Composite Structures 299 (2022) 116053
Contents lists available at ScienceDirect
Composite Structures
journal homepage: www.elsevier.com/locate/compstruct
Numerical and predictive analysis of the low-velocity impact response of
UD composite plate under a controlled environment
K. Zouggar a, *, K. Guerraiche b, c, A. Lousdad a
a
Laboratory of Mechanics of Structures and Solids (LMSS), Mechanical Engineering Department, Faculty of Technology- Djillali Liabès University of Sidi Bel-Abbès, BP
89, Cité Ben M’hidi, Sidi Bel-Abbés 22000, Algeria
b
Mechanical Engineering Department, Faculty of Technology, University of Batna 2, Algeria
c
NMISSI Laboratory, Faculty of Science and Technology, Biskra University, BP 07000 Biskra, Algeria
A R T I C L E I N F O
A B S T R A C T
Keywords:
A. Laminates
B. Impact behaviour
C. Finite element analysis (FEA)
Design of experiments (DOE)
The present paper proposes an investigation and analysis study of a low velocity impact on a unidirectional S2Glass/Polyester composite plate subject to a controlled environment. A set of simulations of low velocity impact
on unaged and aged samples in a bending configuration were carried out. A mass diffusion is studied in order to
use its outputs as a predefined field which will be combined with the velocity of the impact loads. The diffusive
and mechanical responses, such as moisture concentration, the effect of temperature, energy dissipation and
impact force are highlighted and analysed. To ensure the validity of the finite element model, a comparison study
has been carried out and compared against experimental investigation founded in the literature. The adopted
finite element model performance for the low velocity impacted composite plate under hygrothermal conditions
strongly matches with the experimental findings and represents a clear improvement of the model. The impact of
the moisture concentration on recorded contact force and energy is highlighted, particularly the delayed contact
time and the reduction of the contact forces and the recorded energies intensity. Accordingly, two main factors
have affected the contact force responses. These two factors are the drop height and the humidity concentration.
An analysis of the maximum contact forces using the design of experiments (DOE) is performed. The effect of
both factors namely, the drop height and the humidity concentration, on the response is highlighted as well as
the effect of their interaction. The predictive model is highly effective and eases the reproducibility of other
mechanical responses.
Acronyms and abbreviations
F.E.M
Finite Elements Methods
BCs
Boundary conditions
Conc
Concentration
RH
Relative Humidity
SQRT
Square Root of Time
NLCF
Non-Linear Curve Fit
IMP
Impact
Num
Numerical
EXP
Experimental
D.O.E
Design of Experiments
Symbols Physical quantity (Unit)
V
Velocity (m/s)
H
Drop height (m)
Ei
Fi
k
h
E11
E22
E33
G12
G13
G23
+
σ1
σ1
−
σ2
σ 12
ν12
−
* Corresponding author.
E-mail address: zouggarkamel.zk@gmail.com (K. Zouggar).
https://doi.org/10.1016/j.compstruct.2022.116053
Received 2 January 2022; Received in revised form 1 July 2022; Accepted 4 August 2022
Available online 10 August 2022
0263-8223/© 2022 Elsevier Ltd. All rights reserved.
Energy (J)
Contact Force (N)
Slope
thickness (mm)
Young’s modulus in X-direction (MPa)
Young’s modulus in Y-direction (MPa)
Young’s modulus in Z-direction (MPa)
Shear modulus in XY- plane direction (MPa)
Shear modulus in XZ- plane direction (MPa)
Shear modulus in YZ- plane direction (MPa)
Tensile strengths in X-direction (XT) (MPa)
Compressive strengths in X-direction (XC) (MPa)
Compressive strengths in Y-direction (YC) (MPa)
Transverse to fibre direction shear strengths (S12) (MPa)
Poisson’s ratio modulus in XY- Plane direction
K. Zouggar et al.
ν13
ν23
Ki (i=1:3)
αi (i=1:3)
Composite Structures 299 (2022) 116053
Poisson’s ratio modulus in XZ- Plane direction
Poisson’s ratio modulus in YZ- Plane direction
Thermal conductivity coefficients in the three directions
◦
(XYZ)W/mm. K
Thermal expansion coefficients in the three directions (XYZ)
of subroutine developed under ABAQUS especially designed by the au­
thors (see Annex A). The investigation is conducted following three main
phases.
A numerical modelling of the moisture diffusion is performed in the
first standard step. The data collected during this step are injected as
predefined fields in a second explicit simulation where a validation of
the impact at low velocity is performed. The obtained numerical results
of the energies, the contact forces, and those found experimentally by
Boukhoulda et al. [15] on aged and dry plates under environmental
effects are compared and analysed. Finally, the results of the numerical
contact force are injected in MODDE 12 software [20,21] to establish a
DOE analysis to reveal the most influencing parameters and setting a
mathematical model which governs the contact force in the domain
studied. To serve the purpose of the present work, the paper has been
divided into three main sections. the first section describes the mathe­
matical formulation of the moisture loads and diffusion mechanism. Sec.
3 proposes a full description on the numerical implementation meth­
odology while Sec. 4 provides a complete analysis and interpretation of
the outcomes. The last Sec highlights the paper contributions and
conclusions.
1/ K
Volumetric fraction of fibres (%)
Density (g/mm3)
◦
υf
ρ
1. Introduction
In the last few years there has been a noticeable growing interest in
using bonded fibre reinforced polymer composites in different industrial
and constructions sectors such as in mechanical, aeronautics, automo­
tive and civil engineering to name a few [1,2]. Composite materials
bring many solutions to designers and manufacturers but also cause
many problems. For sustainable and light constructions, glass fibre
polyester composites (GFP) are used as beams and columns in structural
engineering. However, the composites interact with environmental
conditions and climate variations such as moisture and temperature
which compromise their performance [3,4].
