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A novel evaluation method for interfacial adhesion strength in ductile

dissimilar materials

Shoji Kamiya a,*, Harunori Furuta a, Masaki Omiya b, Hiroshi Shimomura a

a Department of Engineering Physics, Electronics and Mechanics, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya, 466-8555 Aichi, Japanb Department of Mechanical Engineering, Keio University 3-14-1, Hiyoshi, Kohoku-ku, Yokohama, 247-0006 Kanagawa, Japan

a r t i c l e i n f o

 Article history:

Received 9 January 2007

Received in revised form 15 January 2008

Accepted 16 June 2008

Available online 11 July 2008

Keywords:

Flexible printed circuit

Interface

Adhesion

Strength

Energy

a b s t r a c t

The energy of interface adhesion between two elastic–plastic materials was directly eval-

uated as the mechanical work supplied exclusively to separate the interface. Interface crack

extension was simulated by elastic plastic finite element models, where the nodes along

the interface in the vicinity of crack tip were divided into two nodes and the nodal forces

were gradually decreased to zero. While further plastic deformation takes place in the vol-

ume of materials during crack extension, the work done by these nodal forces against

mutual displacement of crack surfaces should be consumed on the surfaces and thus equals

to the interface adhesion energy. This technique was applied to a copper/polyimide system

for flexible printed circuits in accordance with the new experimental results. In compari-

son to the results obtained by the conventional peel test, this technique yielded far smaller

amount of interface energy successfully excluding the energy dissipated with bulk plastic

deformation without any insertion of cohesive strip along the interface in the model.

 2008 Elsevier Ltd. All rights reserved.

1. Introduction

Recently, thin films deposited on substrates are used as functional materials in various fields. Among those variety of 

combinations of films and substrates, demands for soft and flexible film–substrate systems have recently been emerging

in many application fields. In electronics industries, such kind of materials systems are already widely used as flexible

printed circuits and also expected to play important roles to realize flexible electronic devices such as wearable soft equip-

ments. Because of the flexible features, however, mechanical reliability of these systems is an issue of great importance and

difficult to evaluate as well. Peel test  [1,2] has become a de facto standard method in industries to evaluate the strength of 

adhesion in flexible film–substrate systems. This technique measures the force required to peel off the film per unit width,

thus evaluate the strength in terms of N/m which is equivalent to the energy required to peel off unit area, J/m2. For a purely

elastic case, all the earlier works [3–13] identified that the peeling force  P  (N/m) corresponds to the energy used to separatethe interface, i.e., interface adhesion energyC (J/m2), with a factor of peeling angle as discussed in the next section. However,

in cases where plastic deformation takes place during peeling process, the work done by the peeling force is consumed not

only for separating the interface but also for the plastic deformation in peeled arm and substrate. Since the latter is usually

larger than the former, the results of peeling tests are known to strongly depend on the thickness of peeled-off films.

Extensive works [2,14–22] were devoted to the plastic deformation in the peeling process as the films detached from the

substrate, and bend through the moment-curvature hysteresis loop (including plastic loading, elastic unloading, plastic

reverse loading, and elastic reverse unloading). For the interfacial strength of materials used in flexible micro-electronic

0013-7944/$ - see front matter  2008 Elsevier Ltd. All rights reserved.doi:10.1016/j.engfracmech.2008.06.011

*  Corresponding author. Tel./fax: +81 052 735 5324.

E-mail address:  kamiya.shoji@nitech.ac.jp (S. Kamiya).

Engineering Fracture Mechanics 75 (2008) 5007–5017

Contents lists available at  ScienceDirect

Engineering Fracture Mechanics

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devices, Park et al.  [23–25] measured the interfacial adhesion energy of Cu/Cr/polyimide system by subtracting energy dis-

sipated in plastic deformation from the results of peel test. Although their compensation took into account the effect of plas-

tic deformation in the film on the basis of fundamental beam bending theory, the extra plastic deformation in the vicinity of 

interface crack tip was ignored. Therefore their evaluation results still includes some amount of plastically dissipated energy.

