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Effect of Loading Phase Angle on Interfacial Fracture
Toughness for Circumferentially Notched Tensile
Specimens
Joe Elambasseril
1,2
, Raafat Ibrahim
1
, and Raj Das
2
1
Department of Mechanical Engineering, Monash University,
Clayton VIC 3168, Australia
2
CSIRO Mathematical and Information Sciences,
Clayton VIC 3168, Australia
Abstract— Coatings often used as a covering to enhance the
quality and protect the material to which they are applied to.
The interface between the coating and substrate is the weakest
part of the material system. Understanding the characteristics
of the interfacial fracture toughness is important as it is the
bimaterial property that has the most significant impact on the
performance of the system. Through accurate prediction of the
interfacial fracture toughness, coatings can be produced that
are more reliable as unanticipated failures are less likely to
occur. This paper analyses the new experimental method-
Circumferentially Notched Tensile (CNT) test, using numerical
finite element analysis, in order to create a global testing
method that can determine interfacial fracture toughness of
bimaterial systems.
Keywords: A. coatings B. adhesion, C. Finite Element
Analysis, D. Circumferential Notch Tensile Test.
I. INTRODUCTION
Fabrication of a thin or thick coating of one material
deposited onto a substrate of a different material gives rise to
stresses in the coating due to differing coefficients of thermal
expansion, chemical reactions, lattice mismatch, or other
physical effects. Therefore, the most failure prone area in
this composite system often resides at the interface between
the coating and substrate [1]. In order to make multi-layered
coating devices and structural composites with long-term
reliability, the fracture behaviour of the material interfaces
must be determined. However, none of the existing
interfacial fracture toughness testing methods is fully
conformed to theory of fracture mechanics, as is obvious
from the dispersion in the existing data and unpredictability
in determining the interfacial toughness evaluation
procedure. We proposed an innovative interfacial fracture
toughness testing procedure named Circumferentially
Notched Tensile (CNT) test which is anticipated to
overcome the deficiencies associated with the existing
methods [2, 3].
The evaluation of interfacial strength is a complex task
due to the complexity of loading, small dimension of
coating, material conditions of interface cracking and coating
spallation. The crack propagates along the interface under
mixed mode due to the asymmetry in the material properties
about the interface and possible asymmetry in loading [4]. A
proper interfacial fracture toughness test should be (a) able to
determine the phase angle (mode mixity) effects on
interfacial fracture toughness (Ƚ) (b) inexpensive and
accurate (c) deformations should be within elastic limit and
(d) simple in sample preparation.
Several methods for testing mechanical properties of a
bi-material interface are reviewed by Valli [5], Chalker et al
[6], Volinsky et al [1] and Evans and Hutchinson [7]. Bagchi
and Evans [8] reviewed the mechanics of thin coatings
decohesion and compares the various measuring methods.
K.L Mittal in his book [9] has listed more than 300 methods
used by researchers to determine interfacial fracture
toughness. But none of the testing methods can be
considered as an ideal method for measuring adhesion [9].
From the review it is clear that, in the early studies of
adhesion, the effect of phase angle ȥ was not necessarily
noted. However, in more recent studies [1, 4], the mode
mixity is analysed with the critical interface energy release
rate. From the existing testing methods, it is clear that a
simple method with the ability to change the phase angle is
needed for evaluating the quantitative interfacial strength of
a coated system.
II. A
PPROACH AND METHODOLOGY
The interfacial fracture energy depends on the mode
mixity, Ƚ(ȥ). The crack extends when the energy release rate
(G
c
) reaches the fracture energy given by:
)(
ψ
Γ
=
C
G
(1)
The mode mixity is related to the ratio of the shear stress
to the tensile stress ahead of the crack tip [4, 10] by:
)]/(tan[/
2212
lrε+
ψ
=
σσ
(2)
Where
ε
is a constant determined
b
y the elastic properties
of the coating and the substrate, r is the distance from the
crack tip, and l is an arbitrary length.
978-1-4244-5262-0/10/$26.00 © 2010 IEEE ICONN 2010376
Figure 1. Configuration of the cross-section of a CNT specimen with
notch angle ș (loading phase angle), where ș can be varied for studying the
effect of mode mixity on the interfacial fracture toughness.
The stress intensity factors at the crack tip are estimated
from the J-integrals using the finite element (FE) models.
Therefore, the values of the mode mixity are calculated using
Equation (2) to fit the ratio distribution from the FE results.
The mode mixity or phase angle (ȥ) mainly depends on the
loading phase angle (ș), as shown in Figure 1.
The CNT test methodology is illustrated in figure 2. To
evaluate adhesion strength on the basis of fracture toughness,
well controlled sharp precrack along the interface is
essential. Only the weak interface is separated by applying
an adequate load. Sharp pre-cracking at the interface helps to
initiate the crack from the crack tip and propagate along the
interface because of the high stress concentration at the tip of
the pre-crack. The approach to generate the pre-crack is
based on the presumption that interface strength between
coating and substrate depends on materials used i.e. by
introducing a foreign material between coating-substrate
system as a weak interface. This was achieved by depositing
a thin layer of gold between nickel coating and mild steel
substrate. The dimension of the precrack is achieved by
masking the substrate to form the boundary lines.
a) (b) (c)
Figure 2. Sample preparation procedure for the circumferential notched
tensile (CNT) test (a) Cylindrical substrate machined with U notch (b)
interfacial precrack generation (c) coated precracked CNT specimen.