Several experimental research investigations have been directed to­
ward the performance longevity of the GFP under environmental con­
ditions [5–8]. Unfortunately, to the present date, the effects of extreme
environmental conditions on the composite bonded layers are not yet
well understand, such as water soaking, freeze–thaw cycles or harsh
exposure to moisture [9].
GFP longevity under exposure to moisture is regulated primarily by
the rate of water and noxious ion that penetrates the material [4,10].
The bonded layer interfaces and the constituents of the material are
vulnerable to water aggressiveness. Therefore, the necessity of under­
standing the effect of the moisture diffusion in the GFP is primordial. It is
factual that, the absorbed moisture in glassy polymers acts like a plas­
ticizer, leading to the polymer expansion and thus decreasing the tran­
sition temperature of the polymer [11]. The absorbed moisture in a
substance will cause a hygrothermal stress. Cumulative hygrothermal
aging damage in the microstructure is manifested by the decrease in
mechanical properties and loss of the material capability at the macro
scale [2,12,13]. Thus, the effect of moisture diffusion on the hygro­
thermal stress has to be addressed and assessed.
Diverse techniques for modelling the phenomenon of moisture
diffusion in the GFP sheet/plate or in the bonding of GFP layers have
been proposed by the research community. Accordingly, it was shown
that the results are complex to be translated into subsequent analysis
through simulations [14]. Quite recently, considerable attention has
been given to the study of the effect of these environmental parameters
on choc absorption to perform a structural health monitoring and safety
conditions [8,15–17]. The authors opinions those researches are made
on the low-energy response of composite materials under controlled
hygrothermal setting seems to be very restricted. The combination be­
tween moisture stresses and contact force leads to multiple damage
mechanisms such as the cracking of the matrix and/or delamination
within the composite material [7,18]. These cumulative damages alter
the service life of these materials. For a more in-depth view of the
phenomenon Reis and, Neto [19], analysed the evolution of the
maximum impact load and the impact restored energy under controlled
environment. They observed that thermal aging promotes lower impact
strength until the failure of the laminate.
To the best knowledge of the authors there is no trustful numerical
model that really simulate the impact under hygrothermal conditions.
To this end, the present paper aims to simulate and analyse the effect of
the hygrothermal conditions on the recorded contact force for the case of
composite plate, made of S2-Glass/Polyester, subjected to low velocity
impact. This is carried out using both Standard and Explicit schemes.
The implantation of the proposed analysis has been carried out with help
2. Moisture loads
The diffusive phenomena are treated in a way analogous to thermal
conduction in Fourier’s first law expressed by (Eq. (1)).
(1)
J = − s⋅(D⋅∇ϕ)
where the diffusivity is expressed as:
⎤
⎡
Dxx Dxy Dxz
⎣
D(c, θ, fi ) =
Dyy Dyz ⎦
sym
Dzz
(2)
where: Dx , Dy and Dz are diffusivities through the length l , along the
(
)
width w and across the thickness h of the composite laminate.; s θ, fi =
def
1 is the solubility; ϕ= C/s is the normalized concentration; fi are any
predefined field variables.
Typically, the diffusion and uptake of the moisture in a polymer
matrix composite are supposed to follow Fick’s second law of diffusion.
In the case of an orthotropic composite, diffusion coefficient is given by
the following relationship:
√̅̅̅̅̅̅
√̅̅̅̅̅̅ )2
(
h Dy
h Dz
D(h, ℓ, w) = Dx 1 +
+
ℓ Dx w Dx
(3)
Most evaluations regarding moisture distributions in composites
consider that fibres are impermeable to moisture. Hence, the entire
penetration of water is expected to be retained in the matrix or bound at
the interfaces [22,23]. Generally, analytical model involving a thin layer
of the thickness of h = 2e, exposed to constant C0 on the top and bottom
surfaces, is sufficient to assess the moisture concentration distribution in
the lamina. Many solutions exist for this model, the most used is given as
follows [8]:
⎧
(
)
∑∞
⎪
1
D(2n + 1)2 π 2 t
⎪
⎪ M(t) = 1 − 8
exp
⎪
⎪
⎨ M∞
4e2
π2 n=1 (2n + 1)2
(4)
⎪
(
)3/4
⎪
⎪
M(t)Approximately
Dt
⎪
⎪
≅
1 − exp − 7.3 2
⎩
M∞
4e
Here, M(t) is the percent mass gain of the specimen and describes the
total mass entering as a function of time. M∞ is the moisture equilibrium
content. Diffusivities in this model are expressed as a calibrated diffu­
sivity. It is observed that Fickian modelling considers the GFRP as an
isentropic material and assumes that there is no volume change due to
the fluid adsorption.
2
K. Zouggar et al.
Composite Structures 299 (2022) 116053
The plot of the function (Eq. (4)) presents a single-phase Fickian
diffusion model. In which, it is observed that the moisture level increases
linearly with respect to the square root of time, then progressively de­
creases until becoming asymptotic in equilibrium [8]. When analysing
diffusivity phenomena, it is essential to know how to deal with the
resulting moisture loads. The calculation process of these variables is
presented as follows [16,24,25]:
Δm(z) = Δmck + z⋅Δmzk
(5)
⎧
⎪
ΔmBottom
− ΔmTop
⎪
k
k
⎪
Δmzk =
⎪
⎪
⎪
zk − zk− 1
⎪
⎪
⎪
⎪
⎪
⎨
where Δmck = ΔmTop
− zk− 1 ⋅Δmzk
k
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
)
1(
⎪
⎪
⎩ Δmmid
= Δmzk + ΔmTop
k
k
2
(6)
flexural strains [18].
