx, Eyy, Eyy, 0.001*Exy, 
0.001*νxy] 
Matrix Tension or 
Compression 
[Exx, Eyy, Exy, νxy] → [Exx, 0.001* Eyy, Exy, νxy] 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
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calculating the gradual degradation of stiffness and strength in each 
cycle of life, respectively [27,28]. 
E(n, σ, κ) =
⎡
⎣1 −
(
log(n) − log(0.25)
log(Nf ) − log(0.25)
)λ
⎤
⎦
1/γ
(Es −
σ
εf
)+
σ
εf
(1) 
R(n, σ, κ) =
⎡
⎣1 −
(
log(n) − log(0.25)
log(Nf ) − log(0.25)
)β
⎤
⎦
1/α
(Rs − σ)+ σ (2) 
where E, R, and n are the stiffness, strength, and number of the cycle, 
respectively. Also, k is the stress ratio, Es is the static stiffness, Rs is the 
static strength, εf is the static strain to failure, and α, β, λ, and γ are the 
material constants which are determined using the experiments. More-
over, Nf is the predicted life, which is calculated by the life assessment 
part of the PFD model. 
2.2. Self-heating phenomenon 
Due to the viscoelastic nature of the polymeric matrix, a self- 
temperature rise occurs in the host laminated composites under fa-
tigue loading. In this section, the generated-dissipated energy (GDE) 
model, developed by the present authors [22], was employed to predict 
the temperature rise during cyclic loading. The main parts of this model 
are briefly explained as follows. 
2.2.1. Viscoelastic energy 
The generated energy in laminated composites due to the viscoelastic 
nature of the polymeric matrix in each cycle of fatigue loading is 
calculated by Eq. (3) [29]. 
Egenerated = ε0σ0
πsinδ
4
(3) 
where σ0, ε0, and δ0 are the applied stress, applied strain, and lag-phase 
of the polymeric matrix, respectively. It should be mentioned that the 
magnitude of δ is determined by dynamic mechanical analysis (DMA) 
testing of the polymer. 
2.2.1.1. Dissipated energy through heat transfer mechanisms. To calculate 
the dissipated heat energy, the convection and conduction heat transfer 
mechanisms are considered. Eqs. (4) and (5) are employed to calculate 
the heat convection and conduction for the laminated composites, 
respectively. 
Econvection = hA(Ts − T∞) (4) 
where h is the heat convection coefficient between the air and the 
laminated composites, A is the summation of the area of the lateral 
surfaces of the specimen, Ts is the surface temperature of the specimen, 
and T∞ is the ambient temperate. 
Econduction = 2kA
dT
dx
(5) 
where k is the heat conduction coefficient of the laminate composites, A 
is the cross-section area of the specimen and dT
dX is the temperature 
gradient in the composite specimen. 
2.2.1.2. Temperature rise. After calculating the generated and dissi-
pated energies, the variation in the internal energy is calculated by 
applying the first law of thermodynamics on the laminated composites 
as follows: 
ΔU = Egenerated − (Econvection + Econduction) (6) 
Finally, the temperature rise in each cycle is calculated by Eq. (7): 
ΔT =
ΔU
mc
=
ΔU
ρVc
(7) 
where m is the mass, ρ is the density of the material, V is the volume of 
the laminated composites, and c is the specific heat of the material [22]. 
2.3. One-dimensional thermomechanical constitutive equation for SMAs 
When a mechanically constrained SMA wire with pre-strain is acti-
vated by heating, the wire tends to return to its initial shape and 
consequently generates recovery stress. The recovery stress in the SMA 
wire is calculated by the following equation, developed by Liang and 
Rogers [23]: 
σrec =
Y(ξ)Sres
2
{
1 − cos
[
aA(T − As) −
aA
CA
σrec
]}
(8) 
aA =
π
Af − As
(9) 
where Y(ξ), Sres, CA, T, As, and Af are the elastic modulus of the wire, the 
pre-strain level in the wire, the slope of the stress versus austenitestart 
temperature phase diagram, the applied temperature, austenite start- 
and finish-temperatures, respectively. Moreover, the elastic modulus of 
SMA wires, Y(ξ), is considered as a linear function of the martensitic 
volume fraction (ξ) according to the following equation. 
