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The multitude of ways in which acoating can fail are well known to bothusers and producers of organic coatings.Many failures are gradual and are aes-thetic in nature only, such as gloss lossand color fade. Others are more me-chanical in nature such as cracking orpeeling. These mechanical failures canlead to a loss of substrate protection orcorrosion, which may compromise thestructural integrity of the painted com-ponent as well as produce an unaccept-able appearance. By understanding themanner in which these failures occurone can design coating systems in amore robust fashion to prevent them.

Most of the mechanical failures thatoccur in coatings are due to cracks prop-agating within the coating, at an inter-face between the coating and a sub-strate, or between two coating layers(Figure 1). To truly understand howthese cracks propagate, the principals offracture mechanics must be applied tothe coating system. Fracture mechanicsis the discipline that quantitatively de-scribes how cracks propagate in materi-als and at interfaces. This approach hasbeen used extensively to understandand predict the performance of alu-minum aircraft alloys as well as highstrength composite materials. Its appli-cation to coatings technology was onlyinitiated in the last decade.1,2 However,recent advances have made it a powerfultool to understand the performance ofmany organic coatings. This article aimsto introduce the reader to the principalsof fracture mechanics and how the ap-plication of these principals to organiccoating characterization can improvethe durability and performance of coat-ing systems.

*P.O. Box 2053, MD 3182 SRL, Dearborn, MI 48121. Email: mnichols@ford.com.

Using Fracture Mechanics toCharacterize Organic Coatings

by Mark Nichols, Ford Motor Company*

BASICS OF MECHANICALBEHAVIOR

Before diving into fracture mechan-ics itself, a short review of general me-chanical behavior is required.

When a material (organic coating,metal, plastic, etc.) is subjected to aload it deforms in proportion to theload applied—the larger the load, thegreater the deformation. The behaviorcan be quantified by using the conceptsof stress and strain. The stress a materialexperiences is simply the load (force)applied divided by the cross sectionalarea of the material. The deformation istypically characterized by the strain,which is the change in length of thematerial divided by its original length.When the stress-strain behavior of a ma-terial is studied it is often plotted asshown in Figure 2, where the behaviorof three typical coatings is shown. In allthree cases, as the coating is deformed(in this case, stretched in tension) theload on the coating increases. The slopeof the initial part of the stress-straincurve is called the modulus and is ameasure of the stiffness of the material.The modulus is typically given the sym-bol, E, and has SI units of MPa.

For the curve labeled a the materialruptures at a rather low level of strainand the curve is quite linear up to thebreaking point. This is typical of ahighly crosslinked coating tested wellbelow its Tg. For coatings like this, if thestress-strain test was stopped before thematerial broke and the load was re-leased, all of the strain would be recov-ered, much like the stretching and un-stretching of a rubber band but on a

smaller length scale. The middle curve(b) in Figure 2 shows a moderately duc-tile coating, which is representative of alightly crosslinked coating tested atroom temperature or a highlycrosslinked coating tested at elevatedtemperatures. In this case, the stress-strain curve begins to deviate from lin-earity, indicating the onset of somenon-recoverable deformation. Thisresidual deformation is called plasticdeformation and the point on thestress-strain curve at which it begins toaccumulate is called the yield point(yield stress and yield strain). For or-ganic materials (plastics and coatings),the yield point is strongly dependent ontemperature as well as the rate of defor-mation. For this reason it is not possi-ble to uniquely identify the yield stressor strain without specifying the temper-ature and rate of testing. These pointsare important to remember when dis-cussing the fracture behavior of coat-ings. The bottom curve (c) in Figure 2 istypical of a lacquer or thermoplasticcoating where significant deformationcan occur before the coating ruptures.Here, the load actually goes through amaximum and then drops before signif-icant drawing of the coating occurs.Rupture may not occur till the specimenhas increased in length by over 100%.

