Materials Science and Engineering A 419 (2006) 189–195

Effect of coating thickness on crack initiation andpropagation in non-planar bi-layers

Tarek Qasim, Chris Ford ∗, Malika Bongue-Boma,Mark B. Bush, Xiao-Zhi Hu

School of Mechanical Engineering, The University of Western Australia,35 Stirling Highway Crawley, WA 6009, Australia

Received in revised form 15 December 2005; accepted 15 December 2005

Abstract

Hertzian contact damage is studied in glass coatings (thickness range 160 �m to 1 mm) on polycarbonate polymer substrates. Both planar andnon-planar geometries are considered, subjected to indentation by fixed size spherical indenters of radius 4 mm. Finite element analysis is carriedout to evaluate the stress distribution in the bilayer structure. Radial cracking initiating at the coating undersurface directly under the indenter ist

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he primary focus of this investigation, and cone cracking at the top surface of the coating (inner and outer cone cracks) is also considered.It is concluded that crack propagation is facilitated in coatings of an intermediate thickness. Thick (1000 �m) coatings resist deflection, decreasing

ensile stresses at the coating undersurface, while thin (160 �m) coatings deflect massively, causing a compression zone beneath the indenter whichlso limits undersurface tension.

2006 Published by Elsevier B.V.

eywords: Finite element analysis; Indentation; Crack; Shape irregularity; Bilayer

. Introduction

The development of systems combining the wear resistancef a brittle coating and the toughness of a ductile under layers very important for high damage tolerance applications. The

echanical response of brittle layered structures under Hertzianndentation is of considerable interest in disciplines such asiomechanics and tribology, and in the field of dentistry, forooth restorations such as crowns [1,2]. The contact damageolerance and failure resistance of such systems is affected by aariety of parameters. Careful selection of component propertiesstiff coating/soft interlayer) and coating geometry (planar/non-lanar) may therefore be used to maximize the damage resistancef such systems.

A considerable amount of experimental and analytical inves-igation of systems utilising materials relevant to dental prosthe-es has been carried out using Hertzian indentation, includingork by Zhao et al. [3–5], Lee and Lawn [6,7], Chai [8], Ford

t al. [9] and Shrotriya et al. [10]. However, the bulk of the pre-

vious work focused on the response of flat bilayer or trilayersystems, which did not account for the effects of coating curva-ture. The principle modes of failure observed in these studies areshown in Fig. 1: plastic yielding of the substrate, cone cracking(Hertzian and outer cracks) at the upper surface of the coating,radial (interface) cracks at the lower surface of the coating. Crit-ical loads for radial cracks and cone cracks are denoted as Pr andPc, respectively. Different failure modes dominate for differentmaterial combinations and geometries.

Previous studies by the authors [9,11–13] examined theeffects of changing curvature, of both the indenter and theindented samples. Experimental studies [11–13] were inter-preted using finite element methods [12,13] and concluded thatcurved surfaces on compliant substrates are generally moreresistant to initiation of the dominant radial cracking modethan equivalent planar systems, although convex curvature mayenhance subsequent crack growth to failure [13].

This paper considers the effect of coating thickness, whichwhile well documented in flat multilayers, has not previouslybeen closely examined in curved systems. The focus of this studyis the radial crack system, identified as the primary failure mode

∗ Corresponding author. Tel.: +61 8 6488 1901; fax: +61 8 6488 1024.E-mail address: chrisf@mech.uwa.edu.au (C. Ford).

in brittle coatings on compliant substrates [14–16], and mentionis also made of cone cracking (usually a secondary mode for this

921-5093/$ – see front matter © 2006 Published by Elsevier B.V.oi:10.1016/j.msea.2005.12.023

190 T. Qasim et al. / Materials Science and Engineering A 419 (2006) 189–195

Fig. 1. Schematic of Hertzian indentation of a convex bilayer, showing threefailure modes.

material system). Crack initiation and propagation, and ultimatefailure of the coating are all assessed. It is shown that crackgrowth to failure is facilitated in coatings of an intermediatethickness, since thick coatings are generally more resistant tocrack initiation, and thin coatings exhibit localised damage.