A cohesive strip model inserted along the interface gave a new twist to the problem. The works by Tvergaard and Hutchinson

[26] and Wei and Hutchinson [27] emphasized the influence of cohesive stress on the plastic energy dissipation in film and

substrate. Other interface cohesive laws [28–30] elaborated several delicate issues of interface debonding, including the ef-

fect of mode ratio of crack opening displacement. As a matter of fact, cohesive model figured out the trend of peel force with

a variety of cohesive stress applied to the interface crack surface. However, it did not give a possibility to measure the

strength of interface independent of bulk plastic deformation in that it is difficult to determine the cohesive stress itself from

the experimental results.

In order to overcome the problem mentioned above, development of a new technique is aimed in this study which en-

ables direct evaluation of energy required exclusively to separate the interface between ductile thin films and substrates,

i.e., the interface adhesion energy. Contrary to those trials to improve the evaluation within the framework of peel test, a

new scheme is examined in this study on the basis of one of the author’s recent trials [31,32] for the evaluation of interface

toughness in hard coating systems. The paper is composed of six sections as in the following. In Section  2, after the expla-

nation of the sample examined in this study, details of the conventional peel tests are described along with the results ob-

tained with the sample. The schemes of data compensation to exclude plastic deformation, proposed by Kinloch et al.  [20]

and Moidu et al.  [21], are applied to the results and discussed in detail. In Section 3, the same sample is fabricated into a

different form of specimens to perform the experiment newly proposed in this study. The experimental results are compared

with the numerical simulation in Section  4. Determination of interface adhesion energy is discussed in detail in Section  5,

where independent evaluation of the energy consumed to separate the interface and dissipated by plastic deformation

was confirmed. Section 6  summarizes the paper.

2. Samples and the results of peel test

A commercial copper/polyimide laminate produced for printed flexible circuit fabrication was selected as the sample

examined in this study. The substrate film was a 25lm thick polyimide film, Capton supplied by DUPONT. The stress–strain

curve of this film obtained by uniaxial tensile test was presented in  Fig. 1, which was supplied from DUPONT. Nickel was

sputtered on the polyimide film for the first 6 nm, and then Cu for the next 100 nm. Finally, Cu was electroplated for the rest

of the thickness. Samples with various total thickness of copper layer, from 7 to 22 lm, were subjected to the peel test ex-

plained later. Yield stress and Young’s modulus of the copper film with 8.1 lm thickness was obtained by nanoindentation.

Nanoindentation tests were performed with a number of different depths from 200 to 1500 nm in order to exclude both the

effect of finite tip radius and soft substrate. Yield stress appeared stable with the indentation depth larger than 800 nm andwas evaluated to be 500 MPa. However, evaluated Young’s modulus varied more significantly from 90 GPa to 160 GPa and

did not reach an asymptotic value. This may be because elastic deformation was more sensitive to the soft substrate. It may

also depend on the variation of grain size in depth direction. For this reason, the bulk value of 130 GPa [33] was used in the

simulation models explained later. In the literature [34–36], Young’s modulus of electroplated copper film was found in the

range between 100 and 160 GPa. It is mentioned that because of the significant difference in elastic moduli of copper and

polyimide, variation in Young’s modulus of copper film as well as yield stress had little influence on the simulation results

explained in Section 4. The calculated amount of energy release rate changed only by roughly ±1% when 100 and 160 GPa

was used as Young’s modulus instead of 130 GPa.

Fig. 1.  Stress–strain curve of polyimide film.

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Fig. 2 shows a schematic illustration of peel test. For purely elastic case, the interface adhesion energy C is correlated to

the peeling force  P  and the peeling angle  /   in the following equation [3–13]

C ¼  P ð1 cos/Þ:   ð1Þ

In case plastic deformation takes place during the peeling off process, Eq. (1) gives the whole sum of interface adhesion en-

ergy, elastic strain energy of peeled film and the energy dissipated in plastic deformation. A 90 peel test, where  /  = p/2 in

Eq. (1), was performed with a number of different copper film thicknesses according to the standard of JIS C5012 (A standard

of 90 peel test for flexible printed circuit, equivalent to IEC 346-2,4,5,6  [1]). In this test, copper films were peeled off in the

direction perpendicular to the substrate as illustrated in   Fig. 2. The results are shown in   Fig. 3   with circular symbols.

Although the interface is expected to be identical because the thickness of the specimen was changed only by changing

the thickness of the electroplated second copper layer, the peel strength obviously depends on the thickness of copper films.

There might be an idea [27] that the results could be extrapolated to zero thickness to exclude the effect of plastic deforma-

tion in copper films, which yields roughly 250 J/m2.