Another important point to remem-ber is that materials are rarely free offlaws. Extensive studies have shown thatflaws (voids, scratches, etc.) in a mate-rial are typically the places where fail-ures initiate. For example, during a sim-ple tensile stress-strain test, the samplewill typically fail due to the presence ofa small imperfection on the surface orin the interior of the sample. The stress-

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strain curves shown in Figure 2 havebeen obtained from specimens pre-pared in a way to minimize the numberof edge flaws, but no extraordinarymeasures were taken to remove smallflaws from the specimens. Without thepresence of the flaw the ultimate stressand strain measured would have beenhigher.3 In practice, the theoreticalstrength of materials is never achieveddue to the presence of these flaws,which are often microscopic in size.

FRACTURE MECHANICS—BASICS

Because flaws are always present inmaterials, a method to anticipate thefailure strength of materials necessarilymust incorporate the effect of theseflaws. Over the years, two different ap-proaches have been developed to de-scribe the breaking strength of materialsand how flaws propagate as cracks dur-ing material service. An important pointto remember is that fracture mechanicsdescribes the propagation of cracks in amaterial and not the initiation of thesmall flaws from which the cracks prop-agate. We must assume or experimen-tally determine the size of flaws or a dis-tribution of flaw sizes in order to usefracture mechanics to make predictionsabout the performance of materials inservice.

Energy ApproachThe first method developed to exam-

ine the propagation of cracks in materi-als was proposed by Griffith, who wasstudying the breaking behavior of inor-ganic glass.4 He suggested that the me-chanical energy required to cleave apiece of glass was equal to the surfaceenergy penalty for creating two new sur-faces when a crack propagated throughthe glass (see Figure 3). Thus, the break-ing strength, σ, could be related to thesurface energy, γs; the flaw size, a; andthe elastic modulus, E; by the equation

(1)

For the brittle, inorganic glassesGriffith was studying, experimentsshowed that the theoretical predictionunderestimated the measured value byapproximately a factor of two. However,the discrepancy between the measuredbreaking strength and the strength cal-

culated from the surface energy contri-bution alone is much larger for moreductile materials. This discrepancy islargely due to other energy-absorbingmechanisms that occur near the tip of apropagating crack. These energy-absorb-ing mechanisms are numerous, and in-clude crack deflection, crack pinning,cavitation, and others (Figure 4); but themost important of them is the plasticdeformation of material around the

crack tip. This occurs due to the locallyhigh triaxial stresses that occur near thetip of a propagating crack. For a brittlematerial, such as glass, the amount ofplastic deformation possible is quitesmall. For more ductile materials, theamount of plastic deformation can bequite large and the contribution to thefracture energy will dwarf the surfaceenergy contribution. This is most easilyunderstood by going back to the stress-

(a)

(b)

(c)

Figure 1—Common cracking failures in coatings: (a) cracking of auto-motive topcoat, (b) cracking of architectural paint on wood, and (c)delamination on automotive clearcoat.

strain behavior shown in Figure 2. For abrittle material, such as represented bycurve a in Figure 2, the material aheadof the crack tip can only deform a smallamount before its breaking strength isreached. Little to no plastic deformationis possible. However, for more ductilematerials, such as represented by curve cin Figure 2, the material can plasticallydeform ahead of the crack tip, muchlike it can in the simple stress-straintest. In doing so, much energy is ab-sorbed and propagation of the crack ishindered. Thus, taking these extramechanisms into account, Griffith’soriginal equation can be modified to5

(2)

where, Gc is termed thefracture energy and is amaterial property. Thus,if the size of the flaw isknown, and the fractureenergy is measured, thebreaking strength of thematerial can be calcu-lated. Methods to meas-ure the fracture energywill be discussedshortly.

