3. Failure of Brittle Coatings on Ductile
Metallic Substrates
Proefschrift
ter verkrijging van de graad van doctor
aan de Technische Universiteit Delft,
op gezag van de Rector Magnificus Prof. dr. ir. J. T. Fokkema,
voorzitter van het College voor Promoties,
in het openbaar te verdedigen op dinsdag 26 februari 2002 om 16:00 uur
door Adnan Jawdat Judeh ABDUL-BAQI,
Master of Science, Bergen, Norway
geboren te Zawieh, Palestine.
4. Dit proefschrift is goedgekeurd door de promotor:
Prof. dr. ir. E. van der Giessen
Samenstelling promotiecommissie:
Rector Magnificus, voorzitter
Prof. dr. ir. E. van der Giessen, Rijksuniversiteit Groningen, promotor
Prof. dr. J.Th.M. de Hosson, Rijksuniversiteit Groningen
Prof. dr. ir. M.G.D. Geers, Technische Universiteit Eindhoven
Prof. dr. G. de With, Technische Universiteit Eindhoven
Prof. dr. ir. F. van Keulen, Technische Universiteit Delft
Dr. G.C.A.M. Janssen, Technische Universiteit Delft
The work of A.J.J. Abdul-Baqi was supported by the Program for Innovative Research, surface
technology (IOP oppervlakte technologie), under the contract number IOT96005.
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8. Samenvatting 91
Propositions 93
Stellingen 95
Curriculum Vitae 97
Acknowledgement 99
vi
9. Chapter 1
Introduction
Hard coatings are usually applied to materials to enhance performance and reliability such as
chemical resistance and wear resistance. Ceramic coatings, for example, are used as protective
layers in many mechanical applications such as cutting tools. These coatings are usually brittle
and the enhancement gained by the coating is always accompanied by the risk of its failure
leading to a premature failure of otherwise long lasting systems. Failure may occur in the
coating itself or at the interface with the substrate. Therefore, mechanical characterization of
such systems, including the possible failure modes under various loading circumstances, is
critical for the understanding and the improvement of its performance.
Indentation has become one of the most common methods to determine the mechanical
properties of materials such as elastic properties, plastic properties and strength. In this test, an
indenter is pushed into the surface of a sample under continuous recording of the applied load
and corresponding penetration depth (Weppelmann and Swain, 1996). Indenters have different
geometries including spheres and cones. They are usually made of diamond due to its extreme
properties like hardness and stiffness. For hard coatings, indentation is one of the simplest tests
in terms of sample preparation (Drory and Hutchinson, 1996). However, the interpretation of
indentation results still poses a big challenge. This has motivated extensive experimental as
well as theoretical studies which covers various indenter geometries and constitutive material
models. The material response in an indentation experiment is governed by both its mechanical
properties and the indenter geometry. One of the most common outputs in indentation exper-
iments is the indentation force versus the indentation depth data (load–displacement curve),
from which material parameters can be extracted.
This thesis provides an improved understanding of indentation-induced failure of systems
comprising a strong coating on relatively softer substrate. Qualitative description of the coating
and the interface fracture characteristics is inferred from failure events. In addition, estimation
of the coating and the interface fracture energies from failure events as commonly done in
indentation experiments is also discussed. The analysis is carried out numerically using a finite
strain, finite element method. An overview of the most common methods used to determine
the mechanical properties of materials by indentation is given in Chapter 2. Both the loading
and the unloading are modeled using the finite element method. The emphasis is based on the
load versus displacement data in comparison with the prediction of some existing analytical and
1
10. 2 Chapter 1
empirical relations. The analysis in this chapter assumes that failure events do not occur during
indentation. This assumption holds true if the generated stresses do not reach the material
strength; otherwise, failure is inevitable.
The main failure events discussed in this thesis are interfacial delamination and coating
cracking. Crack initiation and propagation are modeled within a cohesive surface framework
where the fracture characteristics of the material are embedded in a constitutive model for the
cohesive surfaces. This model is a relation between the traction and the separation of the cohe-
sive zone. It is mainly characterized by a peak traction which reflects the material load carrying
capability, and a fracture energy. Additional criteria for crack initiation and propagation are not
required. The cohesive law we adopt in this study is the one given by Xu and Needleman (1993).
The normal response in this law is motivated by the universal binding law of Rose and Ferrante
(1981), while the tangential (shear) response is considered as entirely phenomenological.