3. Numerical modelling procedures
The simulated model is performed in two main phases: in the first
phase a standard analysis of the moisture diffusion was executed in
order to calculate the moisture concentration in terms of ‘Conc’. After­
wards, all the obtained results are injected as a predefined field load
input in an explicit hygro-mechanical analysis which contains a velocity
load. To this end, a user subroutine VUMAT is implemented based on the
well-known 3D_Hashin damage criterion [26–28]. The failure indexes
existing through this criterion are applied, to both fibre and matrix
failures and cover four possible failure modes listed as bellow:
1 Tensile fibres failure for σ11 ≥ 0:
(
)
{
σ11 2 σ 212 + σ 213
⩾1 failure
+
=
(10)
2
+σ
< 1 no failure
S12
1
Combining (Eq. (5)) and (Eq. (6)), the equivalent moisture forces and
moments are determined as:
(
2 Compressive fibres failure for σ11 < 0.
{
)
σ11 2
⩾1 failure
=
− σ
< 1 no failure
1
3. Tensile matrix failure for σ22 + σ33 > 0
{
(σ 22 + σ 33 )2 σ 223 − σ22 σ 33 σ212 + σ213
⩾1 failure
+
+
=
2
2
− σ2
< 1 no failure
S23
S12
2
(11)
(12)
4. Compressive matrix failure for σ22 + σ33 < 0
](
)
)
−
σ2 2
σ22 + σ33
(σ 22 + σ 33 )2 σ 223 − σ22 σ 33 σ212 + σ213
− 1
+
+
+
2
2
2
−
2S23
σ2
4S23
S23
S12
{
⩾1 failure
=
< 1 no failure
[(
(7)
(13)
⎧
∑1 [ ]
⎪
⎪
⎪
AΔm =
Qij n ⋅(zk − zk− 1 )
⎪
k=1
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
1∑1 [ ]
Q ⋅(z2 − z2k− 1 )
BΔm =
⎪
2 k=1 ij n k
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎪
1∑1 [ ]
⎪
Δm
3
3
⎪
⎪
⎩ D = 3 k=1 Qij n ⋅(zk − zk− 1 )
where, σij are stress components. The tensile and compressive allowable
strengths for lamina are denoted by subscripts ( + σ i ) and ( − σi ). Based
on these relationships a VUMAT is build and implemented (see appen­
dices A).
3.1. Material and properties
(8)
In all simulations presented in this study, the configuration of both
the plates specimens and the impactor are following the procedures of
the ASTM 7136M [29]. Therefore, the dimensions of the plate are taken
to be 150 × 100 × 4.5mm3 (Fig. 1). The simulated plate is made of S2Glass/Polyester, stacked as (03 /90)S . To carry out the impact, a steel
impactor having hemispherical shape ending with 8 mm in radius / 25
mm in height of perforation is used and assigned a point inertia mass of
1.825 kg.
The material proprieties and diffusivity constants in the three pri­
mary axes are shown in Table 1. Diffusivities for unidirectional com­
posites are defined as:
Finally, the moisture strains and curvatures can be calculated from
injecting (Eq.8) in (Eq.7) as:
(9)
All the relations presented in this subsection can also be written in
terms of normalized in-plane and flexural stresses and midplane and
(
)
⎧
Dx = D11 1 − υf Diffusivity in parallel direction to the fibre orientation in a lamina;
⎪
⎪
⎪
⎪
√
̅̅̅̅ )
(
⎨
υf
D
Diffusivity in transverse direction to the fibre orientation in a lamina;
=
D
1
−
2
y
22
⎪
π
⎪
⎪
⎪
⎩
Dz = D33 Diffusivity through the thickness of a stacked laminate;
3
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 1. Modelling of the impact test.
3.2. Meshing techniques
Table 1
Mechanical and hygrothermal properties of S2-glass/epoxy plate.
A major goal of the mass diffusion analysis is the ability to introduce
the moisture concentration results to the hygro-mechanical step that
follows. The mesh sizes for both analyses, mass diffusion and hygromechanical, must be exactly the same in order to properly import the
results.
For mass diffusion analysis Abaqus/Standard software offers a large
library of 2D, 3D and axisymmetric solid elements [14,31]. A first-order
brick elements (type DC3D8) were chosen in this step. A convergence
study involving different element sizes has been carried out, and based
on an element size of 1 mm has been found to serve the objective of the
following analysis for both results accuracy and time cost. Globally, 30
000 elements (34 884 nodes) are used, as presented in Fig. 2. The out­
comes results data collected in this step are stored and used as a pre­
defined field input for the hygro-mechanical model. In order to perform
an hygro-mechanical analysis, well suitable element with the name of
C3D8S is used keeping the same element number.
The impactor for impact tests is with a hemispherical ending shape as
mentioned before and modelled using 6 000, R3D4 elements. It is
worthy to mention here that in order to acquire a reliable result, the
mesh is refined along the contact area between the plate and the
impactor, and a general contact algorithm is defined in this zone to take
into account their interactions (Hard contact and friction).