The energy approachis a general one, in thatit can be applied to allmaterials regardless ofductility or stiffness. Formore brittle materials, anumber of simplifica-tions can make themeasurement and cal-culation of a material’s

brittleness much more straightforward.For one specialized case, the bulk of thematerial away from the crack tip is as-sumed to deform in a linear elasticmanner, and plastic deformation is con-fined to a small area adjacent to thecrack tip. When these condition are sat-isfied the mechanics are simplified intowhat is termed linear elastic fracturemechanics (LEFM).

Stress Intensity Factor ApproachBecause the stresses at a crack tip be-

come infinitely large, using the stressesthemselves as a metric for crack propa-gation is not possible. Irwin proposedusing the stress intensity factor as a wayof circumventing this problem for thespecial case when LEFM applies.6 Thestress intensity is a mathematical way ofdescribing the stress field around acrack and is typically given the symbol,K. When the stress intensity reaches acritical value, a crack will propagate.Thus, the criticality condition for crackpropagation is K>Kc. Kc is termed thecritical stress intensity factor, or fracturetoughness, and has units of Pa-m0.5. Avariety of geometries and test set-upscan be used to measure Kc formaterials.7

Because LEFM is a specialized case ofgeneral fracture mechanics, Kc and Gccan be related to each other. For thecase of thin specimens (plane stress),such as paint films

(3)

For thicker specimens (plane strain)

64 October 2005 JCT CoatingsTech

(4)

where E is the modulus (stiffness of thematerial) and ν is Poisson’s ratio.Measuring Gc and converting to Kc isonly possible when the material be-haves in accordance with LEFM. Onemust also remember that because of theviscoelastic nature of polymers, the val-ues of Kc and Gc will vary with testingrate and temperature. [Note: Fracturenomenclature can be confusing. Inmany instances critical properties suchas Kc and Gc are often denoted with anextra subscript, KIc or GIc. These extrasubscripts refer to the mode of fracture,but are beyond the scope of this article.Interested readers can examine appro-priate texts.7]

FRACTURE MECHANICS TESTMETHODS IN COATINGS

For coatings, fracture mechanics canbe used to answer the most basic ofquestions: Will a coating crack or de-laminate? If so, when? How thick can Iapply a coating before it will crack upondrying or in service? These are straight-forward questions that have proven dif-ficult to answer in the past. Fracture me-chanics allows the paint formulator oruser to answer these questions in aquantitative way. The only knowledgerequired is an estimate of the stressesthe coating will experience, the fractureenergy (or related quantity), and theflaw size.

In order to choose the most appro-priate method to characterize a mater-ial’s propensity to crack, a qualitative as-sessment of the materials ductility mustfirst be made. For ductile coatings,where the coating can elongate morethan a few percent in a standard tensiletest at room temperature, the method ofessential work is the preferred approachto testing. For more brittle coatings, Gcor Kc can be measured directly on freefilms or, in certain cases, on coatingsthat are strongly adhering to substrates.Each of these methods will be dis-cussed. The advantage of using fracturemechanics-based tests to evaluate themechanical properties of coatings in-stead of standard tensile testing, is thatthe presence of flaws is expressly ac-counted for. Thus, the link betweenreal-world performance and laboratorymeasured properties can be made withconfidence.

Figure 2—Stress-strain curves of various coating types: (a)rigid, elastic coating showing little strain before break, (b)semi-ductile coating showing some plastic deformation beforebreak, and (c) ductile coating showing extensive plastic defor-mation and flow before rupture.

Figure 3—Cleavage process in materialswhereby two new surfaces (air/material inter-faces) are produced. Surface energy penalty ofeach new surface is γs.

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Ductile Coatings—Method ofEssential Work

Ductile coatings, which includesmany architectural coatings, coatings forplastics, and coil coatings, will elongatesignificantly before rupturing in a ten-sile test. For these coatings, the yieldstrength is low enough that significantplastic deformation will occur beforerupture. Because of this low yieldstrength, the process zone ahead of anadvancing crack will be large and theenergy required to advance that crackwill be substantial. These coatings aregenerally considered quite tough andLEFM does not apply due to the largesize of the plastic zone. However, tech-niques have been developed that do al-low for the quantification of the brittle-ness of the coating.