2. Experimental investigation

Following previous experimental studies [11,12], glass/epoxy layer structures were fabricated to model dental systemsincorporating both flat and curved surfaces. Borosilicate glass(D263, Menzel-Glaser, Germany) was chosen for the brittlecoating, initially supplied as flat plates of 160, 300 and 1000 �mthickness. This glass has a Young’s modulus of 73 GPa, close tothat of dental enamel and crown porcelains, and is transparent,allowing in situ observation of developing crack morphologies.Epoxy resin (Resin R2512, ATL Composites, Australia) with aYoung’s modulus of 3.4 GPa was used for the substrate material,promoting the growth of radial cracks which are the focus of thisstudy.

In order to obtain a curved coating geometry, the glass plateswere slumped over stainless steel balls of radius 8 mm as fol-lows. To prevent the glass from sticking to the steel, the heatedspheres were treated with kiln wash (50% kaolin + 50% aluminahydrate, by weight, mixed with four to six parts distilled water)a ◦afurcP(Tmo

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radial crack initiation at the glass undersurface, eliminating com-plications from premature cone cracking at the top surface, andintroduces a more uniform surface flaw distribution, reducingscatter and improving test repeatability. Half of the samples wereleft in their as-polished state for comparison.

The epoxy substrate was then built up to a thickness of6–8 mm in the case of the flat specimens, and 6 mm from the low-est part of the glass in the curved specimens (i.e. 14 mm thickat the centre). The substrate was deposited under the formedcoating in thin layers, in order to prevent cracking of the glassdue to thermal shrinkage, with each layer allowed to set for 24 hbefore further material was added.

Indentation tests were carried out in air (at room temperature)using a tungsten carbide sphere of radius ri = 4 mm mounted ina screw-driven testing machine (Instron 4501, Instron Corp.,Canton, MA), taking care that the sphere and specimens werealigned so that the contact occurred axisymmetrically. Loads upto 2000 N could be attained in this configuration. The tests wereconducted under displacement control, at a cross-head speed of0.1 mm/min. During loading, the specimens were viewed fromthe side and slightly from above using a video camera, such thatthe contact and side walls of the specimens were within the fieldof view at all times. A light source was placed behind the spec-imens to optimize crack visibility. A single-cycle axisymmetricindentation was performed on each specimen. Critical loads toinitiate radial cracks at the glass undersurfaces were monitorediwptwdo

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t ≈230 C. The sprayed film was then lightly smoothed withlint-free cloth. The glass plates were then subjected to the

ollowing heat treatment in air: (i) heat to ≈750 ◦C and holdntil the glass plates conform to the spherical die curvature; (ii)apidly cool to solidify the plates; (iii) anneal at ≈560 ◦C andool slowly to room temperature to avoid any residual stresses.lates used for flat coatings were subjected to a similar treatmentusing a planar die surface) to maintain consistency in results.he glass thickness did not alter significantly during this treat-ent, with micrometer testing showing a maximum reduction

f 20 �m (or 2%) at the top of the specimen.Prior to addition of the epoxy substrate, the prospective

ndersurfaces of the glass plates were abraded with 50 �m sandarticles using a dental sand blasting machine (Harnish + Rieth,-G4000, Czech Republic). This treatment favours preferential

n each specimen. Subsequent propagation of the radial cracksith further increase in the loading was then followed to theoint of failure (where applicable), i.e. when the cracks reachedhe extremities of the curved surfaces. Some 5–10 separate testsere run at each surface radius for the convex specimens. Noelamination was observed between the glass and epoxy in anyf the tests until ultimate failure, attesting to the sound bonding.

. Finite element modelling

Finite element modeling was used to compute stresses in thelass layers, specifically the tensile hoop (tangential) stress at thendersurface and radial stresses inducing ring cracks at the coat-ng surface, using ABAQUS version 6.4. Input Young’s modulusnd Poisson’s ratio were 73 GPa and 0.21 for the glass, 3.4 GPand 0.33 for the epoxy, and 614 GPa and 0.3 for the tungstenarbide indenter (all manufacturer specifications). The solutionllowed for large deflection and geometric non-linearity.

The meshes were systematically refined, particularly in theritical glass undersurface region, until the solutions attainedonvergence, with mesh size of the order of 20 �m. Loads werepplied monotonically over the experimental range from zero to000 N. A sample mesh and stress contour for a curved specimennder a 200 N indentation, representative of those used in thistudy, is shown in Fig. 2.