The theory proposed by Kinloch et al. [20] and Moidu et al. [21] were applied to the results of peel test in Fig. 3 to subtract

the amount of energy dissipated by plastic deformation. In Kinloch’s theory, the film was modeled as an elastic–plastic beam

adhered to a rigid substrate and the energy dissipated by plastic deformation during the peel off test was estimated on the

basis of simple beam bending theory. The compensated results were plotted in  Fig. 3 with triangular symbols. Moidu et al.

improved Kinloch’s model by considering the substrate as an elastic body. The results compensated by Moidu’s model were

P

Film

Substrate

φ 

Fig. 2.  Schematic illustration of peel test.

1400

1200

1000

800

600

400

200

02520151050

Cu thickness (µm)

 Peel strength

 Kinloch [20]

 Moidu [21]

      Γ 

   (   J   /  m   2   )

Fig. 3.  Behavior of peel strength with respect to copper film thickness.

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also plotted in Fig. 3 with square symbols. However, both the results still tend to gradually decrease with smaller copper film

thickness. This fact suggests that there still is remaining plastic deformation which is not yet considered in those theories.

When those results are again extrapolated to zero thickness, Kinloch’s theory yielded the interface adhesion energy of 

approximately 100 J/m2 and Moidu’s theory yielded 200 J/m2. The energy dissipated by the plastic deformation in the copper

film and polyimide substrate in the vicinity of interface crack tip must still be included in these amounts.

3. Experiment

 3.1. Specimen preparation

Among the samples in the previous section, the laminate with 8.1 lm thick copper film was subjected to a new experi-

ment for the evaluation of interface adhesion energy. According to the technique established by Kamiya et al.  [31,32], the

polyimide substrate film was cut into the specimens of square bricks in the following procedures. First of all, the copper film

side of the laminate was glued onto 2 mm thick aluminum plate with a one liquid epoxy resin supplied by Sanyu Rec Co. Ltd.

The polyimide film exposed on the surface side was cut into about 100 lm wide strips by using two parallel razor blades

combined together. Another set of strips were then cut in the direction perpendicular to the previous cuttings to make

square bricks, as shown in Fig. 4a. Finally, the brick specimens of polyimide left on the copper film were made by removing

the rest of polyimide film surrounding the brick, as illustrated in Fig. 4b. As shown later in the micrographs of the specimens,

Polyimide brick

AlCu

Polyimide film

Scratch off 

Polyimide brick 

Slita   b

Fig. 4.  Specimen of polyimide film in a brick like shape: (a) fabrication process and (b) appearance of a finished specimen.

Strain gauge

Diamond needle

Cantilever beam

Horizontal stage

Al

Cu

Polyimide brick 

Optical microscope

Vertical stage

Polyimide brick 

Diamond needle

Cu

Horizontal loadVertical load

a

b

Fig. 5.  Experimental setup.

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no significant deformation was observed of the copper surface where polyimide was removed. The size of finished specimens

was measured by taking optical micrographs to be 108 108lm.

 3.2. Micro fracture test 

Fig. 5a shows the experimental setup as a schematic illustration of the loading part. The prepared specimen with the alu-

minum plate underneath was set on the stage which is able to move in both horizontal and vertical directions by a minimum

displacement step of 10 nm. A conical diamond needle with the apex angle of 90 and tip radius of 0.5 lm was set at the free

end of a cantilever beam. The needle was fabricated so that the axis of the cone was aligned to [10 0] crystallographic direc-

tion. Another end of the cantilever was fixed to the frame. By moving the stage which the specimen was set on, the horizon-

tal load was applied on the side edge of the brick specimen. The side view of the specimen and the needle while the specimen

is being loaded is shown in  Fig. 5b. In the actual experiment, the stage was driven by a displacement step of 3 lm. The ap-

plied load was measured by the strain gauges glued on the surface of rectangular cantilever beam which supported the dia-

mond needle. In order to eliminate the time dependent behavior of polyimide, the displacement was incremented again

when the load became stable after the increment in the previous step. The whole process of the experiment was observed

from the surface side of the specimen by an optical microscope.

After the needle touched the brick specimen, the load increased monotonically along with the accumulation of displace-

ment given to the substrate. At a certain load, the brick specimen was pushed away and the load dropped unstably to zero.