The method of essential work is themost common method used to charac-terize the fracture resistance of ductilepolymers.8-10 The specimens used arefree films of the coating that have beencarefully prepared. As in all coatingtesting, the thickness of the filmshould be representative of the thick-ness that is used in service. While a fewdifferent specimen geometries are pos-sible, the most common is the doubleedge notch (DEN) shown in Figure 5.Typically the notches are made in arectangular coating sample with achilled razor blade. Care must be takenin handling the free films to insure noother edge flaws of comparable size areproduced.

During crack propagation in a duc-tile coating, the mechanical energy in-put into the coating can be apportionedinto the essential work of fracture, we,and the plastic work of fracture, wp. Theessential work of fracture is that energythat is needed to drive the crack tip for-ward and plastically deform material inthe vicinity of the crack tip. The plasticwork of fracture is that energy that isused to plastically deform material awayfrom the crack tip. These two quantitiescan be used to calculate the total workof fracture

(5)

where l is the ligament length (seeFigure 5), t is the coating thickness, andβ is a shape factor depending on thespecimen geometry. The total work offracture is taken as the area under thestress-strain curve for a given specimen.To determine the essential work of frac-

ture, a number of specimens of varyingligament lengths are tested. The totalwork of fracture divided by the ligamentlength and thickness is then plotted as afunction of ligament length. The essen-tial work of fracture is then determinedby extrapolating back to zero ligamentlength as shown in Figure 6.

The essential work of fracture is amaterial property like the modulus orTg of a coating. Like these other prop-erties, its value will be influenced byextrinsic conditions such as tempera-ture and testing rate as well as compo-sition or crosslink density. Thus, notall polyester coatings will have thesame essential work of fracture, andthe essential work of fracture maychange with time or exposure, as mostcoatings become more brittle duringservice.

Brittle Coatings—LEFMApplications

For coatings that adhere to the re-strictions of LEFM there are two possi-ble routes to determine the resistance tocrack propagation. The first method isto use free films to directly measure Kcor Gc using a number of different speci-men geometries. The second approachis to use the paint and substrate to-gether, provided the coating strongly ad-heres to the substrate.

When using free films to measure Kcor Gc, care must be taken to preventdamage to the specimen. As these filmsare usually brittle, this is not an in-significant experimental difficulty. Oncefree films have been obtained, a startercrack must be inserted in the specimen,usually with a chilled razor blade.Various geometry specimens may beused, the most popular being the singleedge notch (SEN, Figure 5). The equa-tion for calculating Kc in SEN testing isalso shown in Figure 5. Conversion toGc values can be made using equations(3) or (4), depending on sample thick-ness.

The drawbacks to using the free filmmethod outlined above are the same aswith any test method that requires freefilms. Preparation of films can be diffi-cult and time consuming. If the interac-tions between the coating and the un-der layers are important (such asintermixing during cure), the free filmsample may not be representative of thecomposition of the coating in service.Obtaining free films from weathered

Figure 5—Popular geometries for fracture mechanics testing of polymers and coat-ings. Equation below the SEN specimen is for calculating Kc.

Figure 4—Process zone ahead of a crack prop-agating through a material.

samples is usually not possible, so ifchanges in properties during service areimportant, the use of free films is prob-lematic.

For the reasons just outlined, coat-ings that conform to the limits of LEFMare often most easily characterizedwhile still adhering to their substrate.This approach also allows coatings to becharacterized after weathering exposureor other nondestructive testing regi-mens. Another significant advantage ofthis method is that a knowledge of theflaw size is not required to measure thefracture energy. All that is required isthat a population of super-critical flaws(length on the order of the film thick-ness) must be present.11 Specimenpreparation techniques can ensure this.In addition, the strain-to-break of thecoating must also be smaller than thatof the substrate for meaningful testing.