Properties S2-Glass/Polyester
Fibre υf
Layer thickness h
(mm)
E11 (MPa)
E22 (MPa)
E33 (MPa)
G12 (MPa)
G13 (MPa)
G23 (MPa)
ν12
ν13
ν23
α1 (K− 1)
α2 (K− 1)
α3 (K− 1)
D11 (mm2/s)
D22 = D33 (mm2/s)
3.40.10-1
5.6250.10-1
3.19141.10+4
6.64106.10+3
6.64106.10+3
2.2712.10+3
2.2712.10+3
2.1768.10+3
3.1062.10-1
3.1062.10-1
5.2172.10-1
+
+
−
−
σ1 (MPa)
σ2 (MPa)
+1.5606.10+3
+5.4916.10+1
σ1 (MPa)
σ2 (MPa)
− 8.3300.10+2
− 2.6972.10+2
+1.1286.10+2
+4.8900.10-2
+8.2692.10-3
− 2.6101.10-2
− 4.0615.10-2
+4.9691.10-2
5.5776.10-4
σ12 (MPa)
+
ε1 (%)
+
ε2 (%)
ε1 (%)
ε2 (%)
ε12 (%)
K1
(W. mm− 1 .K− 1 )
2.4876.10-5
K2
1.6634.10-4
(W. mm− 1 .K− 1 )
2.2358.10-4
K3
1.6634.10-4
(W. mm− 1 .K− 1 )
2.2358.10-4
ρ (g/mm3)
1.6048.10-3
1.53.10-5 (0.24 %); 3.45.10-5 (0.36 %);6.13.10-5 (0.48 %)
1.015.10-5 (0.24 %), 2.28.10-5 (0.36 %), 4.05.10-5 (0.48 %)
Note. 1. Three energy levels impact corresponding to three drop heights
respectively: E1 = 9J ⇔ H = 0.50m, E2 = 13J ⇔ H = 0.75m and E3 = 9J ⇔ H =
1.0m were simulated. More details of the structure, on the material and
modelling technique can be found in references [15,30].
4
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 2. Quarter model in ABAQUS for diffusion convergence analysis.
Table 2
Simulations conditions.
STEPS
Mass diffusion model
Hygro-Mechanical model
Boundaries
conditions
(BCs)
⨯Temperature field of
T = 323.15◦ K
applied to immersed
surfaces.
Loading
⨯Assignment of a
surface
concentrated flux
φ = 4930 mJ/◦ K
Simulation
time
⨯Time of immersion is
taken from the
experiments [15]
⨯Plate supports are pinned in the zdirection.
⨯ For the impactor, the z-direction is
unconstrained.
✓Ensure impactor-to-plate contact
⨯Assigning a predefined field expressed
by the impact velocity
⎞
⎛
V0.50 = 3.132
⎝ V0.75 = 3.836 ⎠m/s.
V1.00 = 4.430
✓Linking the previous step as a
predefined field
⨯Time of impact is calculated by
Contact time in experiments
number of increments
Note. 2 ⨯ All BCs and loadings are represented respectively in Fig. 1 and Fig. 2.
⨯ Since moisture equilibrium content is not dependent upon the direction of the
fibres, the equilibrium value was the same in different directions.
⨯ The scheme of simulation resolution is as presented in annex A.
3.3. Simulation conditions
Due to geometrical and loading symmetry, only a portion of the
model is modelled. In our case only, a quarter of the model was taken
into account. The principal investigation consisted of studying the
evolution of the moisture content within the composite with respect to
the duration of exposure. In order to produce accurate results similar to
Boukhoulda et al. experiments [15]. The boundary conditions must be
applied identically. The moisture penetration exposure time of 289 days
is simulated with assuming the realistic conditions of 50 ◦ C with various
values of relative humidity [RH = 20%; 40%; 90%], corresponding to
different diffusion coefficient for the mass diffusion step. For the hygromechanical step a contact time of 5.8 ms is assumed. The targeted
boundary conditions (BCs) are listed in Table.2.
4. Results and discussion
Fig. 3. Outputs of the concentrations of the simulated diffusivity models.
In the following subsections the obtained modelling and simulation
results are discussed and analysed.
Table 3
Calculated diffusion according to concentrations curves slopes.
4.1. Mass diffusion step
4.1.1. Concentration records
The simulation results of the humidity concentration in the S2-Glass/
Polyester composite plates under different environments in the midst
and external surfaces with respect to time are depicted in Fig. 3. The
5
k
Concsat (%)
D(mm2/s)
3.86.10-4
5.80.10-4
7.73.10-4
0.239
0.359
0.479
3.83.10-6
8.62.10-6
1.53.10-5
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 4. Concentration distribution in 298 days.
results can be interpretated as follow:
the separation due to the deflection.
- At first glance, the outcomes of the simulated models show a Fickian
behaviour.
- Curves of the moisture concentration evolve into two phases. Firstly,
for each humidity level, it increases linearly, forming a slope k which
is proportional to the diffusion that can be calculated as:
√̅̅̅
√̅̅̅̅
h π
D = k⋅
(14)
2⋅Concsat
- Discrepancies within the simulated and the experimented measures
are observed. This is due to the constraints in the simulated model
such as mesh size, elements type and the most important parameter:
the boundary conditions (BC’S). The error is estimated for the first
level of energy E1 to be approximately 1.43%.
- The estimated impact energy increases over the 3ms of interaction to
reach the ultimate value in the case of unaged samples. The same
evolution is observed on the aged models with a delayed time
ranging from [0.156 ∼ 0.27]ms.
- After a period of time, the curves tend to gradually approach the
equilibrium humidity concentration value.
