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International Journal of Mechanical Sciences 48 (2006) 244–248

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The influence of complex surface geometry on contact damage incurved brittle coatings

Tarek Qasim�, Mark B. Bush, Xiao-Zhi Hu

School of Mechanical Engineering, The University of Western Australia, 35 Stirling Highway Crawley W.A. 6009, Australia

Received 17 February 2005; accepted 1 October 2005

Abstract

The effects of complex geometry on contact damage in bi-layer systems composed of curved brittle coating layers on compliant

polymeric substrate is investigated. Previous studies of this problem utilise relatively simple flat or singly curved (domed) model

structures. It is not known the extent to which conclusions driven from such observations may extended to more complex (practical)

geometry. Glass plates of 1000mm thick are used as representative of the brittle coating layer, and epoxy filler under layer as

representative of under layer support. A series of doubly curved specimens (having curvatures of 4 and 8mm) are produced to allow

investigation of the influence of complex curvature on the evolution of damage. The specimens are tested by indentation with spheres of

4mm radius loaded along the convex axis of symmetry. For comparison, some specimens loaded parallel to the axis of symmetry but off-

centre. The study explores the influence of supporting geometries on the conditions to initiate and propagate subsurface ‘‘radial’’ cracks,

which are believed to be responsible for catastrophic failure of brittle-coating-based structures in certain applications, such as dental

crowns. It is demonstrated that critical loads for initiation of radial cracks and the subsequent crack propagation are insensitive to

complex geometry, so that simple monotonic indentation ‘‘axis and/or off-axis loading’’ with minimum geometrical complication ‘‘flat,

simply curved’’ remains an appropriate route to study the evolution of radial cracks in practical brittle coating structures.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Curved surfaces; Complex surface shapes; Supporting surface; Radial cracks; Brittle coating

1. Introduction

Layered structures composed of a brittle coating on acompliant substrate are of high interest in a variety ofengineering applications such as tribological and electronicpackaging [1,2], coated cutting tools and thermal barriercoatings [3–5] as well as biomechanical implant structures[6–12]. The lifetime and failure resistance of such structuresare affected by a variety of parameters and limited by anyone of a number of damage modes that may develop in thestructure under contact loading. Fig. 1 (top) shows twomajor modes of coating failure: cone cracks (inner‘‘Hertzian’’ and outer cone cracks) initiate at the topsurface of the coating, and radial cracks initiate at thebottom surface of the coating. Careful selection ofcomponent properties and design of layer geometry to

e front matter r 2005 Elsevier Ltd. All rights reserved.

ecsci.2005.10.004

ing author. Tel.: +618 6488 3601; fax: +61 8 6488 1024.

ess: tqasim@mech.uwa.edu.au (T. Qasim).

maximize the damage resistance of such systems is,therefore, essential. Radial cracking may initiate at thelower surface of the coating, where flexure induced byconcentrated loads at the top surface is at its maximum.Radial cracks have been identified as the most dangerous inthe context of system survival [1,13–15]. In particular, inthinner coatings, less than 1mm, they can extend longdistances subsurface, from the loading axis. In severe casesthe cracks extend to the edge of the structure, see Fig. 1,resulting in premature failure.The type of damage illustrated in Fig. 1 (bottom) has

been implicated in catastrophic failure of dental crowns. Aconsiderable amount of experimental and analyticalinvestigation of contact damage modes in brittle/compliantbi-layer structures of the kind under consideration here hasbeen carried out [3–12,16–22]. These studies have enableddetermination of dependence of critical conditions forvarious damage modes on geometrical variables, such as,coating thickness and indenter sphere radius, as well as

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Radial cracks

Conecracks

Coating failure

Fig. 1. Modes of coating failure: (top) cone cracks and extended radial

cracks, (bottom) complete coating failure, showing how a segment of the

coating may become dislodged.

rs- rs

P

P

φ

Coating

Under layer

Pt

Pn

S

ri

ri

Fig. 2. Loading configurations of indenter of radius ri on convex brittle

layers of radius rs in a complex geometry consisting of concave and flat

supporting surfaces. We define the compound multiply curved specimen

shown in this figure as rs ¼ f1; rs;�rsg, indicating the radii of curvature

across the specimen.