Y(ξ) = EA + ξ(EM − EA) (10) 
where EA and EM are the elastic moduli of the austenitic and martensitic 
phases, respectively. Furthermore, the martensite volume fraction of the 
wires, ξ, for the forward transformation (austenitic to martensitic state) 
and the reverse transformation (martensitic to austenitic state) are 
described by Eqs. (10) and (11), respectively. 
ξ =
1 − ξ0
2
cos
[
π
Ms − Mf
(
T − Mf −
σ
CM
)]
+
1 + ξ0
2
(11) 
ξ =
ξ0
2
{
cos
[
π
Af − As
(
T − As −
σ
CA
)]
+ 1
}
(12) 
where martensitic volume fraction at the beginning of the trans-
formation, the slope of stress versus martensitic start temperature phase 
diagram, and the martensitic start and finish temperature are denoted by 
ξ0, CM, Ms, and Mf, respectively. 
2.4. Modeling procedure 
The in-plane stresses were calculated cycle-by-cycle using the CLT 
method. According to the proposed model by Hahn and Tsai [30], 
nonlinear stress–strain behavior for in-plane shear is considered for this 
analysis. Besides, the bridging micromechanical model [31] is used to 
calculate stresses and strains in the host laminated composites and SMA 
wires for calculating the viscoelastic energy and mechanical behavior of 
SMA wires in each loading cycle. To this end, laminated composite (fiber 
and matrix) was considered as the first component, and the wire was 
considered as the second component. Furthermore, the calculated re-
covery force of the SMA wires is considered for the next cycle and is 
subtracted from the total applied load to the SMA-embedded laminated 
composites. 
3. Experiments 
3.1. Materials 
The laminated composite samples were fabricated from carbon fibers 
(T300 12 K, 200 g/m2) and epoxy resin (ML-506 Bisphenol F) hardened 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
5
by HA-11 (Polyamine) with an 85:15 wt fraction according to the 
manufacturer datasheet. The embedded SMA wires were NiTi type SMA 
with a diameter of 0.4 mm supplied by HLMET Co. 
3.2. Fabrication of specimens 
For embedding SMA wires within the laminated composites, a fixture 
was fabricated. The fixture consists of a base plate and two mobile comb- 
shaped holders for griping the wires in pre-determined positions. The 
required pre-strain level was first applied to the SMA wires using a 
tensile machine. Afterward, the wires were wrapped up between the 
grips, and the laminated composite plates were fabricated and then 
placed on the top and bottom of the wires, as demonstrated in Fig. 3. The 
prepared laminated composite plates were cured at ambient tempera-
ture for 7 days. Finally, according to the ASTM D3039 standard, lami-
nated composite plates were cut into 250 × 25 mm specimens using a 
diamond saw. 
3.3. Mechanical tests 
Three categories of experiments were performed in the present 
research to validate the model: 
1. Material characterization tests: The first category of tests consists of 
both static and fatigue experiments performed for mechanical 
characterization of composite specimens to obtain material proper-
ties of the unidirectional ply. 
2. Ultimate tensile strength (UTS) tests: In the second category of tests, 
laminated composite specimens with/without SMA wires were sub-
jected to static tensile tests. 
3. Fatigue tests: In the third category of the experiments, laminated 
composite specimens were subjected to fatigue tests. 
The static tensile and fatigue tests were performed by the SANTAM 
SAF-50 machine, equipped with hydraulic grips. All fatigue tests were 
accomplished at a frequency of 5 Hz under tension–tension mode with a 
stress ratio of 0.1. Each condition was tested with three times repetition. 
Moreover, FLIR C2 infrared thermography camera with a temperature 
range of − 10 ◦C to 150 ◦C, a resolution of 65 × 85 pixels, a sensitivity/ 
NEDT (noise equivalent differential temperature) of 0.1 ◦C, and accu-
racy of ±2% was used to record the surface temperature of the speci-
mens during the experiments. Fig. 4 shows the employed experimental 
setup for fatigue test and temperature monitoring. 