- Results of diffusivities calculated according to equation (Eq.14) are
reported in Table.3.
- Saturation is quickly acquired after 116 days which agreed well with
the results found in the experiments [15].
The delays in time registration in respect to concentration evolution
for each energy level are illustrated on Fig. 8. A slight variation in the
modelled contact times is noticeable compared to those of experiment
[15,30]. This is due to the effects of moisture concentration on the
material strength which result in a loss of rigidity.
For energy cases E2 = 13.40J and E3 = 17.80J, the same simulation
procedures have been established in order to analyse the impact re­
sponses. Identical observations were observed (delays, slight variation
in contact time and energy…etc.). All collected data are presented in
Fig. 8.
Gaps in the recorded concentration between the midst surface and
the external surfaces at the beginning of the simulation are directly
related to the stacking of the plates, see Fig. 3 (a) and (b).
4.1.2. Moisture repartitions
Fig. 4 shows the distribution across the thickness of a modelled
sample underConcsat (%) = 0.36. As expected, in the early stages of the
simulation, the highest concentration appeared in the water contact
area. For each frame on Fig. 5, the limits are kept identical to ease the
interpretation of the concentration results. Beyond day 116, no visible
changes occur in the simulated model occur due to small variations in
concentration rates. The same findings have been established for other
humidity concentration levels.
4.2.2. In-plane computed forces
- Values of the contact force at nodes through the centre of the plates
in the two cases of aged and non-aged specimens for the first energy
level of E1 (Drop high H = 0.5m) are presented in Fig. 9(a)/(b) and
(c).
- Average of the ultimate impact forces of dry and saturated numerical
samples for energy levels E1 were compared to determine the effi­
ciency of the numerical model. It is observed that the contact forces
show the same mathematical behaviour for both models, as can be
seen in Fig. 9(d).
- The same delay is noticed as in the energy recordings on the contact
force measurements in the aged plates;
- The summary results of the impact forces measure are listed in
Table.4; it is noted that the FMax
IMP value matches with a slight dif­
ference to those obtained experimentally. The errors range for
unaged samples are [0.70 ∼ 1.14]% and for aged samples are
[1.00 ∼ 1.29]%.
- After analysis of impact phenomena under hygrothermal conditions,
it can be deduced that the adsorption can have a beneficial effect in
decreasing impact forces see Fig. 10. On the other hand, beyond a
threshold of concentration, it will lead to a disadvantage since it will
generate damage in the composite structure.
4.1.3. Temperature effects
The temperature effect on the concentrations of the modelled sam­
ples for the highest level of ingress Conc = 0.48% is recorded and
plotted on Fig. 6. It is found that increasing the temperature reduces the
time of diffusion significantly for a ratio of [7.66 ∼ 22]%. It also affects
the diffusivity which can be determined using the slope values of the
concentration curves (Eq. (14)).
4.2. Hygro-mechanical step
4.2.1. Numerical energy records
Time history of the impact energy for level E1 = 8.950J for each
concentration value is displayed in Fig. 7. The contact duration is
registered once the impactor and the laminate come into collision until
6
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 5. Progression of the concentration distribution.
7
K. Zouggar et al.
Composite Structures 299 (2022) 116053
- It is found that modelling approach represents a big advantage on the
reproducibility of experimental tests numerically without having
time restraint. For instance, the acquisition of the numerical values
of FMax
IMP in the case of the drop high of one meter.
- The averaged reductions between experiments and numerical results
are highlighted on Table.5. It can be seen that the numerical results
significantly match the experiments.
It is worth mentioning that the calculations of the reduction ratio on
Table.5 are based on the unaged values of each level, and then the error
was determined.
4.3. Design of experiments (DOE) implementation
Design of the experiments show the manner of conducting and
planning experiments in order to get the maximum amount of infor­
mation from the gathered data. In this case of study, the basic idea is to
vary all relevant factors {xi } simultaneously, such as drop high (H) and
moisture concentration values (Conc), over a set of planned experi­
ments. Thereafter, the results expressed in terms of the quantity of in­
terest y (numerical contact force) are connected by means of a
mathematical model. This model is then used for interpretation, pre­
dictions and optimization.
Both factors (H) and (Conc) are represented by a graduated and
oriented axis as shown in Fig. 11. The Design Space is established to
estimate the area of operability or robustness. The range of variation of
each factor is defined by a low level noted (-1) and a high level noted
( + 1). This arrangement permits the elaboration of the design matrix
shown in Table 6. Such a designed plan in which each of the two factors
( )
has only two levels is referred as Factorial plan of 22 .
Fig. 6. Temperature effect on diffusion case: Conc = 0.48%.
4.3.1. Mathematical model
To highlight how vary the response, according to each factor and
improve their interaction a DOE plan is established using the software
Modde 12 (Evaluation version) [21]. Central Composite Designs Face
Centred (CCF) plan is chosen [20,21]. A system of 9 equations with 6
unknowns is resolved. Thus, the following equation is obtained:
y = a0 + a1 x1 + a2 x2 + a1 2 x1 x2 + a11 x21 + a22 x22 + e
(15)
The determination of the coefficients a0 , a1 , a2 , a11 , a12 and a22 of the
model is obtained using Multiple Linear Regression (MLR) in order to
minimize the sum of squares of the residuals.
Fig. 7. Effect of moisture concentration on numerical energy recording.