The load–displacement diagram obtained with one typical specimen is presented in Fig. 6. The circular symbols represent

the load in horizontal direction obtained in the actual experiment where the specimen was loaded. Because the loading

frame was not perfectly rigid, the load in vertical direction pushing the needle down to the surface was also necessary, other-

wise the needle climbed up the side edge and rode over the surface of the brick specimen. However, pushing down the nee-

dle onto the copper surface caused also a considerable amount of load in horizontal direction while the stage was driven

horizontally. The triangular symbols in Fig. 6 represent the load in horizontal direction obtained by driving the stage hori-

zontally in the same way as in the actual experiment but without pushing the brick specimen. The actual load applied to the

500

400

300

200

100

0

   L  o  a   d   P

   (  m   N   )

120100806040200

Stage displacement (µm)

 Polyimide+Cu

 Cu only

Fig. 6.  Load–displacement diagram of a specimen.

50µm

Diamond needle

Polyimide specimen50µm

Debonded specimen

Scratch trace oncopper surface

a   b

Fig. 7.  Micrographs of the specimen: (a) before the experiment, (b) after the experiment where scratch trace made by the diamond needle and debondedpolyimide brick were seen.

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specimen was estimated by subtracting the load without specimen at the corresponding amount of stage displacement.

Reproducibility of measurement was excellent and the average of maximum load applied to the specimens was

413 ± 15 mN, which was obtained with four specimens monotonically loaded up to complete debonding. The appearances

of the specimen before and after the experiment were presented in Fig. 7. Contrary to the peel test where the peeled off film

is largely deformed even with reverse plastic bending far from the crack tip, the interface crack extension took place in this

experiment with a minimum amount of deformation confined around the crack tip. This is an advantage from the view point

of computational accuracy when the fracture process is simulated with numerical models, i.e., additional energy dissipation

far from the crack tip is eliminated and thus energy dissipation in the vicinity of the crack tip can be directly evaluated. The

deformation in the polyimide specimen did not recover after debonded off from the copper surface, which means that time

dependent deformation behavior had only a secondary effect in the evaluation of interface adhesion energy in this study.

The interface crack extension behavior during the experiment was observed in detail with a number of specimens by

interrupting the loading process. A specimen was partially loaded to a certain amount of load smaller than the average max-

imum load, and unloaded. Then, the specimen was soaked in red ink to let the ink penetrate into the interface crack. After the

ink was completely dried up, the specimen was removed. Finally, the area of colored interface was measured with a micro-

scope. Four specimens were subjected to this staining process with different load levels and those micrographs are shown in

Fig. 8. The scratch across the footprint of the specimen was made by the small vertical load applied as explained in the pre-

vious paragraph when the specimen was removed. The shape of the colored part of interface crack was observed to be almost

rectangular whose width was equal to the width of the specimen even under a small load level. The dimension in the loading

direction increased with increasing the load level keeping the crack front roughly straight. From Fig. 8, the area of interface

crack at the average maximum load was estimated as approximately 4400 lm2 by extrapolating the trend of extension

behavior.

Finally, the copper film side of the fracture surface was analyzed by Auger Electron Spectroscopy. Nickel was detected on

the copper film side of fracture surface. Since thin nickel layer was deposited at first on polyimide film surface before sub-

sequent deposition of copper as explained in Section  2,  this fact strongly suggested that the debonding took place as ex-

pected along the metal/polyimide interface.

4. Simulation of interface crack extension

A computational models utilizing the finite element method (FEM) was developed for the calculation of elastic–plastic

deformation in the specimen, and thus for the evaluation of interface adhesion energy in the process of interface crack exten-

sion. Fig. 9 shows the three dimensional FEM model of the actual specimen. A half of the specimen and the diamond needle

was subjected to calculation due to the symmetry with respect to the loading point. The copper side was modeled down to

the layer of epoxy resin with thickness 10 lm. Observed thickness of epoxy layer was eventually larger than 10 lm, but

Fig. 8.   Interface crack extension behavior observed with red ink: (a) at 230 mN, (b) at 259 mN, (c) at 334 mN and (d) at 355 mN.

