Graded Materials for Resistance to ContactDeformation and Damage

S. Suresh

The mechanical response of materials with spatial gradients in composition andstructure is of considerable interest in disciplines as diverse as tribology, geology,optoelectronics, biomechanics, fracture mechanics, and nanotechnology. The damageand failure resistance of surfaces to normal and sliding contact or impact can bechanged substantially through such gradients. This review assesses the current un-derstanding of the resistance of graded materials to contact deformation and damage,and outlines future research directions and possible applications for graded materials.

T he composition, structure, and me-chanical properties of a material mayvary, continuously or in discrete steps,

with depth beneath a free surface. Gradationsin microstructure and/or porosity are com-monly seen in biological structures such asbamboo, plant stems, and bone, where thestrongest elements are located in regions thatexperience the highest stresses (1, 2). Gradualchanges in the elastic properties of sands,soils, and rocks beneath Earth’s surface in-fluence the settlement and stability of struc-tural foundations, plate tectonics, and theease of drilling into the ground (3, 4). Inengineered materials, gradations in composi-tion occur unintentionally, for example, as aconsequence of lattice and grain boundarydiffusion, oxidation, and clustering of atomicspecies or reinforcement particles. In manycases, such gradations may not even be de-sirable. Learning from nature, materials sci-entists increasingly aim to engineer gradedmaterials that are more damage-resistant thantheir conventional homogeneous counter-parts. This is particularly important at surfac-es or at interfaces between dissimilar materi-als, where contact failure commonly occurs.With established methods currently availableto synthesize and process materials, grada-tions in composition, structure, and propertiescould be engineered over a wide range oflength scales ranging from nanometers tometers.

Motivation for the Use of GradedMaterialsIt has long been recognized that gradients insurface composition can improve the me-chanical performance of a material [e.g., (1,2)]. Early examples of the use of syntheticmaterials with graded properties can be

traced back to the blades of Japanese steelswords using a graded transition from a softerand tougher core to a hardened edge (5).Carburizing and nitriding treatments are com-monly given to steel surfaces to impart hard-ness, and fatigue and wear resistance in trans-mission gear teeth. However, theoretical un-derstanding of such phenomena has not re-ceived much attention.

Graded transitions in composition, eithercontinuous or in fine, discrete steps, across aninterface between two dissimilar materials(such as a metal and a ceramic), can be used toredistribute thermal stresses (6, 7), thereby lim-iting the stresses at critical locations and thussuppressing the onset of permanent (plastic)deformation, damage, or cracking (8, 9). Grad-ed transitions can also reduce stress concentra-tions at the intersection between an interfaceand a free surface (10, 11). Similarly, the localdriving force for crack growth across an inter-face can be increased or reduced by altering thegradients in elastic and plastic properties acrossthe interface (12, 13). Smooth transitions incomposition across an interface also improveinterfacial bonding between dissimilar materi-als (2), thereby facilitating the deposition ofmuch thicker surface coatings (typically morethan 1 mm thick) than is feasible with sharpinterfaces. In some applications, such as diesel-engine piston heads, thicker coatings impartbetter protection against thermal degradation.Thin films with graded composition play animportant role in heteroepitaxial multilayersused in semiconductor devices. The gradedfilms are deposited between a substrate and aquantum well to control the density and kineticsof threading dislocations. They protect thequantum wells and light-emitting diodes withspecific optoelectronic properties from the del-eterious effects of these dislocations, which areintroduced at interfaces as a result of latticemismatch and thermal expansion mismatchstrains during layer deposition (14).

In the late 1980s and early 1990s, interest

in graded materials primarily focused on con-trolling thermal stresses in structures exposedto very high temperatures (;2000 K) in com-ponents used in aerospace applications andsolid-oxide fuel cells, and in energy conver-sion systems using thermoelectric or thermi-onic materials (15). The use of graded layersand interfaces in materials exposed to hightemperatures for long periods of time, how-ever, is complicated because of diffusion.Research has therefore increasingly focusedon lower temperature applications of gradedmaterials on the basis of their resistance tocontact damage. This research direction wasalso motivated by advances in techniques forcontrolled indentation and by a growing needto develop damage-resistant surfaces andcoatings—for example, in magnetic storagemedia, nano- and microelectromechanicalsystems, barrier coatings for structural com-ponents, dental implants, articulating surfacesin hip and knee prostheses, and penetration-resistant materials for armor plates and bul-let-proof vests (16).