The static and fatigue tests were performed on carbon/epoxy lami-
nated composites with/without SMA wires to validate the results of the 
proposed model. Effects of different parameters including, layups, stress 
levels, volume fraction (VF) of SMA wires, and the magnitude of pre- 
strain in SMA wires on the fatigue behavior of laminated composites 
are considered. Table 2 presents the test matrix of the conducted 
experiments. 
Fig. 3. The fixture for embedding SMA wires in laminated composites (a) 
alignment of wires (b) laminated composites with embedded wires. 
Fig. 4. Experimental setup for fatigue test and temperature-rise monitoring. 
Table 2 
The test matrix of the performed experiments. 
Test 
Category 
Type of 
experiment 
Specimens Stress 
level 
SMA 
volume 
fraction 
Pre- 
strain 
level 
1 SMA 
characterization 
SMA wire, 
tensile test 
– – 0 
SMA wire, 
DSC test 
– – 0 
Polymer 
characterization 
ML-506 resin, 
DMA test 
– 0 – 
Composites 
characterization 
(static) 
Longitudinal 
tensile [04] 
– 0 – 
Transverse 
tensile [908] 
– 0 – 
Composites 
characterization 
(fatigue) 
Longitudinal 
tensile [04] 
0.60, 
0.70, 
0.80 
0 – 
Transverse 
tensile [908] 
0.60, 
0.70, 
0.80 
0 – 
2 Static Tests [0/907/ 
SMA]s 
– 0 – 
[0/907/ 
SMA]s 
– 1% 6% 
[02/906/ 
SMA]s 
– 0 – 
[02/906/ 
SMA]s 
– 1% 6% 
3 Fatigue Tests [0/907/ 
SMA]s 
0.65, 
0.75, 
0.85 
0 – 
[0/907/ 
SMA]s 
0.65, 
0.75, 
0.85 
1% 0 
[0/907/ 
SMA]s 
0.65, 
0.75, 
0.85 
1% 6% 
[02/906/ 
SMA]s 
0.65, 
0.75, 
0.85 
0 – 
[02/906/ 
SMA]s 
0.65, 
0.75, 
0.85 
1% 6% 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
6
4. Result and discussion 
4.1. Result of material characterization tests 
The characterization experiments were performed based on the test 
matrix, shown in Table 2, and the results were presented in the 
following. 
4.1.1. Characterization of SMA wires 
To characterize the transformation temperatures of the SMA wires, 
the DSC experiment was performed according to the ASTM F2004 
standard. The differential scanning calorimetry (DSC) test was con-
ducted at a rate of 10 ◦C/min (Mettler-Toledo, LLC, Switzerland) be-
tween − 20 ◦C and 120 ◦C. Moreover, mechanical tensile tests on SMA 
wires were also performed according to ASTM F2516 standard with a 
0.3 mm/min rate. The results of the DSC and tensile tests on SMA wires 
are presented in Table 3. 
4.1.2. Characterization of polymer 
The dynamic mechanical analysis (DMA) experiment was conducted 
according to the ASTM E1640 standard for the host polymer (ML-506) at 
the frequency of 5 Hz. The test was operated in tensile mode, specimen 
size was 20 × 10 × 3 mm, and the temperature range was 20 to 110 ◦C. 
Fig. 5 depicts the variation of the storage modulus (E’) and loss factor 
(E“) for the polymer as a function of the applied temperature. 
4.1.3. Characterization of unidirectional composites 
Longitudinal tensile, transverse tensile, and shear experiments were 
performed on the composite specimens to obtain their strengths and 
moduli. Table 4 presents the mechanical properties of composite 
specimens. 
Moreover, according to the test matrix, shown in Table2, fatigue 
characterization experiments were also performed on composite speci-
mens. Fig. 6 presents the fatigue life (S-N diagram) for composite 
specimens in the longitude direction, transverse direction, and in-plane 
shear loading. 
