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

DOI:10.12691/materials-6-1-1

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

1

Production Engineering and Design Department, Faculty of Engineering, Minia University, 61111 Minia, Egypt

2

Mechanical Engineering Department, Faculty of Engineering, South Valley University, Qena, 83523

3

Mechanical Engineering Department, Collage of Engineering and Islamic Architecture, Umm Al-Qura University Makkah, KSA

4

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

2

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]

Phase

Copper film

Glass fiber

Epoxy

Al

0.0005>

Ni

0.0005>

Sn

0.0005>

Pb

Fe

0.0005>

0.0005>

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

Resin-Kemapoxy(150RGL)

Zn

0.0005>

Mn

0.0005>

Table 2. Mechanical properties [1]

Phase

Copper film

Glass fiber

Epoxy

Young modulus, E (GPa)

123

24(Length Wise), 21 (Cross Wise)

1.2-4.5

Thermal of linear expansion, 𝜶/𝑲

1.68 x 10-5

4.0 x 10-5

-----------------

Table 3. Electrical properties

Phase

Copper film

Glass fiber

Epoxy

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

3

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

(1)

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.

4

American Journal of Materials Engineering and Technology

The observed fluctuations in the curve may be due to fiber

breaking.

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

(2)

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

5

American Journal of Materials Engineering and Technology

6

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.

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

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.

References

[1]

M. K. Hassan, T. Torii, and K. Shimizu, "Fatigue fracture

behavior of MEMS Cu thin films."

[11]

[12]

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[14]

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A. Wymysłowski, B. Vandevelde, and D. Andersson, "Thermal,

mechanical and multi-physics simulation and experiments in

micro-electronics and micro-systems," Microelectronics Reliability,

vol. 47, pp. 159-160, 2007.

R. Ballarini, R. Mullen, H. Kahn, and A. Heuer, "The fracture

toughness of polysilicon microdevices," MRS Online Proceedings

Library Archive, vol. 518, 1998.

H. D. Espinosa and B. Peng, "A new methodology to investigate

fracture toughness of freestanding MEMS and advanced materials

in thin film form," Journal of microelectromechanical systems,

vol. 14, pp. 153-159, 2005.

I. Chasiotis and W. G. Knauss, "The mechanical strength of

polysilicon films: Part 1. The influence of fabrication governed

surface conditions," Journal of the Mechanics and Physics of

Solids, vol. 51, pp. 1533-1550, 2003.

H. Kahn, N. Tayebi, R. Ballarini, R. Mullen, and A. Heuer,

"Fracture toughness of polysilicon MEMS devices," Sensors and

Actuators A: Physical, vol. 82, pp. 274-280, 2000.

W. Sharpe, B. Yuan, and R. Edwards, "Fracture tests of polysilicon

film," MRS Online Proceedings Library Archive, vol. 505, 1997.

T. Tsuchiya, J. Sakata, and Y. Taga, "Tensile strength and fracture

toughness of surface micromachined polycrystalline silicon thin

films prepared under various conditions," MRS Online

Proceedings Library Archive, vol. 505, 1997.

M. Y. Abdellah, "Essential work of fracture assessment for thin

aluminium strips using finite element analysis," Engineering

Fracture Mechanics, vol. 179, pp. 190-202, 2017/06/15/ 2017.

Z. P. Bazant and J. Planas, Fracture and size effect in concrete

and other quasibrittle materials vol. 16: CRC press, 1997.

Z. P. Bažant, "Size effect in blunt fracture: concrete, rock, metal,"

Journal of Engineering Mechanics, vol. 110, pp. 518-535, 1984.

P. S. Shinde, K. Singh, V. Tripathi, P. Sarkar, and P. Kumar,

"Fracture toughness of thin aluminum sheets using modified single

edge notch specimen," International Journal of Engineering and

Innovative Technology (IJEIT) Volume, vol. 1, 2012.

M. K. Hassan, Y. Mohammed, T. Salem, and A. Hashem,

"Prediction of nominal strength of composite structure open hole

specimen through cohesive laws," Int. J. Mech. Mech. Eng.

IJMME-IJENS, vol. 12, pp. 1-9, 2012.

Y. Mohammed, K. Mohamed, and A. Hashem, "Finite element

computational approach of fracture toughness in composite

compact-tension specimens," International Journal of Mechanical

and Mechatronics Engineering, vol. 12, pp. 57-61, 2012.

M. Y. Abdellah, "Comparative Study on Prediction of Fracture

Toughness of CFRP Laminates from Size Effect Law of Open

Hole Specimen Using Cohesive Zone Model," Engineering

Fracture Mechanics, vol. 187, 2018.