4.3.2. Results of DOE investigation
4.3.2.1. Quality of predictive model. The efficiency of the predictive
model fit by examining the following plots and lists:
- The Summary of the fit R2 and Q2 represented on Fig. 12 describes
the quality and validity of the model. According to the obtained re­
sults where R2 and Q2 tend to be closer to 1 by reference to the
Analysis of Variance shown in Table 7. It is concluded that the
quality of the model predicting contact force is highly successful. All
these parameters effect plots for screening designs.
- Results shown on Fig. 13 gives a good insight on the effect of the
factors coefficients of the mathematical model. It is found that the
factor of the height of the impact is the most influential (477.2),
followed by the humidity concentration of absorbed moisture
(-108.36). Right after, the registered coefficient in terms of the
square of the height of the impact relapses to the value of (-51.1),
followed in decreasing order by the square of the humidity concen­
tration of absorbed moisture (-147.94) and, finally, by the combined
interaction effect of the height of the impact and the humidity con­
centration of moisture absorbed (4.4). All Factors coefficients
collected data are reported in Table 8.
Fig. 8. Evolution of numerical contact time in respect of moisture ingress.
8
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 9. Contact forces over contact time in z-direction (impact direction), level H = 0.5m.
9
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Table 4
Records of the maximum value of the contact forces FIMP .
H (m)
0.50
0.75
1.00
0.50
0.75
1.00
0.50
0.75
1.00
4.3.2.2. Screening of the response.
Conc (%)
FExp (N) [15]
FNum (N)
Error (%)
0.00
0.00
0.00
0.36
0.36
0.36
0.48
0.48
0.48
3209
3730
4171
3140
3702
//
3002
3500
//
3234
3772.56
4201
3177
3748.43
4146.25
3032
3543.46
3997.67
0.78
1.14
0.70
1.18
1.20
//
1.00
1.29
//
- The mathematical representation of the function given earlier in (Eq.
(11)) is presented in Fig. 14. The graphed function shows the contour
plots of the response i.e., the response surface corresponding to the
contact force as function as the two parameters “H” and “Conc”.
- The graphical representation of the model constitutes an important
and interesting part of this powerful and judicious DOE method. It
reveals that the combined effect of increasing the humidity concen­
tration absorbed and decreasing the drop height reduces the contact
force. The humidity concentration absorbed in this situation gives
the material some damping (Spongious effect) which results in a
decrease in the contact force.
- However, it is noticed that after a certain threshold of absorption
noticed when Conc ∈ [0.30 0.35]% Contact force decreases with the
increase of “Conc” for the same applied level of the impact energy.
The study findings are supported by other investigations [32,33].
The explanation of this reduction is due to the moisture absorption
that leads to the matrix swelling which will modify the residual stress
conditions imposed during composite treatment [9].
- On the other hand, the fibber/matrix interface and inter-layers re­
gion are commonly targeted by environmental attack. Generally, this
is due to the difficulties in achieving a perfect chemical bond be­
tween the fibres and matrix and layers [2,7,33,34].
4.3.2.3. Predicted force.
- On Fig. 15 the evolution of the predicted force is shown according to
each factor. The predictive model gives very close results of the
impact forces to those obtained numerically and experimentally.
Fig. 10. Maximum values of the contact forces as function as the moisture and
the energy level.
- It is observed that when the predicted contact force according to
drop height changes is stored, the contact force present linearly
evolution with this last parameter Fig. 15(a). On the other hand, the
records of the predicted contact force on Fig. 15(b) according to
“Conc” changes show a non-linear shape after a threshold of 0.40 %.
Table 5
Reduction ratio of the contact forces.
Reduction ratio
(%)
Dry values
Moisture (%)
Energy Level
Numeric
Experiments
Error (%)
Conc = 0.36 %
E1
E2
E3
E1
E2
E3
1.76
0.64
1.30
6.25
6.073
4.84
2.15
0.75
//
6.45
6.17
//
18.03 %
14.79 %
Na
3.17 %
1.52 %
Na
Conc = 0.48 %
5. Conclusion
The general conclusions of this study are summarized as follows:
- A finite element model for diffusion analysis was conducted in order
to yield the moisture concentration distribution absorbed by the
composite plates. This led to a better understanding of the diffusion
phenomenon within the material.
- Modelled samples were in good agreement with Fick’s second law; it
is clear that Fickian diffusion overestimates the concentration,
especially during the first days of the simulation.
- The concentration values for each model were compared to the
experimental findings and those values were closely matched. Unlike
the experiment, the simulation provides the concentration values at
the nodes of the symmetry plane of the plate (Fig. 3(b)). With these
data the effect of stacking on the diffusion value can be highlighted.
- The signs of the coefficients are disregarded because the importance
is on the absolute values indicating the weight of the coefficients.
Finally, the proposed model to predict the contact force and covering
both the experimental tests and numerical modelling as function as the
height “H” and the concentration of absorbed moisture “Conc” in the
design space is expressed by:
F =3817.16 + 477.189H − 108.36 Conc + 4.39(H⋅Conc) − 51.0983 H 2
− 147.938 Conc2 + e
(16)
10
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 11. Design space of experiments.
- The computed time history of the contact force acting in the axial
direction on the S2-Glass/Polyester plate is significantly in good
agreement with the experimental data in the two studied cases of
aged and a dry model.
- It is found that the absorption of the moisture leads to a decrease in
contact force which can represent an interesting result.
- However, it was seen that after a threshold of moisture the contact
force decreases with the increasing of “Conc” for the same applied
level of the impact energy.
Table 6
Design matrix.