T. Qasim et al. / International Journal of Mechanical Sciences 48 (2006) 244–248 245

materials properties such as interlayer modulus mismatch,coating layer strength, hardness and toughness.

In previous studies [13–15], we examined the effect ofchanging specimen surface curvature on the evolution ofsubsurface radial cracks. We demonstrated that surfacecurvature could play an important role in the radial crackevolution, by strongly enhancing propagation to failure[13]. This work utilised simple curvature (single curvedspecimens) and central normal loading. Further studieshave examined the effect of complex loading (havingtangential and normal components) [14] and the effect ofcoating thickness [15].

In the current study, we examine the effect of furthercomplications in geometry, by focusing on multiply curvedspecimens. We define the basic form of geometriccomplications and the state of loading in Fig. 2. Themultiply curved structure is defined in terms of curvatureby rs ¼ f1; rs;�rsg, indicating the combination of a flatsection, a convex section and a concave section. It is shownthat the critical loads for initiation of radial cracks incomplex geometrical specimens and subsequent crackpropagation are insensitive to such geometrical complexity.We conclude that normal monotonic indentation ofspecimens having minimum geometrical complication (flat,

singly curved) would appear to be adequate for the study ofthe evolution of radial cracks in brittle coating structures.

2. Experimental procedure

Glass/epoxy layer structures were fabricated as a modelbi-layer system with complex shapes, as indicated in Fig. 2.Borosilicate glass (D263, Menzel-Glaser, Postfach, Ger-many) was chosen as the brittle layer (coating), in the formof 1mm thick plates 75mm� 25mm. This glass has aYoung’s modulus 73GPa. Epoxy resin (Resin R2512, ATLComposites, Southport, Australia) was chosen as thesupport material (substrate), Young’s modulus of 3.4GPa.To obtain curved surfaces, the glass plates were slumped

over stainless steel balls of prescribed radius and subjectedto heat treatment. In order to prevent the glass fromsticking to the steel spheres, the heated spheres weresprayed with kiln wash (50%wt% Kaolin+50wt%alumina hydrate, mixed with 5 parts by volume of distilledwater) at E230 1C. The sprayed film was then lightlysmoothed with a lint-free cloth. The glass plates were thensubjected to the following heat treatment, in air: (1) heat toE750 1C and hold until the glass plates conform to thespherical die curvature, (2) rapidly cool to solidify theglass, (3) anneal to E560 1C and cool slowly to roomtemperature to avoid any residual stresses [13,23]. Glasssurfaces with radius of curvature rs ¼ f1; 8 and � 8gmmand rs ¼ f1; 4 and � 4gmm were prepared in this way.The glass retained its original thickness of 1mm during thistreatment.The prospective undersurface of each glass plate was

given an abrasion treatment with 50 mm sand particlesusing a dental sandblasting machine (P-G4000, Harnish &Rieth, Winterbach, Germany), as in common dental

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1 mm

Concave surface

Concave surface

1 mm

φ

(b)

(a)

Fig. 3. Radial cracks in a convex glass layer (rs ¼ 8mm) of thickness

1mm on epoxy resin substrate, under loading with WC sphere of radius

ri ¼ 4mm: (a) axial loading ð+ ¼ 0Þ at P ¼ 1300N, and (b) off-axis

loading ð+ ¼ 30�Þ at P ¼ 900N.

T. Qasim et al. / International Journal of Mechanical Sciences 48 (2006) 244–248246

practice sandblasting is often used in the preparation ofdental crowns [13,21,24]. This treatment convenientlyreduces the strength level of the glass close to that ofporcelain (a common dental material), as well as enhancingsubsequent epoxy bonding [13,24]. Most importantly, itfavours radial crack initiation at the glass under-surface,eliminating complications from premature cone cracking atthe top surface [10,17]. Bonding of the glass plate to itscompliant substrate was obtained by pouring the epoxyresin directly onto the abraded side of the glass plate.