The gradual stiffness degradation parameters (λ and γ in Eq. (1)) and 
strength degradation parameters (α and β in Eq. (2)) for the longitudinal 
Table 3 
The SMA wires properties. 
Elastic 
properties 
(GPa) 
Transformation 
temperatures (℃) 
Transformation constants 
(MPa/℃) 
EM = 20.78 Mf = 16, Ms = 23 CM = 21.74 
EA = 42.00 As = 28, Af = 45 CA = 29.00 
Fig. 5. Storage (E’) and loss (E“) moduli of ML-506 at a frequency 5 Hz [22]. 
Table 4 
Mechanical characterization of T300/ML-506 [22]. 
Magnitudes Denoted by Parameter 
82 GPa Ex Tensile modulus 
4.9 GPa Ey Transverse modulus 
6.2 GPa Exy In-plane shear modulus 
0.3 νxy Poisson’s ratio 
860 MPa Xt Tensile strength 
18.2 MPa Yt Transverse strength 
64 MPa Sxy In-plane shear strength 
1.204E-8 MPa− 3 α Nonlinearity coefficient 
0.25 mm tply Ply thickness 
65% vf Fiber volume fraction 
Fig. 6. The S-N curve of T300/ML-506 with an R-ratio of 0.1 [22]. 
Table 5 
The stiffness and strength degradation constants for T300/ML-506 [22]. 
Loading λ γ α β 
Longitudinal 1.611 0.757 5.615e-05 669.3 
Transverse 1.561 0.6547 9.6287 0.1255 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
7
direction and transverse directions are presented in Table 5. 
4.2. Results of static tensile tests 
According to the test matrix shown in Table 2, the effect of the 
embedded SMA wires on the UTS of laminated composites was studied. 
The obtained results of the conducted static tests on composite speci-
mens with standard deviation (STD) are shown in Table 6. It can be 
declared that because of the low volume fraction of the embedded SMA 
wires in the present study, embedding SMA wires in laminated com-
posites has neither a strengthening nor weakening effect on the UTS of 
laminated composites. 
Table 6 
The static strength of laminated composites with/without embedded SMA wires. 
Layup Tensile strength (MPa) (STD) 
[01/907]s 116.33 (7) 
[01/907]s with 1% VF SMA 117.66 (6) 
[02/906]s 216.66 (11) 
[02/906]s with 1% VF SMA 213.00 (13) 
Fig. 7. S-N curves for [01/907]s layup (a) laminated composites without SMA (b) laminated composites with SMA wires (VF = 0.01), without pre-strain (c) laminated 
composites with SMA wires (VF = 0.01), with 0.06 pre-strain, (d) experimental data. 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
8
4.3. Assessment of the present model and case studies 
4.3.1. Model assessment 
To examine the validity of the present model, a series of fatigue tests 
were conducted on laminated composites with [01/907]s Fig. 7 com-
pares the results of the present model and experimental data for [01/ 
907]s laminated composites with/without embedded SMA wires. As 
shown in this figure, good agreement between the experimental and 
theoretical results is obtained. 
For a better comparison, the results of the present model and ex-
periments for [01/907]s composites were summarized in Table 7. Both 
the experimental data and results of the present model confirm that 
embedding the SMA wires in the host laminated composites increases 
the fatigue life of [01/907]s composite specimens at the three stress 
levels. It should be noted that by embedding non-pre-strained wires in 
laminated composites, according to Eq. (8), no recovery force is gener-
ated. Therefore, only the PS effect of wires, which cause dissipating 
energy, improves the fatigue life. While, for the cases with 0.06 pre- 
strain, as well as the dissipating energy, a compressive force is also 
generated that decreases the damage propagation rate of the host 
laminated composites and consequently increases the fatigue life. As 
shown in Table 7, it is clear that employing the pre-strained wires, due to 
the simultaneous existence of the PS and SM effects, a better improve-
ment in fatigue life was observed in the comparison of that of the non- 
pre-strained wires that just present the PS effect. 