In modeling interfacial delamination, a single cohesive surface is placed along the interface
prior to indentation. The coating is assumed to remain intact and failure is only allowed to
occur at the interface. Shear delamination (mode II) is possible during the loading stage of
the indentation process as discussed in Chapter 3. It is found that a ring-shaped portion of the
coating, outside the contact region, is detached from the substrate. On the other hand, normal
delamination (mode I) can occur during the unloading stage as discussed in Chapter 4. In
this case, a circular portion of the coating, directly under the contact region, is lifted off from
the substrate. Delamination is imprinted on the load–displacement curve by a rather sudden
decrease in the indentation stiffness. For relatively strong interfaces, the stiffness might even
become negative. This leads to a kink on the loading curve and a hump on the unloading curve
in the case of shear and normal delamination, respectively. The latter has recently been observed
experimentally by Carvalho and De Hosson (2001).
Coating cracking is one of the failure events frequently observed in indentation experiments.
The simulation of coating cracking is presented in Chapter 5. Embedding cohesive zones in
between all continuum elements in the coating leads to serious numerical problems in addition
to an artificial enhancement of the overall compliance (Xu and Needleman, 1994). In this
study we adopt a procedure in which the number of cohesive zones is minimized and placed
only at precalculated locations. The interface between the coating and the substrate is also
modeled by means of cohesive zones but with interface properties. It is shown that successive
circumferential through-thickness cracking occurs outside the contact region with crack spacing
of the order of the coating thickness. Each cracking event is imprinted on the load–displacement
curve as a kink.
Estimation of the interface and coating fracture energies from failure events is also investi-
gated in Chapters 4 and 5, respectively. It is found that methods used in indentation experiments
(Hainsworth et al., 1998; Li et al., 1997) generally result in overestimated values of the fracture
energy compared to the actual values. This is mainly attributed to the fact that, in such a highly
nonlinear problem, these methods oversimplify the estimation of the energy release associated
with the failure event.
11. Introduction 3
References
Carvalho, N.J.M., De Hosson, J.Th.M., 2001. Characterization of mechanical properties of
tungsten carbide/carbon multilayers: Cross-sectional electron microscopy and nanoin-
dentation observations. J. Mater. Res. 16, 2213–2222.
Drory, M.D., Hutchinson, J.W., 1996. Measurement of the adhesion of a brittle film on a
ductile substrate by indentation. Proc. Roy. Soc. Lond. A 452, 2319–2341.
Hainsworth, S.V., McGurk, M.R., Page, T.F., 1998. The effect of coating cracking on the
indentation response of thin hard-coated systems. Surf. Coat. Technol. 102, 97–107.
Li, X., Diao, D., Bhushan, B., 1997. Fracture mechanisms of thin amorphous carbon films in
nanoindentation. Acta Mater. 45, 4453–4461.
Rose, J.H., Ferrante, J., 1981. Universal binding energy curves for metals and bimetallic
interfaces. Phys. Rev. Lett. 47, 675–678.
Weppelmann, E., Swain, M.V., 1996. Investigation of the stresses and stress intensity factors
responsible for fracture of thin protective films during ultra-micro indentation tests with
spherical indenters. Thin Solid Films 286, 111–121.
Xu, X.-P., Needleman, A., 1993. Void nucleation by inclusion debonding in a crystal matrix.
Model. Simul. Mater. Sci. Eng. 1, 111–132.
Xu, X.-P., Needleman, A., 1994. Numerical simulations of fast crack growth in brittle solids.
J. Mech. Phys. Solids 42, 1397–1434.
13. Chapter 2
Indentation of bulk and coated materials
Indentation experiments are widely used to measure mechanical properties of materials.
Such properties are extracted from the material response to indentation by means of ana-
lytical and empirical relations available in the literature. The material response is usually
given in terms of load versus displacement data. In this chapter we will examine some of
the existing relations and compare their predictions with our finite-element results. Inden-
tation is modeled for two indenter geometries, namely spherical and conical. The response
of purely elastic materials, elastic-plastic materials and coated materials is investigated.
2.1 Introduction
In the past few decades, indentation has become a powerful tool to determine the mechani-
cal properties of materials such as elastic properties, plastic properties and strength. This has
motivated extensive experimental as well as theoretical studies which cover various indenter
geometries and material models. The most common indenter geometries are a sphere (Brinell
test), a cone (Rockwell test) and a rectangular pyramid (Vickers test). The response in an in-
dentation experiment is governed by both the material properties and indenter geometry.
