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Fracture toughness of copper/glass-reinforced epoxy laminate composites

American Journal of Materials Engineering and Technology, 2018, Vol. 6, No. 1, 1-7
Available online at http://pubs.sciepub.com/materials/6/1/1
©Science and Education Publishing

Fracture Toughness of Copper/Glass-Reinforced
Epoxy Laminate Composites
Mohamed K. Hassan1,3, Mohammed Y. Abdellah2,3,*, Ahmed F. Mohamed3,4, Tareq S. ElAbiadi1,
S. Azam3, W.W. Marzouk1

Production Engineering and Design Department, Faculty of Engineering, Minia University, 61111 Minia, Egypt
Mechanical Engineering Department, Faculty of Engineering, South Valley University, Qena, 83523
Mechanical Engineering Department, Collage of Engineering and Islamic Architecture, Umm Al-Qura University Makkah, KSA
Mechanical Engineering Department, Faculty of Engineering, Sohage University, Egypt
*Corresponding author: mohammed_yahya42@yahoo.com

Abstract In last decades, hybrid composite materials play a competitive role in many industrial applications such

as electrical and electronic industries. Copper/Glass-Reinforced Epoxy Laminate is a hybrid composite that is used
in almost all electronic devices. Since these elements undergo different stress amplitudes under different working
conditions, therefore the fracture toughness of such material is important to understand the failures occurred under
different operating conditions. The present work aims to investigate the fracture behavior of these composites by
experimentally measuring and predicting their fracture toughness and by numerically building the model. At the first
stage, a center-notched tensile specimen is used to measure fracture toughness in mode I at room temperature; an
average fracture toughness of 34.92 𝑀𝑃𝑎 √𝑚 with SDV 0.5556 𝑀𝑃𝑎 √𝑚 is found. At the second stage, X-FEM is
implemented to a simple numerical model to predict the fracture toughness of such a material and to measure
stresses induced through the specimen during applied stress. The variation of both, predicted fracture toughness and
cohesive stress at the crack face with crack opening displacement, shows that the finite element results are in good
agreement with the experimental results.
Keywords: fracture toughness, X-FEM, MEMS, laminate, center edge notch
Cite This Article: Mohamed K. Hassan, Mohammed Y. Abdellah, Ahmed F. Mohamed, Tareq S. ElAbiadi,
S. Azam, and W.W. Marzouk, “Fracture Toughness of Copper/Glass-Reinforced Epoxy Laminate Composites.”
American Journal of Materials Engineering and Technology, vol. 6, no. 1 (2018): 1-7. doi: 10.12691/materials-6-1-1.

1. Introduction
In recent years, hybrid composite materials have widely
used in electronic industry in the form of micro-electrical
mechanical systems (MEMS) [1]. Mechanical and thermal
properties affect strongly on the performance of (MEMS)
from the reliably perspective [2]. Although, there are many
studies devoted to model, design, selection and fabrication
processes of composite materials used as (MEMS) still
studies concerning with the characteristics of their reliably,
durability, fracture behavior during operating conditions
are not fully reported [3].
The fatigue behaviors of thin copper film bonded to the
steel substrate using two types of bonding techniques
have been envisaged by Hassan et al [1]; one is an epoxy
resin and the other is the diffusion bonding. Their results
showed that the fatigue performance affected by the
diffusion technique.
The fracture Jc for polysilicon specimen has been
studied by R. Ballarini et al [3]. These specimens are
machined in a similar and identical way as (MEMS). The
results indicated that the released energy of these
polysilicon specimen is four times greater than those of
single crystal. On the other hand, the fracture toughness of

thin films used in (MEMS) devices has been investigated [4].
The fracture toughness behaviors of the ultra-nanocrystalline
diamond were measured. This study established that the
initiation fracture for bland crack is larger than that of a
sharp crack tip; it gave a correction factor value for the
material using the model of Drory et al. [5].
The Finite Element Analysis (FEA) for experimental
results is used [6] to measure the fracture toughness of
polysilicon used in (MEMS) devices. An especial sharpened
mechanism has been employed to ensure accurate crack
initiation and propagation prediction. Unlike the work of
Sharpe, et al [7] and Tsuchiya et al. [8], the fracture
toughness of MEMS was measured infinite radius notch
by fracturing their specimen using a piezoelectric load cell.
A simple numerical model, using finite element, was
extracted to predict the parameters of the essential work
of fracture (EWF) [9] in the thin aluminum strip. The
experimental results were in good agreement with the
proposed model, but the specimen was on the scale of a
millimeter. Other works [10,11,12] reported on the size
effect of copper thin film bonded to a steel plate substrate
which is considered as quasi-brittle material.
In another study, cohesive zone model was used to
predict size effect of glass fiber reinforced epoxy[13]. The
predicted results of quasi-brittle material were close to
those of the produced model. Both analytical model and