The test method itself is straightfor-ward. Small strips of the coating/sub-strate composite must be cut or shearedfrom a larger specimen. These strips arethen pulled in tension until cracks areseen or heard to propagate across thespecimen (Figure 7). The strain at whichthe cracks propagate is then used to cal-culate the fracture energy of the coatingby using

(6)

where t is the coating thickness, ε is thestrain at cracking, E is the modulus ofcoating divided by (1-ν2), and g(α,β) isa constant related to the modulus mis-

match between the coatingand the substrate.12 For or-ganic coatings on rigidsubstrates, this value is ap-proximately 0.76. Thismethod has been success-fully used to quantify thebrittleness of automotivecoatings and hardcoats onplastic substrates.1,13,14

Unlike other types ofdata the coatings scientistuses, fracture data containsa significant amount ofvariability, regardless of itssource. This is inherent inthe measurement tech-niques and physical natureof the fracture process.Careful experimental tech-nique can minimize thevariability, but it cannot be

completely eliminated. Even good frac-ture mechanics data typically showsvariability on the order of ± 25%.

FAILURE/PROCESSENVELOPES

The brittleness of a coating is valu-able information in and of itself.However, using this information tomake predictions is even more valuable.The driving force, G, for cracking in acoating attached to a substrate can bedescribed by

(7)

where σ is the stress on the coating andZ is a constant related to the particular

66 October 2005 JCT CoatingsTech

cracking geometry.15 For crackingthrough the thickness of a coating, Z =3.951. Other values have been calcu-lated for delamination and spalling.When G >Gc, crack propagation will oc-cur, much like the criticality conditionfor LEFM, K > Kc. Note that equation(7) has the same form as equation (6) ifεE is substituted in for the stress, σ.Intuitively, this equation makes muchsense, as many paint professionalsknow that thicker coatings tend to crackmore easily than thinner coatings. Thisis explained by the thickness depend-ence of the driving force. Thicker coat-ings have a higher driving force forcracking than thinner coatings. Thus,the criticality condition (G > Gc) will bereached at lower stresses for a thickercoating due to the higher drivingforce, G.

These principles can be used to con-struct failure envelopes for coatings ofvarious fracture energies. This is shownin Figure 8 where the film build is plot-ted against the internal stress for coat-ings possessing various values of frac-ture energy. Plots such as these can beused to place boundaries on processvariables or service lifetimes. For exam-ple, rigid coatings used for outdoor ap-plications can typically expect to besubjected to peak stresses on the orderof 20 MPa.16 These stresses are the resultof thermal expansion mismatch be-tween the coating and the substrate,densification of the coating over time,and moisture absorption by the coating.In Figure 8, the coating with a fractureenergy of 90 J/m2 could be applied at athickness of up to 150 μm and supportstress of 20 MPa without cracking.However, two things must be consid-ered. First, most coatings embrittle asexposure time increases. Thus, a coat-ing’s fracture energy will decrease astime progresses. The coating may ini-tially have a fracture energy of 90 J/m2,but after five years of outdoor exposuremay only have a fracture energy of 30J/m2. At 30 J/m2 the coating can only be50 μm thick and still support the 20MPa stress. Thus, the true limit on thefilm build is 50 μm, as coatings must beformulated and applied to last multipleyears in their given service environment.

The second caveat to remember isthat the stresses imposed on coatingsare typically cyclic in nature. Thus, theirfailure is dominated by fatigueprocesses. These processes have notbeen studied in polymeric coatings, buttheir characteristics should be similar tothose observed in other materials in-

Figure 6—Typical data generated from a series of essentialwork of fracture tests. Extrapolation of the data back tozero ligament length gives the essential work of fracturefor the coating.

Figure 7—Schematic of fracture energy testfor brittle coatings adhering to a substrate.Note parallel cracks that appear in the coat-ing after loading.