The first analysis of the stresses arising from a frictionless contact between two elastic bod-
ies was first studied by Heinrich Hertz in 1881 when he presented his theory to the Berlin
Physical Society (Johnson, 1985). The publication of his classic paper On the contact of elastic
solids in 1882 (Hertz, 1882) may be viewed, according to Johnson (1985), to have started the
subject of contact mechanics. However, developments in the Hertz theory did not appear in the
literature until the beginning of the 20th century (Johnson, 1985). The problem of determining
the stress distribution within an elastic half space due to surface tractions and a concentrated
normal force has been considered first by Boussinesq (1885). Based on his solution, partial
numerical results were derived later by Love for a flat-ended cylindrical punch (Love, 1929)
and for a conical punch (Love, 1939). Starting in 1945, a more comprehensive treatment of
the contact problem was followed up by Sneddon in a series of publications listed in (Sneddon,
1965). He has derived analytical formulas which relate the applied load, the indentation depth
and the contact area for punches of different axisymmetric geometries. In the above studies, the
contact is assumed frictionless. Contact involving a sticking indenter has been latter analyzed
by Spence (1968).
5
23. Indentation of bulk and coated materials 15
0.7
0.6
FEM
Analytical: Eq. (2.3)
0.5
0.4
F (N)
0.3
0.2
0.1
0
0 0.1 0.2 0.3 0.4 0.5
0.2
FEM
0.15 Analytical: Eq. (2.6)
0.1
0.05
0
0 0.1 0.2 0.3 0.4 0.5
h (µm)
Figure 2.6: Force versus indentation depth for an elastic coating on an elastic substrate with
different Young’s modulus. The analytical results in (a) and (b) are obtained from Eqs. (2.3)
and (2.6), respectively. The effective properties (Eq. 2.16) and
ˆ¥
Ž (Eq. 2.17) are used in
ˆb¦
Ž
the definition of 7 ¥(Eq. 2.5).
effective properties and
ˆP¥
Ž in the definition of
ˆb¦
Ž (Eq. 2.5). It is seen that the analytical
7 p¥
solution overestimates the force by a maximum of and € €by
in (a) and (b), respectively.
Gao et al. (1992) also investigated the range of validity of this solution through finite element
analysis. They found that the solution is valid, within an error of , at least for moduli ratio
€ y
up to 2. For larger moduli ratio, the weight functions (Eq. 2.18) fail to accurately represent the
26. 18 Chapter 2
Hill, R., 1992. Similarity analysis of creep indentation tests. Proc. Roy. Soc. Lond. A 436,
617–630.
Hill, R., Stor˚ kers, B., Zdunek, A.B., 1989. A theoretical study of the Brinell hardness test.
a
Proc. Roy. Soc. Lond. A 423, 301–330.
Johnson, K.L., Contact Mechanics (Cambridge University Press, Cambridge, United King-
dom, 1985).
King, R.B., 1987. Elastic analysis of some punch problems for a layered medium. Int. J.
Solids Struct. 23, 1657–1664.
Korsunsky, A.M., McGurk, M.R., Bull, S.J., Page, T.F., 1997. On the hardness of coated
systems. Surf. Coat. Technol. 99, 171–183.
Loubet, J., Georges, J., Marchesini, J., Meille, G., 1984. Vickers indentation curves of mag-
nesium oxide (MgO). J. Tribology 106, 43–48.
Love, A.E.H., 1929. Stress produced in a semi-infinite solid by pressure on part of the bound-
ary. Phil. Trans. A. 228, 377.
Love, A.E.H., 1939. Boussinesq’s problem for a rigid cone. Quart. J. Math. 10, 161.
Matthews, J.R., 1980. Indentation hardness and hot pressing. Acta Metall. 28, 311.
Mesarovic, S.Dj., Fleck, N.A., 1999. Spherical Indentation of elastic-plastic solids. Proc. Roy.
Soc. Lond. A 455, 2707–2728.
Sneddon, I.N., 1965. The relation between load and penetration in the axisymmetric Boussi-
nesq problem for a punch of arbitrary profile. Int. J. Engng. Sci. 3, 47–57.
Spence, D.A., 1968. Self-similar solutions to adhesive contact problems with incremental
loading. Proc. Roy. Soc. Lond. A 305, 55.
Tabor, D., The Hardness of Metals (Clarendon Press, Oxford, 1951).
Tunvisut, K., O’Dowd, N.P., Busso, E.P., 2001. Use of scaling functions to determine me-
chanical properties of thin coatings from microindentation tests. Int. J. Solids Struct. 38,
335–351.
Wittling, M., Bendavid, A., Martin, P.J., Swain, M.V., 1995. Influence of thickness and sub-
strate on the hardness and deformation of TiN films. Thin Solid Films 270, 283–288.
27. Based on: A. Abdul-Baqi and E. Van der Giessen, Indentation-induced interface delamination of a strong film on
a ductile substrate, Thin Solid Films 381 (2001) 143.