American Journal of Materials Engineering and Technology


experimental test investigated the size effect of quasi-brittle
material [14]. This combination established good prediction
for size effect and gave reasons for the size effects on the
nominal strength of this material. Consequently, the study
reached to some solution for size effect on the quasi-brittle
material. Generally, many works measured fracture toughness
of composite laminates materials which are widely used in
many industrial applications [15,16,17,18,19].
This work aims to measure the fracture toughness of
composite materials which consist of a thin copper layer
bonded to a substrate of the glass-reinforced epoxy
laminate. These composites are widely used as a
component in (MEMS) devices. Since, the mechanical
behavior is a dominated parameter when using these
composite as (MEMS) devices, a better knowledge of
fracture behavior would certainly lead to the improvement
of the performance and reliability of these devices.

2. Material and Experimental Procedure
Figure 1 shows the composite structure used in this
study. The structure consists of glass fiber reinforced
epoxy laminate of 1.5 mm thick and a thin copper film
bonded to the base of the fiberglass laminate by epoxy

resin. A thin copper film nearly 35 microns and 24 layers
of woven glass fiber are used to form this composite
structure. Table 1, Table 2 and Table 3 list the chemical
composition, electrical and mechanical properties of the
copper and epoxy, respectively. According to ASTM
D3039 tests standards, the tensile test is performed on all
glass fiber reinforced epoxy laminates [20]. Figure 2
illustrates the tensile specimen dimensions. All tests are
carried out by the universal testing machine (Model
WDW-100) of normal load capacity 200 kN and at a
controlled test speed of 2 mm/min. In order to determine
the unnotched tensile strength of the composite structure,
the unnotched test specimens are used.
In order to measure the surface release energy of hybrid
composite, Soutis et al. [21] established a model and
introduced a center crack plate tension specimen. Therefore,
five center crack plate specimens are prepared with dimensions
as shown in Figure 3. Center crack length (2a) =15 mm is
cut, using Proto Mat S103 PCB milling machine from
LPKF, with 1mm diameter end mill cutter. All specimens
are loaded in tension until failure while the load and
displacement are recorded on a universal testing machine
(model WDW-100) of maximum capacity 200 KN. The
cross-head speed of the test is selected to be 2 mm/min
according to [22]. Each test repeated for the five specimens.

Table 1. Chemical composition of the copper film and base glass fiber [1]
Copper film
Glass fiber




E-glass -roving-pl=2200 gm/km



Table 2. Mechanical properties [1]
Copper film
Glass fiber

Young modulus, E (GPa)
24(Length Wise), 21 (Cross Wise)

Thermal of linear expansion, 𝜶/𝑲
1.68 x 10-5
4.0 x 10-5

Table 3. Electrical properties
Copper film
Glass fiber

Electrical Resistivity, ρ (Ω•m)
1.68×10−8 [22]
10 [23]
>1x105 [24]

Figure 1. Schematic drawing of MEMS components

Figure 2. Un notch composites standard specimen plate (mm)

Dielectric Strength, V/𝒎𝒊𝒍
-------------->762 [23]
500 [24]

American Journal of Materials Engineering and Technology


where ( 𝛿𝑛 , 𝛿𝑠 , 𝛿𝑡 ) is normal, shear and tangential
components of the traction and separation to the cohesive
surface, respectively.

Figure 3. Center edge notch specimen [23]

3. Finite Element Model
A numerical method called extended finite element
method (X-FEM) recently created by Belytschko and
Black [24], is based on Melenk and Babuska [25] who
used the concept of partition of finite element unity and
enrichment function. X-FEM differs from FEM method
by that the mesh does not need to be updated to follow
the crack path [26], this means that there is no need
to mesh and re-mesh the complex discontinuities surfaces.
So, the fracture analysis can be performed when the
crack propagates without re-meshing and refining with
numerical accuracy around the crack tip [27].
The rectangular domain of (45 mm × 90 mm) is created
as a solid part as shown in Figure 3. This creation is based
on basic extended fracture method and three-dimensional
linear elastic finite element model. In this case, the
enrichment function of X-FEM domain with stationary
crack is a straight planar strip.
The value of the un-notched nominal strength,
considered as the maximum principal stress, is measured
as 163 MPa. Besides, the damage evaluation criterion is
maximum traction displacement; the maximum crack
opening of the composite specimen is experimentally
measured as 0.3 mm. Moreover, the swept meshing
technique is used to generate a dense mesh using (C3D8R)
element type of 1433 elements with approximate global
size 2 in the domain as shown in Figure 4. Figure 5 shows
the rectangular cracked domain which is yielded from
the application of the displacement control boundary
conditions at both ends of the rectangular cracked domain
(see ure 5 a-b). Critical fracture toughness (𝐺𝐼𝐶 ) of the
delaminated body is measured as the area under the
cohesive zone model.
The maximum crack opening is considered as the
damage evaluation and it is calculated using the following
equation [28]:

