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

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

Materials Science and Engineering A419(2006)

189–195

Effect of coating thickness on crack initiation and

propagation in non-planar bi-layers

Tarek Qasim,Chris Ford?,Malika Bongu′e-Boma,

Mark B.Bush,Xiao-Zhi Hu

School of Mechanical Engineering,The University of Western Australia,

35Stirling Highway Crawley,WA6009,Australia

Received in revised form15December2005;accepted15December2005

Abstract

Hertzian contact damage is studied in glass coatings(thickness range160?m to1mm)on polycarbonate polymer substrates.Both planar and non-planar geometries are considered,subjected to indentation by?xed size spherical indenters of radius4mm.Finite element analysis is carried out to evaluate the stress distribution in the bilayer structure.Radial cracking initiating at the coating undersurface directly under the indenter is the 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 de?ection,decreasing tensile stresses at the coating undersurface,while thin(160?m)coatings de?ect massively,causing a compression zone beneath the indenter which also limits undersurface tension.

?2006Published by Elsevier B.V.

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

1.Introduction

The development of systems combining the wear resistance of a brittle coating and the toughness of a ductile under layer is very important for high damage tolerance applications.The mechanical response of brittle layered structures under Hertzian indentation is of considerable interest in disciplines such as biomechanics and tribology,and in the?eld of dentistry,for tooth restorations such as crowns[1,2].The contact damage tolerance and failure resistance of such systems is affected by a variety of parameters.Careful selection of component properties (stiff coating/soft interlayer)and coating geometry(planar/non-planar)may therefore be used to maximize the damage resistance of such systems.

A considerable amount of experimental and analytical inves-tigation of systems utilising materials relevant to dental prosthe-ses has been carried out using Hertzian indentation,including work by Zhao et al.[3–5],Lee and Lawn[6,7],Chai[8],Ford et al.[9]and Shrotriya et al.[10].However,the bulk of the pre-

?Corresponding author.Tel.:+61864881901;fax:+61864881024.

E-mail address:chrisf@https://www.360docs.net/doc/f413755835.html,.au(C.Ford).vious work focused on the response of?at bilayer or trilayer systems,which did not account for the effects of coating curva-ture.The principle modes of failure observed in these studies are shown 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 P r and P c,respectively.Different failure modes dominate for different material combinations and geometries.

Previous studies by the authors[9,11–13]examined the effects of changing curvature,of both the indenter and the indented samples.Experimental studies[11–13]were inter-preted using?nite element methods[12,13]and concluded that curved surfaces on compliant substrates are generally more resistant to initiation of the dominant radial cracking mode than equivalent planar systems,although convex curvature may enhance subsequent crack growth to failure[13].

This paper considers the effect of coating thickness,which while well documented in?at multilayers,has not previously been closely examined in curved systems.The focus of this study is the radial crack system,identi?ed as the primary failure mode in brittle coatings on compliant substrates[14–16],and mention is also made of cone cracking(usually a secondary mode for this

0921-5093/$–see front matter?2006Published by Elsevier B.V. doi:10.1016/j.msea.2005.12.023

190T.Qasim et al./Materials Science and Engineering A419(2006)

189–195

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

material system).Crack initiation and propagation,and ultimate failure of the coating are all assessed.It is shown that crack growth to failure is facilitated in coatings of an intermediate thickness,since thick coatings are generally more resistant to crack 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 systems incorporating both?at and curved surfaces.Borosilicate glass (D263,Menzel-Glaser,Germany)was chosen for the brittle coating,initially supplied as?at plates of160,300and1000?m thickness.This glass has a Young’s modulus of73GPa,close to that 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 a Young’s modulus of3.4GPa was used for the substrate material, promoting the growth of radial cracks which are the focus of this study.

In order to obtain a curved coating geometry,the glass plates were slumped over stainless steel balls of radius8mm as fol-lows.To prevent the glass from sticking to the steel,the heated spheres were treated with kiln wash(50%kaolin+50%alumina hydrate,by weight,mixed with four to six parts distilled water) at≈230?C.The sprayed?lm was then lightly smoothed with a lint-free cloth.The glass plates were then subjected to the following heat treatment in air:(i)heat to≈750?C and hold until the glass plates conform to the spherical die curvature;(ii) rapidly cool to solidify the plates;(iii)anneal at≈560?C and cool slowly to room temperature to avoid any residual stresses. Plates used for?at coatings were subjected to a similar treatment (using a planar die surface)to maintain consistency in results. The glass thickness did not alter signi?cantly during this treat-ment,with micrometer testing showing a maximum reduction of20?m(or2%)at the top of the specimen.