4.3.2. Recovery force in SMA wires 
Using the present model, a detailed study on the recovery force in 
SMA wires embedded in [01/907]s laminated composites was per-
formed. Fig. 8 shows the generated recovery force by SMA wires in 
laminated composites at stress levels of 0.65 and 0.85. As shown in this 
figure, the evolution trend of the generated recovery force at a stress 
level of 0.85 (red curve) proceeds in a two-step behavior. At the first few 
cycles of life, the magnitude of the generated recovery force by SMA 
wires shows a fast decrease, and then it increases fast for the remaining 
part of the life. However, the generated recovery force in SMA wires at a 
stress level of 0.65 (blue curve) has a five-step behavior. At the first few 
cycles of life, the magnitude of the generated recovery force by SMA 
wires shows a very slow decrease, followed by a fast increase, then a 
sharp fall, again followed by a sharp increase, and after that a slow in-
crease for the remaining part of the life. 
The above-mentioned trends can be justified by using the present 
model and evaluating the stiffness degradation of the host laminated 
Table 7 
The results of the present model and experiments for [01/907]s composites. 
Stress 
level 
Mean value of experimental 
fatigue life (STD) 
Predicted fatigue life 
by the model 
Improved fatigue life by 
experiments (%) 
Improved fatigue life 
predicted by the model (%) 
Without SMA 0.65 91,070 (28840) 85,140 – – 
0.75 15,320 (7770) 13,710 – – 
0.85 1470 (260) 1310 – – 
With SMA wires (VF = 0.01), 
without pre-strain 
0.65 124,700 (59260) 120,880 36 41 
0.75 19,310 (8530) 18,240 26 33 
0.85 1730 (770) 1700 19 28 
With SMA wires (VF = 0.01), 
with 0.06 pre-strain 
0.65 148,400 (65060) 133,690 62 57 
0.75 22,530 (8120) 19,610 47 43 
0.85 1990 (910) 1750 35 33 
Fig. 8. The generated recovery force of SMA wires in [01/907]s lami-
nated composites. 
Fig. 9. Fatigue behavior of [01/907]s laminated composites at the stress level of 0.85 (a) stiffness degradation (b) self-heating phenomenon. 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
9
composites (that changes the applied stress on SMA wires) and the self- 
temperature rise phenomenon. For instance, the results of the model 
show that at the same number of cycles of the sharp fall (blue color 
curve), the 90-degree layers failed. Therefore, the sharp fall is due to the 
failure of 90-degree layers. The other trends can also be justified by the 
model, but to avoid the lengthening are not mentioned here. 
4.3.3. Stiffness degradation and self-heating phenomenon 
Fig. 9a and b show the longitudinal stiffness degradation and self- 
heating phenomenon for [01/907]s laminated composites at a stress 
level of 0.85, respectively. As shown in Fig. 9a, a fast longitudinal 
stiffness degradation occurs during the first cycles. This fast degradation 
increases the applied stress on SMA wires. According to Eq. (8), it results 
in a decrease in the amount of the generated recovery force. While, at 
the same time, the temperature of the laminate is rising due to the 
viscoelastic behavior of the polymeric matrix (see Fig. 9b). This self-temperature rise, according to Eq. (8), increases the generated recov-
ery force by the wires. By increasing the fatigue cycles, the stiffness 
degradation rate decreases significantly (the slope of the curves in 
Fig. 9a), and the effect of the self-temperature rise increases the 
magnitude of the generated recovery force. It should be noted that ac-
cording to Ref. [32], SMA wires do not exhibit considerable self-heating 
behavior during cyclic loading. Hence, the viscoelastic nature of the 
polymeric matrix is the major reason for the temperature variation in 
laminated composites with embedded SMA wires. The idea of using self- 
heating temperature rise of laminated composites to activate SMA wires 
is practical in laboratory-controlled conditions. However, in real cases 
for operational structures, wires can be activated by using external 
sources, such as electrical or thermal excitations. 
Fig. 10a and b show the longitudinal stiffness degradation and self- 
heating phenomenon [01/907]s laminated composites at a stress level 
of 0.65. In comparison with the case of the stress level of 0.85 (Fig. 9b), 
for the case of the stress level of 0.65 (Fig. 10b), the self-heating 
Fig. 10. Fatigue behavior of [01/907]s laminated composites at the stress level of 0.65 (a) stiffness degradation (b) self-heating phenomenon. 