Experience N◦
Factor 1: High(m)
Factor 2: Conc (%)
1
2
3
4
5
6
7
8
9
− 1
0
1
− 1
0
+1
− 1
0
1
− 1
− 1
− 1
+1/2
+1/2
+1/2
+1
+1
+1
From the outcome of our investigation on the application of the DOE
it is possible to conclude that:
- The proposed method permits the establishment of an analytical
model of the impact force.
- The interaction effect of the two parameters “H” and “Conc” is
illustrated.
- A significantly and robust accurate predictive model of the impact
force is exposed.
- A temperature effect was highlighted showing benefit on a reduced
diffusive time by an increase of diffusivities with a ratio
[7.66 ∼ 22]%.
- The effect of moisture on an impact at low velocity in S2-Glass/
Polyester composite laminate have been analysed using finite
element method (FEM).
Fig. 12. Descriptive quality of the model.
11
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Table 7
Analysis of Variance (ANOVA) summary.
Numerical Contact Force
DF
SS
MS (variance)
Total
Constant
Total corrected
Regression
Residual
9
1
8
5
3
N=9
DF = 3
1.21625e + 08
1.35139e + 07
1.20171e + 08
1.20171e + 08
1.45394e + 06
181,742
1.45266e + 06
290,532
1279.86
426.62
Q2 = 0.994, R2 = 0.999, R2 adj. = 0.998
F
p
SD
681.008
0.000
426.312
539.01
20.6548
Cond. no. = 5.759
RSD = 20.65
Fig. 13. Factors influencing the contact force.
Table 8
Coefficients of the factors and their interactions.
Numerical Contact Force
Constant
H
Conc
H2
Conc2
H × Conc
Coeff. SC
Std. Err.
3817.16
477.189
− 108.36
− 51.0983
− 147.938
4.39473
19.6753
8.5929
8.4322
14.6051
20.2687
9.9222
P
Conf. int (±)
-7
3.0197.10
1.2862.10-5
1.0169.10-3
3.9519.10-2
5.3102.10-3
68.781.10-2
Fig. 14. Contours of the response surface according to each level of drop high and concentration.
12
62.6160
27.3466
26.8354
46.4803
64.5043
31.5771
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Fig. 15. Predicted force as function as the influent parameters.
CRediT authorship contribution statement
Declaration of Competing Interest
K. Zouggar: Conceptualization, Methodology, Software, Validation,
Formal analysis, Investigation, Writing – review & editing, Visualiza­
tion. K. Guerraiche: Conceptualization, Methodology, Software,
Investigation, Data curation, Validation. A. Lousdad: Supervision,
Writing – original draft, Writing – review & editing.
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.
Data availability
No data was used for the research described in the article.
Appendix A
Simulations flowcharts
13
K. Zouggar et al.
Composite Structures 299 (2022) 116053
Appendix B
Time averaged concentration - python script
A python program is developed, in order to, perform post-processing tasks, Python scripts are commonly used under the Abaqus environment. For
the purpose of averaging the concentration of the whole model according to the following equation [33]:
∑n
ISOL
Mean(Conc) = ∑ni=1
i=1 IVOL
For further details on the functions and variables used in the code, the Abaqus documentation includes an Abaqus Scripting User’s Guide and an
Abaqus Scripting Reference Guide [31].
Bloc number
Program #Time-averaged concentration#.
1: Data Import
from odbAccess import *
from abaqusConstants import *
odb = openOdb(path=’Field.odb’)
endSet = odb.rootAssembly.instances[’Composite’]
myFile = open (’Av_Conc_Field.txt’,’w+’)myFile.write
(“# Time Sum-Vol _Sum-ISOL Av_Conc \ n”)
for step in odb.steps.values():
numFrame = len(step.frames)for Pic in range (0, numFrame)
:
frame = step.frames[Pic]
Vfield = frame. fieldOutputs[’IVOL’]
VsubField = Vfield.getSubset(region = Concentre)
Sfield = frame. fieldOutputs[’ISOL’]
SsubField = Sfield.getSubset(region = Concentre)
Ssum = 0
Vsum = 0for N in range(len(VsubField.values)
):
Vval = VsubField.values[N].data
Vsum = Vsum + Vval
Sval = SsubField.values[N].data
2: Data Collection
3: Initialization calculation
#Access to Outputs
#Sweeping Data from Step Increments
#Loop for Mean calculation of Concentration
(continued on next page)
14
K. Zouggar et al.
Composite Structures 299 (2022) 116053
(continued )
Bloc number
4: Data Collection Writting
Program #Time-averaged concentration#.
Ssum = Ssum + Sval
Mean = Ssum / Vsum
frametotalTime = step.totalTime + frame.frameValue myFile.write(str(frametotalTime))myFile.
write
(“ ”)myFile.write(str(Vsum)
)myFile.write
(“ ”)myFile.write(str(Ssum)
)myFile.write
(“ ”)myFile.write(str(Mean)
)myFile.write
(“text\ n”)myFile.close
()
References
#Data Storage After Mean Collection
[17] Ahmad F, Hong J-W, Choi HS, Park MK. Hygro effects on the low-velocity impact
behavior of unidirectional CFRP composite plates for aircraft applications. Compos
Struct 2016;135:276–85.
[18] Idolor O, Guha RD, Berkowitz K, Geiger C, Davenport M, Grace L. Polymer-water
interactions and damage detection in polymer matrix composites. Compos B Eng
2021;211:108637.
[19] Reis P, Neto M, Amaro A. Multi-impact behaviour of composite laminates under
constant and different energy levels. Compos Struct 2022;115788.
[20] Introduction aux plans d’expériences - 5ed. toutes les techniques necessaires à la
conduite d’une étude; 2012.