Algorithms for fracture predictions have been well docu-ented in the literature [17,18]. In this study, for prediction

f radial crack critical loads, two different critical stresses weresed, following previous works [13,14]. This method relies onn estimation of critical stress based on an assumed flaw size.

here the glass undersurface was abraded prior to addition of

T. Qasim et al. / Materials Science and Engineering A 419 (2006) 189–195 191

Fig. 2. Sample finite element mesh and tensile stress contour.

the epoxy substrate, a critical stress of 75 MPa was used, whereasfor samples with the coating left in an as-polished condition, acritical stress of 295 MPa was used, reflecting the difference inflaw state following surface treatment. Since radial cracking wasalways observed prior to cone cracking, no FEA predictions forcone cracks are included.

4. Results and discussion

4.1. Critical loads

In all of the systems under consideration, radial cracking wasfound to be the primary mode of cracking, as shown in Fig. 3.Both radial and cone cracks can be observed, however the seg-mentation of the cone cracks indicates the prior presence ofradial cracks. Consequently, radial cracking is the focus of thisstudy.

In the both the flat and curved specimens, radial crack criticalloads increased with coating thickness in the curved specimens,as seen in Fig. 4, with the critical loads in curved specimenshigher than for equivalent flat systems, indicating increasedresistance to radial cracking due to the convex curvature. In eachcase, the abraded specimens exhibited a significantly lower crit-ical load than the equivalent as-polished systems, highlightingthe effect of larger, more evenly distributed flaws from whichc

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discrepancy between the values of the predicted and observedcritical loads for the abraded systems. A possible explanationfor this result is that the flaw sizes used to calculate the 75 MPacritical stress used [13,14] are an overestimation of the actualflaw distribution.

4.2. Crack propagation

Fig. 5 shows the evolution of radial crack length (measuredas a circumferential length in curved coatings) with increasingindentation load, for both as polished samples (a) and abradedspecimens (b). Each set of curves shows the results for the threecoating thicknesses considered in this study, with flat specimensrepresented by solid curves and convex specimens representedby dashed curves.

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racks can nucleate.Curves showing FEA predictions for Pr are also shown in

ig. 4. The FEA curves reflect the trends seen both the flatnd curved systems, and the as-polished critical loads are pre-icted with reasonable accuracy. However, there is a significant

Fig. 3. Contact damage in unloaded flat as-polished specimens after 1000

ig. 4. Radial crack critical loads plotted against coating thickness, showingEA predictions (curves) and experimental observations (data points) for bothonvex and flat systems, with as-polished and abraded treatment of the coatingndersurface.

entation: (a) 160 �m coating; (b) 300 �m coating; (c) 1000 �m coating.

192 T. Qasim et al. / Materials Science and Engineering A 419 (2006) 189–195

Fig. 5. Experimentally determined evolution of radial crack length with increas-ing indentation load, for (a) as-polished and (b) abraded specimens.

Several trends are immediately obvious from Fig. 5. Firstly,the flat samples exhibit stable crack propagation at much higherindentation loads, whereas in the curved specimens, the crackgrows much more rapidly, at a lower load. This is a reversal ofthe trend observed for crack initiation—curved specimens thushave increased resistance to radial crack initiation but are moreprone to subsequent crack growth.

Secondly, the flat abraded systems are generally more resis-tant to radial crack growth than the flat as-polished systems,as shown by the use of the same scales in each plot—the loadsrequired to produce a crack of a given length in the abraded spec-imens are lower, and the cracks propagate more slowly. Thereis very little difference between as-polished and abraded resultsin curved systems.

Fig. 6. Peak tensile hoop stress at the coating undersurface plotted against inden-tation load for curved and flat systems with coating thicknesses of 160, 300 and1000 �m.

Fig. 7. Hoop stresses at the coating undersurface in curved systems, plottedagainst radial distance from the axis of symmetry, for loads of 100 N (filledsymbols) and 1000 N (unfilled symbols). Note the change of location for thepeak hoop stress in the 160 �m system under the higher load.

The thickest (1000 �m) coatings require the highest loadto cause the radial cracks to propagate, as expected. For allof the 1000 �m systems (with the exception of the curved as-polished system) an initial period of slow steady crack growthwas observed, followed by a relatively rapid (but still stable)crack growth to the edge of the specimen.

Additionally, in each case, the 160 �m coatings requiredgreater loading to force crack growth than similar 300 �m coat-ings (of the same curvature and undersurface treatment), eventhough the critical loads for radial crack initiation are alwayslower in the thinner coatings. For any combination of surfacetreatment and curvature, the 300 �m coatings proved least resis-tant to radial crack growth.