Fig. 11. The applied stress on SMA wires embedded in [01/907]s lami-
nated composites. 
Fig. 12. S-N curves for [02/906]s laminated composites (a) without SMA (b) with SMA wires (VF = 0.01), and 0.06 pre-strain. 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
10
phenomenon starts faster. Therefore, more enhancement in the fatigue 
life of [01/907]s laminated composites, in comparison with that of [02/ 
906]s laminated composites were obtained. 
4.3.4. Applied stress on SMA wires 
Fig. 11 shows the applied stress on SMA wires in [01/907]s laminated 
composites. As illustrated in this figure, under cyclic loading, the applied 
stress to SMA wires was increased as a result of the stiffness degradation 
of the composites. Also, a jump on the curve of the cases with the stress 
level of 0.65 happened, which is due to the 90-degree plies failure. 
Fig. 11 shows the good capability of the present model in revealing the 
detailed mechanisms of failure which cannot be easily observed by 
experiments. 
4.3.5. Effect of the layup of laminated composites 
The fatigue behavior of [01/907]s laminated composites was studied 
in detail in the previous section. In here, for considering the effect of the 
layup of the host laminated composites on the results, [02/906]s lami-
nated composites were subjected to fatigue tests at three different stress 
levels. Fig. 12a and b present the experimental and theoretical results of 
the specimens with and without embedded SMA wires. Table 8 sum-
marizes the results of the present model and experimental data of [02/ 
906]s laminated composites. By comparing the results obtained for [01/ 
907]s and [02/906]s laminated composites, it can be concluded that 
embedding SMA wires in [01/907]s laminated composites leads to better 
enhancement in fatigue life at both stress levels of 0.65 and 0.85. The 
magnitude of stiffness of [02/906]s laminated composites is higher than 
that of [01/907]s laminated composites. Therefore, the ratio of the 
stiffness of SMA wires to the stiffness of [01/907]s laminated composites 
is higher. It means that SMA wires are more effective in improvement of 
the fatigue life of laminated composites with lower stiffness. 
4.3.6. Effect of some other parameters 
In this section, the effects of SMA pre-strain, modulus, and volume 
fraction (Vf) of SMA wires on the fatigue life of [01/907]s layup are 
evaluated. Table 9 exhibits the modeling results for the aforementioned 
factors. The studied cases were consisted of decreasing the magnitude of 
pre-strain from 0.06 to 0.02, increasing the VF of SMA wires from 0.01 to 
0.04, and increasing the SMA wires modulus by 1.5 times. It is deter-
mined that variation in Vf of SMA wires has a significant effect on the 
fatigue life improvement so that by embedding more SMA wires, fatigue 
life improvement increases dramatically for both load levels considering 
in this study. For this case, for example, by increasing the Vf of SMA 
wires to 0.04, at the loading level of 0.65 and 0.85 UTS, the life 
improvement increases by 372% and 168%, respectively. 
5. Summary and conclusion 
In the present research, an experimental program was conducted to 
study the fatigue behavior of the carbon/epoxy laminated composites 
with/without embedded SMA wires. Also, a novel model was developed 
to simulate the fatigue behavior of laminated composites with 
embedded SMA wires. The present model was developed by integrating 
three submodels a) the PFD model for predicting the fatigue behavior of 
the host laminated composites, b) the GDE model to simulate the self- 
temperature rise in laminated composites, and c) the Liang and Rogers 
nonlinear thermomechanical constitutive model for prediction of the 
mechanical behavior of SMA wires. 
Then, the present model was verified by conducting an experimental 
program on carbon/epoxy composites with/without SMA wire for [01/ 
907]s and [02/908]s layups at different fatigue stress levels (0.65, 0.75, 
and 0.85), 0.01 vol fraction of SMA wires, and 0.06 pre-strain induced in 
SMA wires. The results show that: 
• The ratio of the stiffness of SMA wires to the stiffness of the host 
laminated composites plays a critical role in the fatigue life 
improvement of laminated composites. By increasing this ratio, both 
PS and SM effects (dissipating a part of the applied energy and 
generating a recovery force) of embedded SMA wires are enhanced. 