III. NUMERICAL MODELLING APPROACH
The finite element (FE) studies developed models that
can closely simulate the CNT specimen with the crack
orientated at various angles to the central axis of the
cylindrical specimen. The CNT specimens used in the FEM
investigation has an outside diameter of 9.5 mm and length
of 120 mm. A “U” notch, which is 2 mm in width and 4 mm
in length, is considered in the middle of the specimen. The
coating thickness modelled is 15 ȝm. The stress state along
the interface is also analysed. The tensile loadings on the
coating/substrate CNT system are modelled as axisymmetric
finite element analyses with 8-node biquadratic
axisymmetric quadrilateral, reduced integration elements
(CAX8R). Analysis of crack growth is computationally
expensive as a very fine mesh is required to model the high
stress concentrations at the crack tip. To increase the
computational efficiency, we used a combination of a very
fine mesh around the crack front with a relatively coarse
mesh for the rest of the specimen in the global model. This
was achieved using a sub-modelling approach to resolve the
stress field around the crack in details [11]. Each submodel
was compared with the previous submodel or global model
using overlay method to avoid the deviations in results. The
FE models were analysed with up to six submodels and it
was optimised for two submodels. An axisymmetric global
model was created for the coated CNT specimen with coarse
mesh of size 0.015 mm and submodel II with mesh size of
0.0025mm. Elastic-plastic material model was used to
represent the nickel coating and steel substrate properties as
to analyse plastic as well as elastic stresses and strains. The
properties are listed in table 1 [12]. The tensile load and
axisymmetric and symmetric boundary conditions were
applied.
TABLE I. TYPICAL MATERIAL PROPERTIES USED IN FEM ANALYSIS
Young’s
Modulus
MPa
Poisson
ratio
Ȟ
Yield
stress
MPa
Exponent Yield
offset
%
Substrate 210000 0.29 300 5 0.2
Coating 185000 0.3 240 3.8 0.2
The nickel coating and steel substrate were assumed to be
homogeneous, continuous and isotropic. Since the effects of
residual stresses and circumferential stresses are very small
in the electroplated coatings, they are neglected [13]. The
plastic deformation was taken into consideration in
estimating the strain energy of the debonding due to the
ductile nature of the coating. Deformation theory, Ramberg-
Osgood plasticity model was used in ABAQUS to define the
behaviour of ductile coating under static loading.
IV. R
ESULTS AND DISCUSSION
A thorough elastic and elastic-plastic finite element analysis
has been carried out in the current analysis, to study the
initiation and development of the plastic zone in nickel
coating/steel substrate systems under tensile loading. The
377
CNT configurations with notch angles (ș) of 0, 15, 30, 45
and 60 degrees were considered in these analyses (refer
figure 1 for notch angle). The fracture mechanics parameter,
J-integral was used to relate the energy release associated
with crack growth and also to measure the deformation
intensity at a crack tip. The estimated J-integral value was
compared with the critical energy release value for the
bimaterial system under consideration to predict its fracture.
The crack was modelled as a seam using ABAQUS
interaction property definition, since the interface crack
surfaces in the unloaded state lie next to each other with no
gap. The q vector was used to define the direction of crack
extension. The J-integral and stress intensity factors are path
independent, and evaluated using six integral contours. The
first contour was provided at the crack tip, and subsequent
contours are generated as contours passing through the
adjacent neighbouring elements, moving out from the crack
tip. The values from the last three contours are identical up to
five digits and the reported values are from the sixth contour
in all cases for consistency. Small variations of values
between integral contours signify the quality of the mesh for
calculating the fracture parameters.
A. Elastic-Plastic Stress analyses for different crack
position
In this section the effect of crack position was analysed
for stress and strain distributions on different notch angled
(ș) CNT specimens. The notch angles considered are
0,15,30,45 and 60 degrees for the analyses. Various crack
positions investigated were at distances of 0.01, 0.1, 0.2, 0.3,
0.4 and 0.5 mm from the notch corner. All the specimens
were modelled at a load of 3750 N. The crack length
considered was 0.5mm. The Crack surface displacement
method and J-integral method were used to predict the
possibility of crack propagation along the interface. The
stress and strain distributions for a crack positioned at 0.01
mm from the notch corner are shown in figure 3.