Contact Resistance of Graded SurfacesThe indentation of a surface with a sharp orblunt probe (indenter) provides basic andquantitative information that typifies the re-sistance of the surface to normal contact. Ifthe spatial variation of the mechanical prop-erty with depth beneath the indented surfaceis well defined and known a priori, analysisof the indentation load versus indenter pene-tration depth into the surface can also providevaluable information about the contact-dam-age resistance of the surface.

Theories of normal elastic contact. Overthe past several decades, the geomechanicscommunity has studied the evolution ofstresses and displacements, under a pointload, in elastically graded substrates (3, 4,17–22). In these studies, the Young’s modu-lus, E, was varied as a function of depthbeneath the indented surface, z, according tothe power-law function E 5 E0zk, where E0 isthe reference Young’s modulus at the surfaceand 0 # k , 1 (k 5 0 for a homogeneousmaterial). Such variations in elastic modulusare typically seen in sandy soils and consol-idated clay deposits. These studies did notprovide general solutions of the variation ofindentation load (P) with the depth of pene-tration (h) of the indenter into the surface forcommon indenter geometries (such as asphere, cone, cylinder, or a pyramid) or with

Department of Materials Science and Engineering,Massachusetts Institute of Technology, 77 Massachu-setts Avenue, Cambridge, MA 02139–4307, USA.

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the contact radius, a, of the indenter with thesubstrate, which are needed for direct exper-imental validation of such theories.

A general theory for frictionless normalindentation of elastically graded materials bypoint loads and axisymmetric indenters wasrecently developed (23) for two general vari-ations in Young’s modulus with respect todepth: the power-law variation, E 5 E0zk,and an exponential variation, E 5 E0eaz

(where 1/a signifies a length scale associatedwith the gradient in modulus beneath thesurface when a Þ 0), for any specific valueof Poisson ratio, n (the ratio of the negative ofthe lateral strain to the axial strain in a uni-axial tension test), which was taken to bespatially invariant. Explicit analytical expres-sions were derived to relate the indentationload, P, to the penetration depth, h, or thecontact radius, a, for different indenter geom-etries. Computer simulations of the simulta-neous variation of the Poisson ratio, n, withdepth revealed that the effect of varying nwas substantially smaller than that of varyingE.

Predictions of resistance to normal elasticcontact. Consider an elastically graded mate-rial with constant n that is subjected to inden-tation by a rigid sphere of radius R (Fig. 1A).Let the Young’s modulus increase or de-crease exponentially, or remain constant as afunction z (Fig. 1B). A homogeneous elasticmaterial exhibits an indentation response forwhich P scales with h1.5 (Fig. 1C). If Eincreases beneath the indented surface, theindentation response is stiffer; the stiffness ofthe response reaches a vertical asymptote asthe limit of the exponential increase in elasticmodulus is reached. If a , 0, the elasticallysofter material beneath the indented surfacepromotes a compliant response comparedwith a homogeneous solid; the indentationload-carrying capacity vanishes in the asymp-totic limit as E decreases exponentially be-neath the surface.

Theory (23) also predicts that when themodulus increases (or decreases) monotoni-cally with depth, peak values of local tensilestresses, which result in the nucleation ofdamage at the surface, are spread further intothe interior (or moved closer to the surface)compared with a homogeneous material. Thisis because the underlying material has a high-er (or lower) E than the surface and can thussustain a greater (or lower) stress.

Experimental evidence. Experimental ver-ification of the effect of a continuous elasticgradation on indentation cracking resistancerequires a composite microstructure with atleast two different constituent phases of dif-ferent elastic moduli, whose relative concen-trations are gradually changed beneath thesurface. Synthesis of such a system at elevat-ed temperatures and subsequent cooling toroom temperature would introduce large ther-

mal residual stresses, thereby complicatinginterpretations of such experiments. Thisproblem can be circumvented by synthesizinga “clean” model system in which the constit-uent phases have the same coefficient of ther-mal expansion (CTE) and Poisson ratio (n),but markedly different Young’s moduli.