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subsequent layer including aluminum had little influence on calculation results and thus eliminated. While the actual dia-

mond needle has a tip radius of 0.5 lm, it was simply modeled as perfectly sharp. To avoid computational difficulties and

also to simulate the situation in the experiment where the diamond tip was pushed down and eventually scratched the cop-

per surface as explained in Fig. 5b, the diamond tip was located in the model beneath the copper surface without any contact

to copper. The vertical position of diamond needle tip had no significant influence on the evaluation of energy release rate

along the crack front, where average values along the front changed less than 1% even if compared down to 10 and 15 lm.

Since shallower cases resulted in significantly severer difficulties with far longer computational time, subsequent simula-

tions were performed with the needle located 15 lm beneath the surface. The model consisted of 8-noded hexahedral ele-

ments, and the total numbers of nodes and elements are 3553 and 2560, respectively. The copper film was modeled as an

elastic perfectly-plastic material with Young’s modulus 130 GPa and yield stress 500 MPa as explained in Section 2. Poisson’s

ratio of copper was set as 0.34 according to the literature [37]. Young’s modulus and Poisson’s ratio of epoxy were 9.0 GPa

and 0.31 according to the supplier. Because of the fact that all the experiment was performed at so slow a loading rate as

mentioned in Section 3.2 as to eliminate the time dependent behavior, the polyimide film was modeled as an elastic linear

hardening material according to the stress–strain curve in Fig. 1. Its Young’s modulus was 5.7 GPa and yield stress was

100 MPa. After the data supplied by DUPONT, 0.3 was used as Poisson’s ratio of the polyimide film. Residual stress in this

system was expected to be small and therefore ignored, since the samples were composed of two thin films and flat enough

as supplied before subjected to experiment. The loading needle was modeled simply as a rigid body because diamond is far

stiffer than copper or polyimide. All the computation in this study was performed by a commercial FEM code ABAQUS 5.8 on

the computer Hitachi VR380 in Information Technology Center, Nagoya Institute of Technology.

For the sake of simplicity, interface crack extension was not simulated from the beginning. Instead, the shape of the inter-

face crack at the maximum load estimated in Section 3 was introduced to the model as the initial crack. Roughly straight but

slightly curved shape of crack front was appropriately modeled as shown in  Fig. 9 according to the observation. The speci-

men model with this initial crack was loaded up to the maximum load with the modeled diamond needle to represent the

deformation at the interface crack tip just before the specimen was unstably pushed off. The amount of interface adhesion

energy was estimated at this maximum loading point because of the ease of averaging all the data obtained from individual

specimens.

Interface crack extension is simulated in the finite element model by dividing each node along the interface crack front

into two nodes on the copper side and the polyimide side, i.e., releasing the two nodes from the mutual constraint of com-

mon displacement. The amount of energy released when the interface crack extends by a unit area, which is balanced with

the interface adhesion energyC during interface crack extension process and hereafter denoted as energy release rate G, was

calculated by the following equation

G

 ¼

 1

 AZ   F 

n dndd

n:

  ð2Þ

In Eq. (2), dn represents the mutual displacement of released two nodes and  F n is the nodal force as a function of the mutual

displacement.  A means the area of the new crack surface corresponding to the released node. To evaluate Eq. (2), F n was step-

wise decreased from the initial nodal force on the original crack front and resulting dn was obtained. However, it was even-

tually found that F n was almost a linear function of  dn even though the possible increment of plastic deformation during the

crack extension process was adequately taken into account. Therefore, in the three-dimensional model, all the nodes on the

interface crack front were released at once according to the interface crack extension behavior observed in the actual spec-

imens. The displacement of the loading needle was kept constant during this process. The energy release rate was evaluated

in this way to be ranging from36.6 to 40.4 J/m2 along the crack front with the average value of 38.2 J/m2, as shown in Fig. 10.

This fact, i.e., the released energy per unit area of extension appears almost constant along the front, suggests that the inter-

face crack extends with the slightly curved front as a consequence of constant interface toughness. In the case of crack exten-

sion in homogeneous elastic–plastic materials, the meaning of energy evaluated as such might be ambiguous in that the

definition of crack surface is not so straightforward as defined in this model. However, for the case of clearly defined inter-

face, it is persuasive enough in the model to explain that this amount of energy was used exclusively to break the adhesion

Cu Epoxy

Polyimide brick Needle

Initial crack Cu

Polyimide brick Needle

Cu

Polyimide brick Needle

Initial crack  Epoxy

Fig. 9.  Three-dimensional finite element model of the specimen.