Chapter 3
Indentation-induced interface
delamination of a strong film on a ductile
substrate
The objective of this work is to study indentation-induced delamination of a strong film
from a ductile substrate. To this end, spherical indentation of an elastic-perfectly plas-
tic substrate coated by an elastic thin film is simulated, with the interface being modeled
by means of a cohesive surface. The constitutive law of the cohesive surface includes a
coupled description of normal and tangential failure. Cracking of the coating itself is not
included and residual stresses are ignored. Delamination initiation and growth are analyzed
for several interfacial strengths and properties of the substrate. It is found that delamination
occurs in a tangential mode rather than a normal one and is initiated at two to three times
the contact radius. It is also demonstrated that the higher the interfacial strength, the higher
the initial speed of propagation of the delamination and the lower the steady state speed.
Indentation load vs depth curves are obtained where, for relatively strong interfaces, the
delamination initiation is imprinted on this curve as a kink.
3.1 Introduction
Indentation is one of the traditional methods to quantify the mechanical properties of materials
and during the last decades it has also been advocated as a tool to characterize the properties of
thin films or coatings. At the same time, for example for hard wear-resistant coatings, inden-
tation can be viewed as an elementary step of concentrated loading. For these reasons, many
experimental as well as theoretical studies have been devoted to indentation of coated systems
during recent years.
Proceeding from a review by Page and Hainsworth (1993) on the ability of using indenta-
tion to determine the properties of thin films, Swain and Menˇ ik (1994) have considered the
c
possibility to extract the interfacial energy from indentation tests. Assuming the use of a small
spherical indenter, they identified five different classes of interfacial failure, depending on the
relative properties of film and substrate (hard/brittle versus ductile), and the quality of the ad-
hesion. Except for elastic complaint films, they envisioned that plastic deformation plays an
important role when indentation is continued until interface failure. As emphasized further by
Bagchi and Evans (1996), this makes the deduction of the interface energy from global inden-
19
28. 20 Chapter 3
tation load versus depth curves a complex matter.
Viable procedures to extract the interfacial energy will depend strongly on the precise mech-
anisms involved during indentation. In the case of ductile films on a hard substrate, coating
delamination is coupled to plastic expansion of the film with the driving force for delamination
being delivered via buckling of the film. The key mechanics ingredients of this mechanism have
been presented by Marshall and Evans (1984), and Kriese and Gerberich (1999) have recently
extended the analysis to multilayer films. On the other hand, coatings on relatively ductile sub-
strates often fail during indentation by radial and in some cases circumferential cracks through
the film. The mechanics of delamination in such systems has been analyzed by Drory and
Hutchinson (1996) for deep indentation with depths that are two to three orders of magnitude
larger than the coating thickness. The determination of interface toughness in systems that show
coating cracking has been demonstrated recently by e.g. Wang et al. (1998). In both types of
material systems there have been reports of ”fingerprints” on the load–displacement curves in
the form of kinks (Kriese and Gerberich, 1999; Hainsworth et al., 1997; Li and Bhushan, 1997),
in addition to the reduction of hardness (softening) envisaged in (Swain and Menˇ ik, 1994). The
c
origin of these kinks remains somewhat unclear, however.
A final class considered in (Swain and Menˇ ik, 1994) is that of hard, strong coatings on
c
ductile substrates, where Swain and Menˇ ik hypothesized that indentation with a spherical in-
c
denter would not lead to cracking of the coating but just to delamination. This class has not
yet received much attention, probably because most deposited coatings, except diamond or
diamond-like carbon, are not sufficiently strong to remain intact until delamination. On the
other hand, it provides a relatively simple system that serves well to gain a deep understanding
of the coupling between interfacial delamination and plasticity in the substrate. An analysis of
this class is the subject of this paper.
In the present study, we perform a numerical simulation of the process of indentation of
thin elastic film on a relatively softer substrate with a small spherical indenter. The inden-
ter is assumed to be rigid, the film is elastic and strong, and the substrate is elastic- perfectly
plastic. The interface is modeled by a cohesive surface, which allows to study initiation and
propagation of delamination during the indentation process. Separate criteria for delamination
growth are not needed in this way. The aim of this study is to investigate the possibility and
the phenomenology of interfacial delamination. Once we have established the critical condi-
tions for delamination to occur, we can address more design-like questions, such as what is the
interface strength needed to avoid delamination. We will also study the ”fingerprint” left on
the load–displacement curve by delamination, and see if delamination itself can lead to kinks
as mentioned above in other systems. It is emphasized that the calculations assume that other
failure events, mainly through-thickness coating cracks, do not occur.