Such a graded elastic system has beenproduced by infiltrating an oxynitride glassinto a fine-grained a-Si3N4 matrix (24). Thea-Si3N4 matrix, consisting of 93.7% of thebulk Si3N4, contained elongated grains, 0.5mm in diameter and 2 mm in length, in a glassmatrix. The infiltrated oxynitride glass, here-after referred to as SiAlYON, had a chemicalcomposition close to that of the glass matrixin the bulk Si3N4. Infiltration of SiAlYON at1500°C for 2 hours produced a continuouslygraded elastic composite, with ;30 volume% glass at the surface gradually decreasing to0% about 0.5 mm beneath the surface (Fig.2A). The elastic modulus of a-Si3N4 is 320GPa and that of SiAlYON glass is ;110GPa; n ' 0.22 for both materials. The CTE ofa-Si3N4 is essentially the same as that of theinfiltrated glass, and therefore no long-rangeinternal stresses develop in the graded com-posite. However, because the modulus a-Si3N4 is three times that of glass, a change inglass composition from 30% at the surface to0% 0.5 mm beneath the surface resulted in acorresponding smooth variation of elasticmodulus from about 225 GPa at the surface toabout 315 GPa over the same depth (Fig. 2B).

In a cross section perpendicular to theindented free surface of the homogeneousa-Si

3N4 ceramic (Fig. 2C), classic Hertzian

cone cracks are seen after spherical indenta-tion to a maximum load of 3 kN with aWC-Co indenter with a radius of 4.76 mm.These cracks form at the contact perimeterwhere the maximum tensile stresses develop.Homogeneous SiAlYON glass, and a nitride/glass composite of uniform compositionequal to the surface composition of the grad-ed material, develop similar cone cracks un-der spherical indentation. Despite the lowerstrength and lower toughness of the glass atthe surface, the graded nitride-glass compos-ite could sustain an indentation load as highas that in homogeneous a-Si3N4 withoutforming any cone cracks (Fig. 2D), solely asa consequence of the reduction in maximumtensile stress at the contact surface due tograding. Similar beneficial effects of modu-lus gradations have been demonstrated in afine-grained aluminum oxide infiltrated withaluminosilicate glass (25).

Resistance of graded materials to sliding-contact damage. Experiments of frictionalsliding of spheres on elastically graded sur-faces also point to the beneficial effects ofmodulus gradients. Frictional sliding by asteel sphere on an alumina-glass graded com-posite (with CTE-matched alumina and glass

phases), with a power-law increase in modu-lus beneath the sliding surface, showed that agraded material with a 40 vol. % soft glassphase at the surface could sustain as high aload as the homogeneous alumina withoutdeveloping any “herringbone” cracks (26).These circular cracks develop around thecontact perimeter under the influence of themaximum principal tensile stress (27, 28).The graded composite could sustain a normalload more than twice that carried by themonolithic glass before herringbone cracksdeveloped in the glass. Despite its lowstrength and low toughness at the contact

Fig. 1. Indentation response of an elasticallygraded surface. (A) Details of the contact re-gion underneath the spherical indenter subject-ed to a load P. (B) Schematic illustration of anexponential increase (a . 0) or decrease (a ,0) in Young’s modulus as a function of depth zbeneath the indented surface; E 5 E0e az, whereE0 is Young’s modulus at the surface and a 5 0represents an elastically homogeneous materi-al. (C) Schematic illustration of the variation ofnormalized indentation load as a function ofnormalized depth of penetration for the homo-geneous and graded surfaces. For the gradedsurfaces, the variation of P with the penetrationdepth h is a complex function of the surfaceand indenter properties, the indenter radius,and the gradient in elastic modulus a (23).

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response is a function of the gradient instrength, m, indenter shape and tip geometry,and strength (Fig. 4C). If sy decreases withdepth, the material rapidly loses its capabilityto sustain the indentation load, and the in-denter sinks into the substrate. If sy increasesbeneath the indented surface, the indentationstiffness is higher compared with that of aplastically homogeneous material.