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bonds which had connected a unit area of two dissimilar materials. This calculation may also be comprehended that equiv-

alent cohesive stress was automatically taken into account and determined according to the experimental result.

In order to confirm convergence of calculation, two-dimensional models were made because the capacity of our computer

did not allow three-dimensional model to be more finely meshed. For this purpose, a three dimensional model with the same

area of initial crack but a straight crack front was calculated at first with the same load applied to the specimen in the exper-

iment. The distribution of energy release rate obtained with this straight front model is shown in  Fig. 10 together with the

result of curved front model obtained above. The amount of energy release rate varied significantly along the front for the

case of straight front model, with the average value of 40.4 J/m2, which was however only about 5% larger than the average

value obtained with the curved front model. According to these findings, the first two-dimensional model was meshed to be

the same as the pattern appeared on the symmetry plane of the three-dimensional straight front model. This model was then

pushed by the two-dimensional needle until the obtained energy release rate reached the same amount as obtained with the

three-dimensional curved front model, i.e., 38.2 J/m2. The resulting load, 476 mN per the width of the specimen, i.e., 108 lm,

was defined as the equivalent two dimensional load and it was used as a boundary condition in the subsequent calculations

to check the convergence with finer meshes. It is mentioned that this load appears 15% larger than the load applied to the

three-dimensional model, i.e., obtained in the experiment. The difference may be partly due to the effect of stress concen-

tration at the side edges of the specimen, which is obvious in Figs. 8 and 10. The observed crack front close to the side edge in

addition to the loading point extends longer than that in between in Fig. 8, while the straight front model resulted in a larger

energy release rate at the edge of the specimen in  Fig. 10. The second two-dimensional model was meshed with elements

which have half the size of elements in the first two-dimensional model. By repeating this, total four two dimensional mod-

els were generated. Released energy per unit area of simulated interface crack extension was evaluated with these models

under the same condition. In order to keep the influence of finite crack extension the same, the interface crack was extended

in the same length in all the four models. Therefore the more number of nodes were released at once in the model with the

finer mesh along the interface in the vicinity of crack tip in order to simulate the same length of crack extension.  Fig. 11

shows the results of calculation plotted with respect to the number of nodes released at once, where the trend of conver-

gence is clearly observed. Since the fourth two-dimensional model was the finest one affordable in our system, the subse-

quent study as discussed in the following Section 5  was made with this model.

5. Evaluation of interface adhesion energy 

To verify the adequacy of evaluation, two different methods to calculate the energy release rate were compared in the two

dimensional model. One is the method explained above in Eq.  (2), where not only with fixed needle displacement but also

under constant load condition was examined. Another method is to consider energy balance before and after releasing the

nodes at the crack front, as formulated below:

DU e þ DU p þ DU s  ¼  F  _NDdN:   ð3Þ

The right hand side of Eq. (3) means the work done by the applied external force F N through the diamond needle against the

increment of load point displacement dN during the interface crack extension process. Again two conditions of fixed displace-

ment, where right hand side equals zero, and constant load were examined. In the left hand side, DU e  and DU p denote the

increment of elastic strain energy in the model and plastically dissipated energy, respectively. The calculated sum of these

two kinds of energies was eventually found not to agree with the work done by the external load, and thus we needed to

define the increment of another kind of energy  DU s  corresponding to the increment of surface energy of the separated

60

50

40

30

20

10

0

 Curved front model

 Straight front model

60

50

40

30

20

10

0

   G

   (   J   /  m   2   )

8642

Node number along the crack front

 Curved front model

 Straight front model

Center Edge

Fig. 10.  Distribution of energy release rate along the interface crack front.

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interface. When DU s   is divided by the area of extended interface crack, it should directly correspond to the energy release

rate in the model. The results were presented in Fig. 12, where the ordinate indicates the amount of released energy  G  eval-uated by the methods with two conditions explained above. The abscissa means the simulated length of interface crack

extension, i.e., the number of nodes released at once in the vicinity of interface crack tip. It is noteworthy that energy release

rates obtained by two different methods agree well with each other. It is also well understood that the amount of energy

release rate changes depending on the location of crack tip. With a fixed displacement of loading point, the load drops with

crack extension, leading to a smaller amount of energy release rate. In contrast, the energy release rate increases with a long-

er crack when the load is kept constant independent of crack length, corresponding to the unstable fracture observed in the