Fig. 8. Contact damage in unloaded curved abraded specimens: (a) 160 �m coating after 1500 N indentation; (b) 300 �m coating after 600 N indentation; (c) 1000 �mcoating after 1050 N indentation.

T. Qasim et al. / Materials Science and Engineering A 419 (2006) 189–195 193

Fig. 9. Evolution of contact damage in curved abraded specimens. Pictures on the left show damage evolution in a 300 �m coating as indentation load increasesfrom 400 to 600 N; the series at right shows a 1000 �m coating under indentation loads from 1000 to 1050 N.

194 T. Qasim et al. / Materials Science and Engineering A 419 (2006) 189–195

The peak hoop stresses calculated from FEA (shown in Fig. 6)provide an interpretation for these observations. In the 1000 �mcoatings, the hoop stress is weakest, but increases steadily asload is increased, and extends outwards with a gradual decreasefurther away from the indentation axis. The peak stresses in the300 �m systems also increase with load, with higher values thanthe 1000 �m systems, but the rate of increase drops off at higherloads.

However, the 160 �m systems exhibit markedly differentbehaviour. Although the initial stresses in the 160 �m systemsare the highest (providing an explanation for the lowest valuesof Pr), the curves level out, and in the case of the curved system,decrease, causing the peak hoop stress to fall below the valueseen in the 300 �m systems, and providing an explanation forthe increased resistance to crack growth.

The reason for this is highlighted in Fig. 7, which shows hoopstresses in curved coatings plotted against radial distance forthe three coating thicknesses considered, at indentation loads of100 and 1000 N. The initiation load for the thin coating is lower,and this is reflected the curves for 100 N (chosen as represen-tative of the stresses at low loads), where the 160 �m coatingclearly has the highest hoop stress. However, as load increases,the peak stress in the 160 �m coating does not increase signifi-cantly, unlike the pattern for the thicker coatings. An explanationfor his effect is that the 160 �m coating does not have the sameload spreading capacity as the thicker coatings, so the compres-si1dsv

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much higher load. Fig. 9 shows the evolution of contact damagefor 300 �m (left) and 1000 �m (right) coatings.

Fig. 10 shows the loads required to cause failure of the coat-ing. As reported in earlier work [13], material loss occurred incurved coatings at lower loads than similar flat coatings, whichremained intact to the 2000 N limit of testing. The 1000 �mcurved coatings exhibited much more resistance to complete fail-ure than the thinner coatings, which had similar failure loads.However, the failure in thin coatings was limited to the areadirectly under the indenter, and involved much less material lossthan seen in the 1000 �m coatings, which tended to lose largetriangular sections to the edge of the specimen.

5. Conclusions

Radial cracking, initiating at the coating undersurface directlybeneath the indentation, is the primary mode of failure in brittlecoatings on compliant substrates [14–16]. To increase resistanceto radial crack initiation, coatings should be made as thick aspossible, with a high degree of convex curvature. Abrasion of thecoating undersurface, leading to the introduction of a relativelyeven distribution of larger flaws (than existed in the as-polishedstate) reduces resistance to radial cracking.

However, after initiation, the situation changes. Thick(1000 �m) coatings resist crack propagation through continuedresistance to deflection, decreasing tensile stresses at the coatinguclIo

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ive stresses due to indentation limit the tensile area under thendenter. This argument is supported by the plots for the curved60 �m coating, which show the hoop stress under the indenterecreasing from 100 to 1000 N, and the peak hoop stress con-equently moving away from the indenter, with a lower peakalue.

.3. Failure of coating

Coating failure is defined as the point where one or moreracks reach the edge of the curved specimen—a precursor toaterial loss. Fig. 8 shows failure patterns for three abraded

onvex systems. In part (a), a 160 �m coating displays a highegree of material loss, but the damage is relatively localised.

similar pattern is seen in part (b), with a 300 �m coating. Inart (c), however, a large segment of the coating (to the edge ofhe curved surface) has separated from the sample, although at a

Fig. 10. Failure loads for as-polished and abraded convex systems.

ndersurface, while thin (160 �m) coatings deflect massively,ausing a compression zone beneath the indenter which alsoimits undersurface tension, and thus limits crack propagation.t is concluded that crack propagation is facilitated in coatingsf an intermediate thickness.

cknowledgments

The authors gratefully acknowledge Dr. Brian Lawn (NIST,aryland) and Mr. Matthew Rudas (University of Western Aus-

ralia) for many useful discussions. This work is supported by arant from the Australian Research Council.

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