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cluding bulk polymers and composites.In the case of those materials, the fail-ure stress during fatigue loading is al-ways significantly lower than duringstatic loading.7 Therefore, failure en-velopes developed using the above tech-nique should be taken as upper bondson the allowable thickness, with the ac-tual allowable thickness somewhatlower. The fatigue of coatings is worthfuture investigation.

ADHESION TESTSThe proceeding discussion dealt pre-

dominately with the propagation ofcracks within a material. However, frac-ture mechanics can be used to describethe propagation of cracks at an interfaceas well, where they lead to delamina-tion. Unfortunately, the usefulness ofthis approach has not been sufficientlyexploited yet. The attempts that havebeen made to characterize the tough-ness or fracture energy of paint inter-faces have been unwieldy.17 Thus, theindustry remains saddled with less thanideal tests such as tape pull adhesion.18

SUMMARYFracture mechanics is a powerful tool

for the coatings technologist.Application of its methods allows forthe prediction of failure envelopes andthe optimization of formulations formechanical integrity. Adoption of theprincipals involved in fracture mechan-ics is also useful in assessing the qualityof current coatings tests and in develop-ing new tests that are meaningful andreproducible.

References(1) Nichols, M.E., Darr, C.A., Smith, C.A.,

Thouless, M.D., and Fischer, E.R., Polym.Degrad. Stab., 60, 291 (1998).

(2) Ryntz, R.A., Abell, B.D., Pollano, G.M.,Nguyen, L.H., and Shen, W.C., “ScratchResistance Behavior of Model CoatingSystems,” JOURNAL OF COATINGS

TECHNOLOGY, 72, No. 904, 47 (2000).(3) Kelly, A., Strong Solids, Clarendon Press,

Oxford, 1966.(4) Griffith, A.A., Phil. Trans. Roy. Soc.,

A221, 163 (1920).(5) Orowan, E., Rep. Prog. in Phys. Soc., 12,

185 (1949).(6) Irwin, G.R., Appl. Mats. Res., 3, 65

(1964).

Figure 8—Cracking failure en-velope for coatings with vari-ous fracture energies.Embrittlement moves coatingbehavior from curves withhigher fracture energy to lowerfracture energy. Note coatingwith fracture energy of 90J/m2 can support a stress of20 MPa at a film build of 150μm, but only 50 μm at 30J/m2.

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(7) Kinloch, A.J. and Young, R.J., FractureBehavior of Polymers, Applied SciencePublishers, Essex, 1983.

(8) Mai, Y-W. and Cotterell, B., Int. J. Fract.,32, 105 (1986).

(9) Saleemi, A.S. and Narin, J.A., Polym.Eng. Sci., 30, 211 (1990).

(10) Chan, W.Y.F. and Williams, J.G., Polym.,35, 1666 (1994).

(11) Hu, M.S. and Evans, A.G., Acta Metall.,37, 917 (1989).

(12) Beuth, J.L., Int. J. Solids Struct., 29, 1657(1992).

(13) Nichols, M.E. and Peters, C.A., Polym.Degrad. Stab., 75, 439 (2002).

(14) Nichols, M.E., “Anticipating PaintCracking: The Application of FractureMechanics to the Study of PaintWeathering,” JOURNAL OF COATINGS

TECHNOLOGY, 74, No. 924, 39 (2002).(15) Hutchinson, J.W. and Suo, Z., in Advan.

in Appl. Mech., 29, Academic Press, 63(1992).

(16) Nichols, M.E. and Darr, C.A., “Effect ofWeathering on the Stress Distributionand Mechanical Performance ofAutomotive Paint Systems,” JOURNAL OF

COATINGS TECHNOLOGY, 70, No. 885, 141(1998).

(17) Meth, J.S., Sanderson, D., Mutchler, C.,Bennison, S.J., J. Adhes., 68, 117 (1998).

(18) Asbeck, W.K., “A Retrospective View ofCoatings Adhesion Testing,” JOURNAL OF

COATINGS TECHNOLOGY, 2, No. 12, 48(2005).