[21] User guide and tutorial to MODDE : version 8.0. Umetrics: Umetrics, 2006.
[22] Broughton W, Maxwell A. Measurement good practice guide No. 103: accelerated
environmental ageing of polymeric materials. tech. rep., National Physics
Laboratory, Teddington, Middlesex, United Kingdom; 2007.
[23] Duncan B, Broughton W. Measurement good practice guide No. 102 absorption and
diffusion of moisture in polymeric materials. Tech. Rep. 102, National Physics
Laboratory, Teddington, Middlesex, United …; 2007.
[24] Altair ESAComp 2020 -theoretical background of ESA Comp analyses.: Altair 2020.
[25] Masari F. Virtual characterization of composite materials for aero-engine
components; 2020.
[26] Hashin Z. Failure criteria for unidirectional fiber composites. J Appl Mech-Trans
Asme 1980;47:329–34.
[27] Li D. Analysis of composite laminates: theories and their applications: Elsevier,
2022.
[28] Barbero EJ. Finite element analysis of composite materials using AbaqusTM. CRC
Press Boca Raton; 2013.
[29] Materials ACDoC. Standard test method for measuring the damage resistance of a
fiber-reinforced polymer matrix composite to a drop-weight impact event: D7136/
D7136M-15: ASTM International; 2015.
[30] Zouggar K, Boukhoulda F, Haddag B, Nouari M. Numerical and experimental
investigations of S-Glass/Polyester composite laminate plate under low energy
impact. Compos B Eng 2016;89:169–86.
[31] Corp DSS. Abaqus Scripting Reference Guide. 2016. URL: http://50.16.225.63/
v2016/books/ker/default.htm.2016.
[32] Nunemaker JD, Voth MM, Miller DA, Samborsky DD, Murdy P, Cairns DS. Effects of
moisture absorption on damage progression and strength of unidirectional and
cross-ply fiberglass–epoxy composites. Wind Energy Sci 2018;3:427–38.
[33] Mora VB, Mieloszyk M, Ostachowicz W. Model of moisture absorption by adhesive
joint. Mech Syst Sig Process 2018;99:534–49.
[34] Belhadj B, Abdelkader L, Chateauneuf A. Weibull probabilistic model of moisture
concentration build up in a fiber graphite/epoxy polymer composite under varying
hydrothermal conditions. Periodica Polytechnica Mech Eng 2021;65:27–37.
[1] Shrestha J, Ueda T, Zhang D. Durability of FRP concrete bonds and its constituent
properties under the influence of moisture conditions. J Mater Civ Eng 2015;27:
A4014009.
[2] Yilmaz T, Sinmazcelik T. Effects of hydrothermal aging on glass–fiber/
polyetherimide (PEI) composites. J Mater Sci 2010;45(2):399–404.
[3] Mirzaei G, Mohebby B, Ebrahimi G. Glulam beam made from hydrothermally
treated poplar wood with reduced moisture induced stresses. Constr Build Mater
2017;135:386–93.
[4] Ridzuan M, Majid MA, Khasri A, Basaruddin K, Gibson A. Effect of moisture
exposure and elevated temperatures on impact response of Pennisetum
purpureum/glass-reinforced epoxy (PGRE) hybrid composites. Compos B Eng
2019;160:84–93.
[5] Gemi L, Kayrıcı M, Uludağ M, Gemi DS, Şahin ÖS. Experimental and statistical
analysis of low velocity impact response of filament wound composite pipes.
Compos B Eng 2018;149:38–48.
[6] Zenkour AM, Alghanmi RA. Bending of symmetric cross-ply multilayered plates in
hygrothermal environments. Math Models Eng 2016;2:94–107.
[7] Bandyopadhyay T, Karmakar A. Low-velocity impact response of delaminated
composite conical shells in hygrothermal environment due to time-delay. Procedia
Eng 2017;173:463–70.
[8] Wang B. Moisture absorption and diffusion of a carbon composite structure. 2020.
2020;1.
[9] Li R, Cao P, Xu W, Ekevad M, Wang XA. Experimental and numerical study of
moisture-induced stress formation in hexagonal glulam using X-ray computed
tomography and finite-element analysis. BioResources 2018;13:7395–403.
[10] Li Z, Zhang J, Sun Y. Influence of accelerated aging tests on properties of gluedlaminated timber. China Forestry Science and Technology 2015;01.
[11] Khoshtinat S, Carvelli V, Marano C. Moisture absorption measurement and
modelling of a cellulose acetate. Cellulose 2021;28(14):9039–50.
[12] Yu Y, Li P, Sui G, Yang X, Liu H. Effects of hygrothermal aging on the
thermal–mechanical properties of vinylester resin and its pultruded carbon fiber
composites. Polym Compos 2009;30(10):1458–64.
[13] Alessi S, Pitarresi G, Spadaro G. Effect of hydrothermal ageing on the thermal and
delamination fracture behaviour of CFRP composites. Compos B Eng 2014;67:
145–53.
[14] Boulbes RJ. Troubleshooting finite-element modeling with abaqus: Springer, 2020.
[15] Boukhoulda FB, Guillaumat L, Lataillade JL, Adda-Bedia E, Lousdad A. Agingimpact coupling based analysis upon glass/polyester composite material in
hygrothermal environment. Mater Des 2011;32(7):4080–7.
[16] Katajisto H, Kere P, Lyly M. A model for fast delamination analysis of laminated
composite structures. Rakenteiden Mekaniikka 2020;53:67–84.
15