Prior to addition of the epoxy substrate,the prospective undersurfaces of the glass plates were abraded with50?m sand particles using a dental sand blasting machine(Harnish+Rieth, P-G4000,Czech Republic).This treatment favours preferential radial crack initiation at the glass undersurface,eliminating com-plications from premature cone cracking at the top surface,and introduces a more uniform surface?aw distribution,reducing scatter and improving test repeatability.Half of the samples were left in their as-polished state for comparison.

The epoxy substrate was then built up to a thickness of 6–8mm in the case of the?at specimens,and6mm from the low-est part of the glass in the curved specimens(i.e.14mm thick at the centre).The substrate was deposited under the formed coating in thin layers,in order to prevent cracking of the glass due to thermal shrinkage,with each layer allowed to set for24h before further material was added.

Indentation tests were carried out in air(at room temperature) using a tungsten carbide sphere of radius r i=4mm mounted in a screw-driven testing machine(Instron4501,Instron Corp., Canton,MA),taking care that the sphere and specimens were aligned so that the contact occurred axisymmetrically.Loads up to2000N could be attained in this con?guration.The tests were conducted under displacement control,at a cross-head speed of 0.1mm/min.During loading,the specimens were viewed from the side and slightly from above using a video camera,such that the contact and side walls of the specimens were within the?eld of view at all times.A light source was placed behind the spec-imens to optimize crack visibility.A single-cycle axisymmetric indentation was performed on each specimen.Critical loads to initiate radial cracks at the glass undersurfaces were monitored in each specimen.Subsequent propagation of the radial cracks with further increase in the loading was then followed to the point of failure(where applicable),i.e.when the cracks reached the extremities of the curved surfaces.Some5–10separate tests were run at each surface radius for the convex specimens.No delamination was observed between the glass and epoxy in any of the tests until ultimate failure,attesting to the sound bonding.

3.Finite element modelling

Finite element modeling was used to compute stresses in the glass layers,speci?cally the tensile hoop(tangential)stress at the undersurface and radial stresses inducing ring cracks at the coat-ing surface,using ABAQUS version6.4.Input Young’s modulus and Poisson’s ratio were73GPa and0.21for the glass,3.4GPa and0.33for the epoxy,and614GPa and0.3for the tungsten carbide indenter(all manufacturer speci?cations).The solution allowed for large de?ection and geometric non-linearity.

The meshes were systematically re?ned,particularly in the critical glass undersurface region,until the solutions attained convergence,with mesh size of the order of20?m.Loads were applied monotonically over the experimental range from zero to 2000N.A sample mesh and stress contour for a curved specimen under a200N indentation,representative of those used in this study,is shown in Fig.2.

Algorithms for fracture predictions have been well docu-mented in the literature[17,18].In this study,for prediction of radial crack critical loads,two different critical stresses were used,following previous works[13,14].This method relies on an estimation of critical stress based on an assumed?aw size. Where 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 ?nite element mesh and tensile stress contour.

the epoxy substrate,a critical stress of 75MPa was used,whereas for samples with the coating left in an as-polished condition,a critical stress of 295MPa was used,re?ecting the difference in ?aw state following surface treatment.Since radial cracking was always observed prior to cone cracking,no FEA predictions for cone cracks are included.4.Results and discussion 4.1.Critical loads

In all of the systems under consideration,radial cracking was found 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 of radial cracks.Consequently,radial cracking is the focus of this study.

In the both the ?at and curved specimens,radial crack critical loads increased with coating thickness in the curved specimens,as seen in Fig.4,with the critical loads in curved specimens higher than for equivalent ?at systems,indicating increased resistance to radial cracking due to the convex curvature.In each case,the abraded specimens exhibited a signi?cantly lower crit-ical load than the equivalent as-polished systems,highlighting the effect of larger,more evenly distributed ?aws from which cracks can nucleate.

Curves showing FEA predictions for P r are also shown in Fig.4.The FEA curves re?ect the trends seen both the ?at and curved systems,and the as-polished critical loads are pre-dicted with reasonable accuracy.However,there is a signi?cant

discrepancy between the values of the predicted and observed critical loads for the abraded systems.A possible explanation for this result is that the ?aw sizes used to calculate the 75MPa critical stress used [13,14]are an overestimation of the actual ?aw distribution.4.2.Crack propagation

Fig.5shows the evolution of radial crack length (measured as a circumferential length in curved coatings)with increasing indentation load,for both as polished samples (a)and abraded specimens (b).Each set of curves shows the results for the three coating thicknesses considered in this study,with ?at specimens represented by solid curves and convex specimens represented by dashed

curves.