Indentation tests were carried out in air using a tungstencarbide sphere of radius ri ¼ 4mm mounted in a screw-driven mechanical testing machine (Instron 4301. InstronCorporation Canton, MA). Care was taken to align thesphere and specimen so that the contact occurred eitheralong the axis of symmetry for the axial loading tests, andparallel to the axis but contacting the surface at a pointcorresponding to + ¼ 30� (Fig. 2) for the off-axis cases.The specimens were clamped to prevent any sliding duringtesting. The load was applied to the convex surfaces atconstant crosshead speed 0.1mmmin�1 (�10N s�1). Loadup to 1500N could be attained in this configuration.During loading, the specimens were viewed from the sideand slightly from above using a video camera, such that thecontact and side walls of the specimens were within thefield of view at all times. A light source was placed behindthe specimens to optimize crack visibility. A single-cycleindentation was performed on each specimen. Criticalloads to initiate radial cracks at the glass under-surfacewere monitored in each specimen. Subsequent propagationof the radial cracks with further increase in the loading wasthen followed to the point of failure. Four to eight separatetests were run at each for each configuration. Nodelamination between the glass and the epoxy wasobserved in any of the tests until ultimate failure, attestingto the good bonding.

3. Results

3.1. Crack morphology

Fig. 3 shows representative photographs from video clipsduring indentation for specimens with complex geometryand different loading combinations (a) rs ¼ f1; 8;�8gmm(axial loading, + ¼ 0) at P ¼ 1300N, (b) rs ¼

f1; 8;�8gmm (off-axis loading, + ¼ 30�) at P ¼ 900N.In both systems, radial crack initiation and subsequentpropagation followed the same pattern. Multiple radialcracks initiate as the load increased while individual crackselongate and extend steadily to the convex hemisphericalbase. Further, increase in indentation load causes failure ofthe coating in the same manner observed for the singleconvex surface geometry [13,14]. Coating failure is definedas the point where material loss from the coating occurs (asegment of the coating pops off the surface, see Fig. 1 and2(b). No extension of the radial cracks to the supporting

geometries (flat and concave) where observed in thisconfiguration.Fig. 4 compares crack patterns in the geometry

combinations mentioned above, but in this case indenta-tion was carried out on a highly convex surface, radius ofcurvature rs ¼ 4mm (a) rs ¼ f1; 4;�4gmm (axial loading,+ ¼ 0) P ¼ 930N, (b) rs ¼ f1; 4;�4gmm (off-axis load-ing, + ¼ 30�) P ¼ 620N. In this system, (highly convexsurface) steady propagation of the radial cracks from thenear contact zone is followed by a sudden jump to the baseof the hemispherical convex surface. In some specimens theinitiation load was so high that the radial cracks popped-inimmediately to the convex hemispherical base and ex-tended in to the adjacent flat surface (Figs. 4(a) and (b)).Further increase in load resulted in specimen failure(material dislodgement) without any further propagationof the cracks into the adjacent concave surface. In ourprevious study [13], radial cracking was also found to beinhibited in axial contact on concave surfaces.

3.2. Radial cracks evolution

Critical loads PR to initiate subsurface radial cracks weremeasured as a function of specimen curvature r�1s . Data areplotted in Fig. 5 for both axial loading,+ ¼ 0 (circles) andoff-axis loading, + ¼ 30� (triangles). Filled symbols fromprevious studies on singly curved specimens are also shown

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0

50

100

150

200

250

0 0.1 0.2 0.3Surface curvature, 1/rs (1/mm)

Crit

ical

laod

,PR (

N)

Axial loading

Off-axis loading

Fig. 5. Critical load PR to initiate radial cracks in glass layer of thickness

1mm, as function of glass surface curvature 1/rs. Loading with WC sphere

of radius ri ¼ 4mm, filled symbols from previous study [13]. The data

indicate mean and standard deviation.

0

500

1000

1500

2000

0 5 10 15 20Circumferential crack length, s (mm)

Inde

ntat

ion

load

,P (

N).

rs =∞

rs =4mm

rs =8m

Axial loading

Fig. 6. Evolution of radial cracks in convex glass surfaces of specified

radius rs and thickness 1mm, under monotonic axial loading with WC

sphere of radius ri ¼ 4mm. Note abrupt propagation to edge of glass

convex base. Arrows indicate further loading on arrested cracks.

Flat

surfaceConcavesurface

1 mm

1 mm Flatsurface

Concave surface

(a)

(b)

Fig. 4. Radial cracks in a convex glass layer (rs ¼ 4mm) of thickness

1mm on epoxy resin substrate, under loading with WC sphere of radius

ri ¼ 4mm: (a) axial loading ð+ ¼ 0Þ at P ¼ 930N, and (b) off-axis

loading ð+ ¼ 30�Þ at P ¼ 620N.