(a) (b)
(c) (d)
Figure 3. Stress -strain distribution for a crack positioned at 0.01mm
from notch (a)Von Mises (b)Longitudinal normal stress (c) Shear stress (d)
Plastic strain
Crack near to the notch corner shows higher stress
concentrations at the crack tip compared to crack positioned
away from the notch corner. Energy available at the crack tip
reduces as the crack moves away from the notch corner. The
comparison is shown in figure 4. The FE analyses pointed up
that for 0 and 15 degree notch angles the crack position
between 0.01 and 0.2 mm is superior option and for 30, 45
and 60 degree notch angles the crack position between 0.01
and 0.1 mm are better options. Crack lengths also show an
effect in the fracture of coatings. Crack lengths between 0.1
and 0.5 mm were also analysed. When the crack length is
more than 0.2 mm, crack shows an opening at the end near to
notch corner and closure at the other end. This will result in
cohesive fracture of coating.
Figure 4. Effect of crack positions on energy release rate
If the crack is away from the notch the energy available
at the crack tip is less and if it is at the notch corner the crack
propagation in unpredictable. So the crack position between
0.01 and 0.2 mm from the notch corner is found to be the
better option depending on the notch angle and interfacial
fracture toughness of coating.
B. Energy release rate and phase angle
The phase angles (mode mixity) were estimated at
different crack positions for different notch angles as shown
in figure 5.
Figure 5. Phase angles calculated for CNT specimens
The 0, 15 and 30 degree notch angles were considered for
the elastic analyses. The 45 and 60 degree specimens were
not included in linear elastic analyses due to the significant
effect of plasticity at the crack tip from the geometry of the
378
specimen. The maximum stress in the coating-substrate
system is much less than the yield stress when the
delamination occurs. This justifies the elastic analyses of
ductile coatings for specimens having notch angle under 30
0
.
Figure 6. Variation of energy release rate with phase angle
C. Analysis on ratio of elastic modulus
The CNT specimens were also analysed for the elastic
ratio effect on energy release rate, phase angle and stress
intensity factors. Let E1 be the Young’s modulus of coating
and E2 be the Young’s modulus of substrate. Poisson’s Ratio
is considered as 0.3 for coating in the young’s modulus ratio
analysis.
Figure 7. Energy release rate with phase angle for different ratios of
modulus
Figure 8. Variation of energy release rate with ratios of modulus
Figure 9. Variation of phase angle (mode mixity) with ratios of modulus
V. CONCLUSION
In this study the finite element analyses were carried out
in two stages: (1) elastic- Plastic analysis to study the effect
of interface pre-crack position on energy release rate and
stresses distributions (2) Elastic analysis to study the energy
release rate , mode mixity for different notch angles, crack
positions and elastic modulus ratios. The cracking resistance
of the interface is characterised by notch angle of CNT
specimens. The analysis shows an increase of interfacial
fracture toughness as the mode mixity increases. This is
significant when the mode mixity is large.
R
EFERENCES
[1] A. A. Volinsky, N. R. Moody and W. W. Gerberich,Interfacial
toughness measurements for thin films on substrates,Acta
Materialia,50,2002,441-466.
[2] J. Elambasseril, R. N. Ibrahim and R. Das,A novel technique to
characterise and evaluate the interfacial fracture toughness of coatings
The Seventeenth Annual International Conference on
COMPOSITES/NANO ENGINEERING Hawaii, USA,2009
[3] J. Elambasseril, R. N. Ibrahim and R. Das,Determination of interfacial
fracture toughness of coating using notched cylindrical
substrate,Composites Part B: Engineering,2009,Unpublished.
[4] J. W. Hutchinson, Suo, Z,Mixed mode cracking in layered materials
Advances in Applied Mechanics 29,1992,63-191.
[5] J. Valli,A review of adhesion test methods for thin hard
coatings,AVS,4,1986,3007-3014.
[6] P. R. Chalker, S. J. Bull and D. S. Rickerby,A review of the methods
for the evaluation of coating-substrate adhesion,Materials Science and
Engineering A,140,1991,583-592.
[7] A. G. Evans and J. W. Hutchinson,The thermomechanical integrity of
thin films and multilayers,Acta Metallurgica et
Materialia,43,1995,2507-2530.
[8] A. Bagchi and A. G. Evans,The mechanics and physics of thin film
decohesion and its measurement,Interface Science,3,1996,169-193.
[9] K. L. Mittal,Adhesion measurement of films and coatings,VSP,1995,
[10] J. R. J. R. Rice,Elastic fracture mechanics concepts for interfacial
cracks,Journal of applied mechanics,55,1988,98-103.
[11] A. E. Bogdanovich and I. Kizhakkethara,Three-dimensional finite
element analysis of double-lap composite adhesive bonded joint using
submodeling approach,Composites Part B:Engineering,30,1999,537-
551.
[12] L. Q. Zhou, Y. P. Li and Y. C. Zhou,Numerical analysis of
electrodeposited nickel coating in multistage drawing
processes,Journal of Engineering Materials and
Technology,127,2005,233-243.
[13] L. H. Xiao, X. P. Su, J. H. Wang and Y. C. Zhou,A novel blister test to
evaluate the interface strength between nickel coating and low carbon
steel substrate,Materials Science and Engineering: A,501,2009,235-
241.
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