• By embedding the SMA wires in [01/907]s laminated composites 
with 0.01 VF of SMA, and 0.06 pre-strain, at stress levels of 0.65 and 
0.85, the fatigue life was improved by 62% and 35%, respectively. 
• By embedding the SMA wires in [02/906]s laminated composites 
with 0.01 VF of SMA, and 0.06 pre-strain, at stress levels of 0.65 and 
0.85, the fatigue life was improved by 23% and 12%, respectively. 
• Embedding of SMA wires in laminated composites with lower stiff-
ness and strength causes a greater improvement in fatigue life. It 
means that the magnitude of generated recovery force by the 
embedded wires becomes more effective. 
• A good agreement between theoretical and experimental results 
revealed the ability of the present model in predicting the fatigue 
behavior of laminated composites with embedded SMA wires. 
Declaration of Competing Interest 
The authors declare that they have no known competing financial 
interests or personal relationships that could have appeared to influence 
the work reported in this paper. 
Acknowledgments 
The authors would like to thank the Iran National Science Founda-
tion (INSF) for the Grant numbers 97024007 and 98005981. 
Table 8 
The results of the present model and experiments for [02/906]s composites. 
Stress 
level 
Mean value of experimental 
fatigue life (STD) 
Predicted fatigue life by 
the model 
Improved fatigue life by 
experiments (%) 
Improved fatigue life by 
the model (%) 
Without SMA 0.65 209,100 (67520) 253,340 – – 
0.75 32,530 (9260) 31,730 – – 
0.85 3520 (1580) 3940 – – 
With SMA wires (VF = 0.01), 
with 0.06 pre-strain 
0.65 256,900 (64260) 298,700 23 18 
0.75 37,980 (17030) 36,030 17 13 
0.85 4010 (1720) 4270 12 9 
Table 9 
Influence of the SMA wire pre-strain, Vf of SMA wire, and modulus on fatigue life 
of [01/907]s layup. 
Stress 
level 
(UTS( 
Life 
(cycles) 
Life by 
decreasing SMA 
wire pre-strain 
(from 0.06 to 
0.02) 
Life by 
increasing VF of 
SMA wire (from 
0.01 to 0.04) 
Lifeby 
increasing 
SMA wire 
modulus 
(SMA 
modulus £
1.5) 
0.65 133,690 132,010 623,940 189,060 
085 1750 1730 4630 2240 
A.H. Mirzaei et al. 
Composite Structures 293 (2022) 115753
11
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	Fatigue behavior of laminated composites with embedded SMA wires
	1 Introduction
	2 Theoretical model
	2.1 The progressive fatigue damage model
	2.1.1 Stress calculation
	2.1.2 Failure analysis
	2.1.3 Material properties degradation
	2.2 Self-heating phenomenon
	2.2.1 Viscoelastic energy
	2.2.1.1 Dissipated energy through heat transfer mechanisms
	2.2.1.2 Temperature rise
	2.3 One-dimensional thermomechanical constitutive equation for SMAs
	2.4 Modeling procedure
	3 Experiments
	3.1 Materials
	3.2 Fabrication of specimens
	3.3 Mechanical tests
	4 Result and discussion
	4.1 Result of material characterization tests
	4.1.1 Characterization of SMA wires
	4.1.2 Characterization of polymer
	4.1.3 Characterization of unidirectional composites
	4.2 Results of static tensile tests
	4.3 Assessment of the present model and case studies
	4.3.1 Model assessment
	4.3.2 Recovery force in SMA wires
	4.3.3 Stiffness degradation and self-heating phenomenon
	4.3.4 Applied stress on SMA wires
	4.3.5 Effect of the layup of laminated composites
	4.3.6 Effect of some other parameters
	5 Summary and conclusion
	Declaration of Competing Interest
	Acknowledgments
	References