δ n=

δ n 2 + δ s2 + δ t2


Figure 4. X-FEM Mesh domain

Figure 5. X-FEM a) interaction domain, b) B. C domain

4. Results and Discussion
Figure 6 shows the stress-strain curve for the composite
structure (untouched specimen). The modes of failure are
shown in Figure 7-a, where the net tension failure mode is
observed, and a delamination crack through the thickness
occurs. This can be attributed to shear stress induced in
the laminated structure. It is observed that a thin copper
film has a little influence on the global behavior of the
plate and the linear behaviors are the general trend in the
failure flow of the composite material. The woven fiber in
the laminates arises a complex state of stress through the
fiber direction which led to reduce the laminate strength.


American Journal of Materials Engineering and Technology

The observed fluctuations in the curve may be due to fiber
The stress-strain relation for the center cracked test
specimens, with dimensions of width=45 mm, gauge
section length; L=90 mm and thickness; t=1.5 mm,
respectively, is shown in Figure 8. The value of failure
stress was calculated for all the specimens and the average
value was found to be 160.9 MPA. The fracture toughness
(KIC) was also calculated by substituting in Eq. (2), the
values of (σ) and center crack length (2a) 15 mm. The
result showed the fracture toughness (KIC) equal to

34.92 𝑀𝑃𝑎 √𝑚 with standard deviation (SDV) of 0.5556
𝑀𝑃𝑎 √𝑚.
πa 
K IC = σ π a sec   .
 w


It is observed in Figure 7-b, that delamination occurred
at copper glass fiber interface of the composite panel. It
was probably, due to that weakening of epoxy resin
adhesive used in manufacturing the laminates panel and
there was net tension in laminates panel’s specimens.

Figure 6. Tensile stress-strain curve for composite material (un notched specimens)

Figure 7. Mode of failure image a) tension test, b) center cracked plate

Figure 8. Stress-strain curve for center notched specimen

American Journal of Materials Engineering and Technology

Figure 9. Variation of predicted fracture toughness with crack opening displacement; COD

Figure 10. Variation of predicted cohesive stress at crack face with crack opening displacement; COD

Figure 11. X-FEM contour a) PHILSM, b) STATUS XFEM


American Journal of Materials Engineering and Technology


Figure 12. Stress contours a) Displacement, b) Von-Mises

Figure 9 shows validation of critical stress intensity
factor (KIC) extracted from the finite element model and
the one measured experimentally. It is obvious that the
two values are very close, this can be attributed to that
linear X-FEM based on the real properties of the
composite panel. This curve is the average of 5 contour
integrals. The cohesive stress which was implemented in
the damage criteria in the simulation is 160 MPa, the
predicted value is very close and gives good agreement
with the implemented value as shown in Figure 10.
PHILSM functions are used to define and show the
location of crack inside a body as clearly shown in
Figure 11-a. In Figure 11 b, STUTUS X-FEM shows the
extent of damage or “cracking” inside an element. In other
words, XFEM has three important parameters: (i) PHILSM
(ϕ); describes the face of fracture, (ii) PSILSM (ψ);
describes the forehead of initial fracture, and (iii)
STATUSXFEM; which specifies whether the item is full,
partial or not cracked. The stress contours are shown in
Figure 12; the displacement contour illustrates the
maximum displacement at the location of tension, while
maximum Von-Mises stress at the crack tip.






5. Conclusion
The fracture toughness of Copper/Glass-Reinforced
Epoxy Laminate Composites was investigated both
experimentally, using center notch specimens, as well as
numerically by the extended finite element method. From
this investigation, it may conclude that center notch
specimen can be standardized as a dependent test for the
hybrid composite panel. Moreover, the finite element
model effectively predicts the fracture toughness of
this composite and gives good agreement with the
experimental results of fracture toughness. On the other
hand, the thin copper film gives an insignificant effect on
the trend of the tensile properties of the composite panel
whereas, it gives an increase in composite strength,
therefore, linear behaviors are the global trend.


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