T. Qasim et al. / International Journal of Mechanical Sciences 48 (2006) 244–248 247

[13,14]. Error bars are standard deviations, for a minimumof four indentations at each condition. As before [13], thedata for axial and off-axis loading overlap within thescatter bands, indicating that the small reduction in normalloading ðPn ¼ 0:87PÞ is inconsequential to the crackinitiation, as is superposition of the tangential componentðPt ¼ 0:5PÞ. Furthermore, the data show that while thecritical loads, PR, are insensitive to the curvature of thespecimen immediately beneath the indenter, they are

insensitive to the geometrical complexity of the surround-ing support structure.Fig. 6 shows typical circumferential plots of radial crack

length (s) (crack length measured around the curvedsurface) as a function of indentation load, for axial loadingð+ ¼ 0Þ on convex specimens rs ¼ 8 and 4mm as well ason flat specimens from the previous study [13] forcomparison. The popped in radial cracks first extendsteadily with increasing load, but then propagate relativelyabruptly to the base of the hemispherical cap (convexsurface), with increasing abruptness at smaller rs ¼ 4mm.Further, increase in load does not extend the cracks intothe adjacent surfaces (flat and concave) but instead causeslinkage of neighbouring radial arms and, ultimately,material dislodgment. Note that for the highly convexsurface ðrs ¼ 4mmÞ the radial cracks extended slightly intothe flat surface, as represented by the dashed line in Fig. 6.Apart from this observation, there is no significantdifference between these data and the data observed onsingly curved specimens [13].The loads to achieve crack propagation to the base (edge

of the convex dome) are summarized in Fig. 7 for all suchtests, filled symbols (circles) for axial loading ð+ ¼ 0Þfrom the previous study [13] and un-filled circles for off-axis loading [14]. Where as the effect of surface curvatureon the failure condition is strongly evident, the complexityof the surrounding support structure once again has littleeffect on the failure loads. The complex geometryconsidered here slightly reduces the failure loads for axialloading.

4. Discussion

In this report, we investigated the initiation andpropagation of radial cracks in curved (convex) brittlecoating layers on compliant substrates due to axisymmetricand off-axis contacts on the top of convex surface adjacent

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0

500

1000

1500

2000

0 0.05 0.1 0.15 0.2 0.25 0.3Surface curvature, 1/rs (1/mm)

Failu

re lo

ad, P

F (N

)

Convex -Axis loading

Complex geometry-Axis loading

Convex- Off-axis loading

Complex geometry-Off-axis loading

Fig. 7. Failure loads to propagate radial cracks to the base of the convex

glass layer of radius rs and thickness 1mm with abraded undersurfaces,

under loading with WC sphere of radius ri ¼ 4mm. The data indicate

mean and standard deviation.

T. Qasim et al. / International Journal of Mechanical Sciences 48 (2006) 244–248248

to flat and concave surfaces. The observations from theprevious studies [13–15] and the current study highlight theimportance of local surface curvature on the fracturebehaviour. Generally, higher contact loads are required toinitiate radial cracks in curved surfaces (Fig. 5), while theload to complete failure is reduced (Fig. 6). On the otherhand, complexity in the surrounding support structure hasrelatively little effect on the failure load.

The methodology used in this study provides usefulguidelines, but the data do not provide general quantitativepredictions of failure in all brittle-coating structures. Adetailed three-dimensional stress analysis is needed tounderstand the enhancement of stress distribution aroundthe indenter and the extension of stress contours toadjacent surfaces at higher loads. We have considered onlysingle-cycle loading. Fatigue due to repeated loading mustexacerbate the failure process.

The results in this study show the insensitivity of thecritical loads for radial crack initiation in complexgeometrical specimens. Normal indentation loading withminimum geometrical complication (single shape) wouldappear to be adequate route to study the evolution ofradial cracks in brittle coating structures, in single-cycleloading considered in this study.

Acknowledgements

The authors gratefully acknowledge useful discussionswith Dr. C. Ford (UWA) and Dr. Brian Lawn (NIST,Maryland). This work was supported by a grant from theAustralian Research Council.

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