A comprehensive theoretical frameworkfor the interpretation of blunt and sharp in-dentation of plastically graded metals withdifferent strain-hardening characteristics ispresently unavailable. The extent to whichchanges in the P-h response arising fromplasticity gradients at the surface translate

into contact-damage suppression and wearresistance remains to be established throughsystematic experiments. Such studies shouldalso assess the complex interactions amongcontact loads, contact geometry, propertygradients, the mechanics of contact fractureand fatigue at surfaces, and the evolution ofwear damage in different environments.

Issues of length scale. Analyses of homo-geneous, isotropic materials by contact me-chanics require consideration of differentlength scales. For continuum analyses to bevalid, mechanical length scales, such as thecontact radius a or the depth of penetration h(which are influenced by the shape and sizeof the indenter), should be large comparedwith the characteristic structural size scalesuch as grain size. In graded systems (forexample, Fig. 2), the zone of influence of thecontact loads beneath the indented surfaceshould be sufficiently large to capture signif-icant variations in elastic and plastic proper-ties. In geological systems, this size scalecould be hundreds of meters (as in the case ofdrilling to lay the foundation for a tall struc-ture), whereas for nanostructured coatings itcould be as small as a few nanometers. Theyield strength of metallic films scales withthe square root of the dislocation density, andtherefore gradients in dislocation density oversmall distances beneath a surface could alsoinduce plasticity gradients which, in turn,could strongly influence nanoindentation re-sponse. Although strain-gradient plasticitytheories seek to address such length-scaleissues by accounting for higher order effects(32, 33), systematic experiments at differentlength scales, which would provide estimatesof the regions of validity of such theories, arecurrently unavailable.

Continuum descriptions of elastic indenta-tion response are known to be valid to indenta-tion penetration depths as small as a few nano-meters (34). However, experiments show (34,35) that even homogeneous thin films of crys-talline metals exhibit discrete jumps in inden-tation response as a consequence of defect nu-cleation and motion. In general, gradients inelastic and plastic properties in the vicinity ofthe surface should be tailored in such a way thatthe field of indentation produced around thecontact region samples the entire length scaleover which property gradients occur, so that thefull effect of compositional gradation can berealized.

Outstanding Scientific Issues andChallengesThe use of graded materials in contact-criticalapplications has important implications for amultitude of disciplines. Studies of the effectsof compositional, structural, and property gra-dients on the resistance of surfaces to normal,sliding, rolling, or fretting contact and wearhave only recently begun to emerge. This sec-

tion highlights some possible applications, andexamines key challenges.

With recent advances in instrumentedmicro- and nano-indentation (36 ), depth-sensing indentation is rapidly becoming aresearch tool to characterize the elastic,plastic, and fracture characteristics of avariety of engineering materials and surfac-es at length scales approaching atomic andmolecular dimensions. Such interest is alsospurred by the rapid miniaturization of fea-tures and components in microelectronicdevices, magnetic storage media, and nano-and microelectromechanical structures. Ex-amples include electromechanical and bio-logical sensors and actuators, and miniaturepower devices such as microturbines, mo-tors, and pumps (37, 38).

In many of these applications, graded sur-faces provide appealing prospects for control-ling surface damage and failure during re-peated contact. Progress in materials synthe-sis—for example, by molecular beam epi-taxy, vapor deposition, three-dimensionalprinting, bulk and surface micromachining,and lithography—now afford the flexibilityto fabricate gradients at surfaces with dimen-sions approaching a few atomic layers tomacroscopic size scales (1, 2, 37, 38). How-ever, systematic studies of the effects of com-positional gradation on the indentation re-sponse and contact-damage resistance andfailure of crystalline and amorphous solidsand surface coatings have thus far not beenconducted. The mechanisms of damage evo-lution in these situations also have not beenexamined by characterization techniquessuch as atomic force or electron microscopy.Further interest in the resistance of gradedmaterials to contact loading stems from theirpossible use as penetration-resistant surfaces.