M. Q. K. Mohammed Y. Abdellah, Mohammad S. Alsoufi, Nouby

M. Ghazaly, G. T. Abdel-Jaber, "Mechanical Properties of Lab

Joint Composite Structure of Glass Fiber Reinforced Polymers,"

Materials Sciences and Applications, vol. 8, pp. 553-565, 2017.

M. Y. A. Mohamed K. Hassan, Tareq S. ElAbiadi, Ahmed F.

Mohamed, S. Azam and W. W. Marzouk, "Essential Work of

Fracture and Size Effect in Copper/Glass-Reinforced Epoxy

Laminate Composites Used as MEMS Devices," American

Journal of Mechanical Engineering, vol. 5, pp. 234-238, 2017.

American Journal of Materials Engineering and Technology

[18] M. Y. Abdellah, "Delamination Modeling of Double Cantilever

[19]

[20]

[21]

[22]

Beam of Unidirectional Composite Laminates," Failure analysis

and prevention, 2017.

H. A. EI-Aini, Y. Mohammed, and M. K. Hassan, "Effect of mold

types and cooling rate on mechanical properties of Al alloy 6061

within ceramic additives," in Second International conference of

Energy Engineering; ICEE-2, 2010.

A. Standard, "Standard test method for tensile properties of

polymer matrix composite materials," ASTM D3039/D 3039M,

1995.

C. Soutis, P. Curtis, and N. Fleck, "Compressive failure of notched

carbon fibre composites," in Proceedings of the Royal Society of

London A: Mathematical, Physical and Engineering Sciences,

1993, pp. 241-256.

T. Kuno, Y. Yamagishi, T. Kawamura, and K. Nitta,

"Deformation mechanism under essential work of fracture process

in polycyclo-olefin materials," Express Polym Lett, vol. 2, pp.

404-412, 2008.

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[23] Y. Mohammed, M. K. Hassan, and A. Hashem, "Effect of stacking

[24]

[25]

[26]

[27]

[28]

sequence and geometric scaling on the brittleness number of glass

fiber composite laminate with stress raiser," Science and

Engineering of Composite Materials, vol. 21, pp. 281-288, 2014.

T. Belytschko and T. Black, "Elastic crack growth in finite

elements with minimal remeshing," International journal for

numerical methods in engineering, vol. 45, pp. 601-620, 1999.

J. M. Melenk and I. Babuška, "The partition of unity finite

element method: basic theory and applications," Computer

methods in applied mechanics and engineering, vol. 139, pp. 289314, 1996.

D. Datta, "Introduction to eXtended Finite Element (XFEM)

Method," arXiv preprint arXiv: 1308. 5208, 2013.

N. S. K. Montasser Dewidar, Mohammed Y. Abdellah, Ayman

M.M. Abdelhaleem, "Finite element modeling of mechanical

properties of titanium foam and dental application," in The third

international conference on energy engineering (ICEE), 2015.

A. V. ABAQUS, "6.9 Documentation," Providence, RI: Dassault

Systemes Simulia Corporation, 2009.

Available online at http://pubs.sciepub.com/materials/6/1/1

©Science and Education Publishing

DOI:10.12691/materials-6-1-1

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

1

Production Engineering and Design Department, Faculty of Engineering, Minia University, 61111 Minia, Egypt

2

Mechanical Engineering Department, Faculty of Engineering, South Valley University, Qena, 83523

3

Mechanical Engineering Department, Collage of Engineering and Islamic Architecture, Umm Al-Qura University Makkah, KSA

4

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

2

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]

Phase

Copper film

Glass fiber

Epoxy

Al

0.0005>

Ni

0.0005>

Sn

0.0005>

Pb

Fe

0.0005>

0.0005>

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

Resin-Kemapoxy(150RGL)

Zn

0.0005>

Mn

0.0005>

Table 2. Mechanical properties [1]

Phase

Copper film

Glass fiber

Epoxy

Young modulus, E (GPa)

123

24(Length Wise), 21 (Cross Wise)

1.2-4.5

Thermal of linear expansion, 𝜶/𝑲

1.68 x 10-5

4.0 x 10-5

-----------------

Table 3. Electrical properties

Phase

Copper film

Glass fiber

Epoxy

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

3

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

(1)

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.

4

American Journal of Materials Engineering and Technology

The observed fluctuations in the curve may be due to fiber

breaking.

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

(2)

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

5

American Journal of Materials Engineering and Technology

6

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.

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[9]

[10]

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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