experiment. Therefore to eliminate the effect of finite crack extension length, the results in Fig. 12 were extrapolated to zero

extension length. Abrupt decrease of calculated energy release rate was noted with the data in Fig. 12 close to the crack tip. It

is likely due to the fact that approximation of displacement during the crack opening process is not accurate enough with

 just one or two element. Thus the first set of four data points in Fig. 12 was neglected in extrapolation as indicated with

the linear lines. Almost the same energy release rate, approximately 30 J/m2 was obtained by the extrapolation in both

the cases of fixed load point displacement and constant load, which should have been balanced with the energy required

to separate a unit area of interface at the original position of interface crack tip. It is now concluded that the evaluated inter-face adhesion energy was 30 J/m2 for the case of copper/polyimide system examined in this study.

In Section 2,  it was mentioned that simple extrapolation of peel test results towards zero copper film thickness yields

250 J/m2. This means that the amount of energy consumed to peel off composed of more than 80% of plastic energy even

for the case of extremely thin film. By subtracting the amount of energy for the plastic bending of peeled films, the theory

proposed by Kinloch et al. [20] and Moidu et al. [21] yielded approximately 100 J/m2 and 200 J/m2, respectively. Direct com-

parison of these values with that obtained in this study may not be adequate due to the different mode ratio. However, it is

still obvious that there remains in those values obtained with compensated peel tests a considerable amount of plastically

60

50

40

30

20

10

0

   G 

   (   J   /  m   2   )

9876543210

Number of released elements

Fig. 11.  Convergence of energy release rate calculated with two dimensional models.

   G ,

       ∆   U  s

   /       ∆   A   (   J   /  m   2   )

Length of release delements (µm)

G (Fixed displacement)

G (Constant load)

∆U s / ∆ A(Fixed displacement)

∆U s / ∆ A(Constant load)

8765432

120

100

80

60

40

20

100

Fig. 12.  Evaluation of interface adhesion energy by means of extrapolation.

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dissipated energy both on the metal and polyimide side in the vicinity of extending crack front, which is not taken into ac-

count in their theory. In comparison to those former trials to compensate the results of peel tests, our methods proposed

here has given the most direct evaluation of interface adhesion energy, the amount of energy consumed exclusively to sep-

arate the interface.

Due to the optimized configuration of the specimen and a large difference in the yield stress of two materials, i.e., copper

and polyimide, no significant plastic deformation was observed on the copper side of the interface in the micro fracture test

preformed in this study. However, it is here noted that both the materials were appropriately modeled as elastic–plastic and

that there was no limitation on the yield stress of the materials on both the sides of the interface in the simulation process. It

is therefore well expected that the method of evaluation for the interface adhesion energy proposed above can in principle be

applied directly to any combination of two dissimilar ductile materials without any modification, even for the case where

both the materials have comparable extension of plastic deformation at the crack tip.

6. Conclusion

A new technique was developed to measure bonding strength of copper/polyimide interface in flexible printed circuits.

The strength was evaluated in terms of energy required exclusively to separate the bond on the interface of unit area be-

tween the two materials, which means interface adhesion energy. Contrary to the conventional peel off tests, a new exper-

iment was performed where interface crack was extended with a minimum amount of plastic deformation to improve the

accuracy of numerical computation to separate the energy dissipated with plastic deformation. By dividing the nodes along

the interface in the vicinity of crack tip into two nodes and gradually decreasing the nodal forces to zero, crack extension

process was simulated. The energy supplied to separate the interface was evaluated as the sum of work done by the nodalforces against the mutual displacement. The increment of elastic plastic deformation in the bulk of materials during this pro-

cess was also calculated and was confirmed to agree with the balance of total energy when the interface adhesion energy

was taken into account.

The interface adhesion energy of the sample was obtained to be 30 J/m2, while the conventional peel tests performed on

the same sample yielded 250 J/m2. It is also emphasized that the evaluation was realized without any ambiguous cohesive

stress model. Instead, the equivalent cohesive stress was automatically taken into account according to the experimental

result. The technique developed here can be applied in principle to any configuration of specimens made of any kinds of 

two dissimilar ductile materials, thus a candidate to give a reliable tool for the reliability issues of interface.

 Acknowledgement

The authors would like to acknowledge that this work was performed partly under the support of the Foundation for

Technology Promotion of Electronic Circuit Board.

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