Hertzian cone cracks (Fig. 2C) areknown to be deleterious to contact resis-tance and tribological performance at sur-faces. The suppression of such cracksthrough modulus gradients provides oneavenue for enhancing the contact-damageresistance without introducing tensile resid-ual stresses in the bulk. Alternative meth-ods, such as tempering, layering, phase-transformation, coating, ion-exchange, dif-ferential densification, grinding, and sur-face heat treatment, promote compressiveresidual stresses at contact surfaces but alsolead to the concomitant generation of ten-sile residual stresses in the bulk of thematerial (24, 25), which can promote crack-ing. On the other hand, the introduction ofheterogeneities, such as second-phase parti-cles, to introduce compressive residual stress-es at surfaces and thereby suppress contactcracks has the deleterious effect of impartingnonlinearity to the deformation response ofthe material which, in turn, can lead to aninferior tribological response and fatigue life.

Fig. 4. Conical sharp indentation of a plasti-cally graded surface. (A) Details of contactaround the conical indenter. The included tipangle of the conical indenter is 2g. (B) Stress-stress response, s, versus ε at three differentpoints (1, 2, 3) below the indented surface.(C) The yield strength of this rigid plasticmaterial, sy, either increases or decreaseslinearly with depth below the surface z (asindicated by the red or green straight line,respectively). The yield strength value is sy,0at the surface, and the slope of the sy versusz plot is m. For a plastically homogeneoussurface indented by a conical indenter, Pscales with h2. However, for the graded sur-face, theory (31) indicates that P 5 C1h2 1C2h3, where C1 5 11.88sy,0(tan g)2, and C2 5Bmsy,0(tan g)3, where B 5 13.86 for m . 0and B 5 16 for m , 0. A positive (negative)value of m leads to a stiffer (more compliant)indentation response than that for a homo-geneous material for which m 5 0.

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It is important to note that the use of alow-strength and low-toughness layer at acontact surface could lead to an increasedsusceptibility to wear damage and materialloss, despite the benefits of suppressing in-dentation cracks during normal loading andfrictional sliding. Several different strategiescan be implemented to overcome these limi-tations. First, methods other than infiltrationcan be used to develop stepwise gradients inelastic moduli at the surface where the mod-ulus increases from a hard surface layer (suchas Si3N4) to a graded layer (with Si3N4 andSiC phases). Such graded materials havebeen synthesized by sintering to enhance re-sistance to both contact damage and wear(24). Second, a thin (less than 1 mm thick)surface layer of a hard, wear-resistant coat-ing, such as a layer of diamond-like carbon,could be deposited on the graded surface.Because such coatings could be depositedwith a Young’s modulus range of 45 to 250GP and with significant improvements inwear resistance, elastic moduli gradationscould be introduced near the contact surfacewhile maintaining a wear-resistant layer atthe top layer of contact. If the elastic field ofindentation spreads well into the graded lay-er, beneficial effects of modulus gradationswould be expected with respect to contact-damage suppression and wear resistance.

Wear-resistant, nanocrystalline surfacecoatings, with grain sizes as small as a fewtens of nanometers, can now be synthe-sized—for example, with thermal spray, elec-trodeposition, eletrophoretic deposition, sput-ter deposition, and metal-organic chemicalvapor deposition (39). Many of these meth-ods can create surface layers in which thegrain sizes are graded smoothly from thesurface to the bulk, thereby inducing con-trolled gradients in strength and fracturetoughness. Similarly, gradients in porositycan be tailored beneath contact surfaces toimprove resistance to contact damage as, forexample, in coatings used to protect articu-lating surfaces in hip and knee prostheses.

Such gradients in pore concentration couldalso be used to facilitate the growth of boneand tissue in many biomedical applications.In polymeric materials (such as ultrahigh mo-lecular weight polyethylene, which is used,for example, in knee prosthesis), gradients inelastic properties can be induced by the in-troduction of spatial variations in degree ofcrystallinity and/or molecular weight.

In summary, recent theoretical and experi-mental work has established that controlled gra-dients in mechanical properties offer unprece-dented opportunities for the design of surfaceswith resistance to contact deformation anddamage that cannot be realized in conventionalhomogeneous materials. With currently avail-able materials synthesis and processing capabil-ities, engineered gradations in properties, overnanometer to macroscopic length scales, offerappealing prospects for the design of damage-,fracture-, and wear-resistant surfaces in appli-cations as diverse as magnetic storage media,microelectronics, bioimplants for humans, load-bearing engineering structures, protective coat-ings, and nano- and microelectromechanicalsystems.

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