Fig.4.Radial crack critical loads plotted against coating thickness,showing FEA predictions (curves)and experimental observations (data points)for both convex and ?at systems,with as-polished and abraded treatment of the coating

undersurface.

Fig.3.Contact damage in unloaded ?at as-polished specimens after 1000N indentation:(a)160?m coating;(b)300?m coating;(c)1000?m coating.

192T.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 ?at samples exhibit stable crack propagation at much higher indentation loads,whereas in the curved specimens,the crack grows much more rapidly,at a lower load.This is a reversal of the trend observed for crack initiation—curved specimens thus have increased resistance to radial crack initiation but are more prone to subsequent crack growth.

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

systems.

Fig.6.Peak tensile hoop stress at the coating undersurface plotted against inden-tation load for curved and ?at systems with coating thicknesses of 160,300and 1000?

m.

Fig.7.Hoop stresses at the coating undersurface in curved systems,plotted against radial distance from the axis of symmetry,for loads of 100N (?lled symbols)and 1000N (un?lled symbols).Note the change of location for the peak hoop stress in the 160?m system under the higher load.

The thickest (1000?m)coatings require the highest load to cause the radial cracks to propagate,as expected.For all of the 1000?m systems (with the exception of the curved as-polished system)an initial period of slow steady crack growth was 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 required greater loading to force crack growth than similar 300?m coat-ings (of the same curvature and undersurface treatment),even though the critical loads for radial crack initiation are always lower in the thinner coatings.For any combination of surface treatment 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 1500N indentation;(b)300?m coating after 600N indentation;(c)1000?m coating after 1050N indentation.

T.Qasim et al./Materials Science and Engineering A419(2006)189–195193

Fig.9.Evolution of contact damage in curved abraded specimens.Pictures on the left show damage evolution in a300?m coating as indentation load increases from400to600N;the series at right shows a1000?m coating under indentation loads from1000to1050N.

194T.Qasim et al./Materials Science and Engineering A419(2006)189–195 The peak hoop stresses calculated from FEA(shown in Fig.6)

provide an interpretation for these observations.In the1000?m

coatings,the hoop stress is weakest,but increases steadily as

load is increased,and extends outwards with a gradual decrease

further away from the indentation axis.The peak stresses in the

300?m systems also increase with load,with higher values than

the1000?m systems,but the rate of increase drops off at higher

loads.

However,the160?m systems exhibit markedly different

behaviour.Although the initial stresses in the160?m systems

are the highest(providing an explanation for the lowest values

of P r),the curves level out,and in the case of the curved system,

decrease,causing the peak hoop stress to fall below the value

seen in the300?m systems,and providing an explanation for

the increased resistance to crack growth.

The reason for this is highlighted in Fig.7,which shows hoop

stresses in curved coatings plotted against radial distance for

the three coating thicknesses considered,at indentation loads of

100and1000N.The initiation load for the thin coating is lower,

and this is re?ected the curves for100N(chosen as represen-

tative of the stresses at low loads),where the160?m coating

clearly has the highest hoop stress.However,as load increases,

the peak stress in the160?m coating does not increase signi?-

cantly,unlike the pattern for the thicker coatings.An explanation

for his effect is that the160?m coating does not have the same

load spreading capacity as the thicker coatings,so the compres-

sive stresses due to indentation limit the tensile area under the

indenter.This argument is supported by the plots for the curved

160?m coating,which show the hoop stress under the indenter

decreasing from100to1000N,and the peak hoop stress con-

sequently moving away from the indenter,with a lower peak

value.

4.3.Failure of coating

Coating failure is de?ned as the point where one or more

cracks reach the edge of the curved specimen—a precursor to

material loss.Fig.8shows failure patterns for three abraded

convex systems.In part(a),a160?m coating displays a high

degree of material loss,but the damage is relatively localised.

A similar pattern is seen in part(b),with a300?m coating.In

part(c),however,a large segment of the coating(to the edge of

the curved surface)has separated from the sample,although at

a

Fig.10.Failure loads for as-polished and abraded convex systems.much higher load.Fig.9shows the evolution of contact damage for300?m(left)and1000?m(right)coatings.

Fig.10shows the loads required to cause failure of the coat-ing.As reported in earlier work[13],material loss occurred in curved coatings at lower loads than similar?at coatings,which remained intact to the2000N limit of testing.The1000?m curved 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 area directly under the indenter,and involved much less material loss than seen in the1000?m coatings,which tended to lose large triangular sections to the edge of the specimen.

5.Conclusions

Radial cracking,initiating at the coating undersurface directly beneath the indentation,is the primary mode of failure in brittle coatings on compliant substrates[14–16].To increase resistance to radial crack initiation,coatings should be made as thick as possible,with a high degree of convex curvature.Abrasion of the coating undersurface,leading to the introduction of a relatively even distribution of larger?aws(than existed in the as-polished state)reduces resistance to radial cracking.

However,after initiation,the situation changes.Thick (1000?m)coatings resist crack propagation through continued resistance to de?ection,decreasing tensile stresses at the coating undersurface,while thin(160?m)coatings de?ect massively, causing a compression zone beneath the indenter which also limits undersurface tension,and thus limits crack propagation. It is concluded that crack propagation is facilitated in coatings of an intermediate thickness.

Acknowledgments

The authors gratefully acknowledge Dr.Brian Lawn(NIST, Maryland)and Mr.Matthew Rudas(University of Western Aus-tralia)for many useful discussions.This work is supported by a grant from the Australian Research Council.

References

[1]I.M.Peterson,A.Pajares,https://www.360docs.net/doc/f413755835.html,wn,V.P.Thompson,E.D.Rekow,J.

Dental Res.77(4)(1998)589–602.

[2]Y.G.Jung,S.Wuttiphan,I.M.Peterson,https://www.360docs.net/doc/f413755835.html,wn,J.Dental Res.78

(4)(1999)887–897.

[3]H.Zhao,X.-Z.Hu,M.B.Bush,https://www.360docs.net/doc/f413755835.html,wn,J.Mater.Res.15(3)(2000)

676–682.

[4]H.Zhao,X.Z.Hu,M.B.Bush,https://www.360docs.net/doc/f413755835.html,wn,J.Mater.Res.16(5)(2001)

1471–1478.

[5]H.Zhao,X.Hu,M.B.Bush,Key Engineering Materials Fourth Inter-

national Conference on Fracture and Strength of Solids,vol.183–187, Pt2,16–18August,2000,pp.1261–1266.

[6]https://www.360docs.net/doc/f413755835.html,wn,Curr.Opin.Solid State Mater.Sci.6(3)(2002)229–235.

[7]C.S.Lee,https://www.360docs.net/doc/f413755835.html,wn,D.K.Kim,J.Am.Ceram.Soc.84(11)(2001)

2719–2721.

[8]H.Chai,Int.J.Solids Struct.40(3)(2003)591–610.

[9]C.Ford,M.B.Bush,X.-Z.Hu,Comp.Sci.Technol.64(13–14)(2004)

2207–2212.

[10]P.Shrotriya,R.Wang,N.Katsube,R.Seghi,W.O.Soboyejo,J.Mater.

Sci.Mater.Med.14(1)(2003)17–26.

T.Qasim et al./Materials Science and Engineering A419(2006)189–195195

[11]T.Qasim,M.Bush,X.-Z.Hu,Advances in Fracture and Failure Pre-

vention:Proceedings of the Fifth International Conference on Fracture and Strength of Solids(FEOFS2003):Second International Conference on Physics and Chemistry of Fracture and Failure Prevention(2nd ICPCF),October20–22,2003,Sendai,Japan:Trans Tech Publications Ltd.,Zurich-Ueticon,Switzerland,2004.

[12]T.Qasim,M.Bush,X.-Z.Hu,Int.J.Mech.Sci.46(6)(2004)827–840.

[13]T.Qasim,M.B.Bush,X.-Z.Hu,https://www.360docs.net/doc/f413755835.html,wn,J.Biomed.Mater.Res.B,

in press.[14]H.Chai,https://www.360docs.net/doc/f413755835.html,wn,S.Wuttiphan,J.Mater.Res.14(9)(1999)3805–

3817.

[15]https://www.360docs.net/doc/f413755835.html,wn,J.Am.Ceram.Soc.81(8)(1998)1977–1994.

[16]P.Miranda,A.Pajares,F.Guiberteau,F.L.Cumbrera,https://www.360docs.net/doc/f413755835.html,wn,J.

Mater.Res.16(1)(2001)115–126.

[17]C.Ford,M.Bush,X.-Z.Hu,H.Zhao,Mater.Sci.Eng.A364(1–2)

(2004)202–206.

[18]C.Ford,M.B.Bush,X.-Z.Hu,H.Zhao,Mater.Sci.Eng.A380(1)

(2004)137–142.

相关主题
相关文档
最新文档