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The Role of Adhesion in Contact Fatigue

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The Role of Adhesion in Contact Fatigue Acta mater. Vol. 47, No. 18, pp. 4653±4664, 1999 # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Printed in Great Britain PII: S1359-6454(99)00312-2 1359-6454/99 $20.00 + 0.00 THE ROLE OF ADHESION IN CONTACT FATIGUE A. E. GIANNAKOPOULOS, T. A. VENKATESH, T. C. LINDLEY{ and S. SURESH{ Department of Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, U.S.A. (Received 26 May 1999; accepted in revised form 12 August 1999) AbstractÐBy incorporating the eects of interfacial adhesion in the mechanics of rounded contact between two bodies, a new approach is proposed for the quantitative analysis of a wide variety of contact fatigue situations involving cyclic normal, tangential or torsional loading. In this method, conditions of ``strong'' and ``weak'' adhesion are identi®ed by relating contact mechanics and fracture mechanics theories. Invok- ing the notion that for strong and weak adhesive contact, a square-root stress singularity exists at the rounded contact edge or at the stick±slip boundary, respectively, mode I, II or III stress intensity factors are obtained for normal, sliding and torsional contact loading, accordingly. A comparison of the cyclic variations in local stress intensity factors with the threshold stress intensity factor range for the onset of fatigue crack growth then provides critical conditions for crack initiation in contact fatigue. It is shown that the location of crack initiation within the contact area and the initial direction of crack growth from the contact surface into the substrate can be quantitatively determined by this approach. This method obvi- ates the need for the assumption of an arti®cal length scale, i.e. the initial crack size, in the use of known fracture mechanics concepts for the analyses of complex contact fatigue situations involving rounded con- tact edges. Predictions of the present approach are compared with a wide variety of experimental observations. # 1999 Acta Metallurgica Inc. Published by Elsevier Science Ltd. All rights reserved. Keywords: Adhesion; Fracture; Fatigue; Wear; Surfaces and interfaces 1. INTRODUCTION the total energy of the system, while elastic defor- Functional structures, at macro or micro size-scales, mation across the interface that accomodates ad- by design or default, involve contact between simi- hesion leads to an increase in the potential energy lar or dissimilar materials, under static or cyclic of the system. The resulting thermodynamic equili- loading conditions, in a passive or aggressive, brium and extent of adhesion is then determined by thermo-chemical environment. Consequently, in the the relative dominance of these competing phenom- most general case, dierent aspects of contact such ena. as material properties, interface chemistry and con- For monotonic contact loading, adhesion has tact mechanics can independently or interdepen- been well documented analytically and experimen- dently in¯uence the overall mechanical behavior of tally under normal loads [1±5], and to a lesser the contacting system. extent under tangential loads [6]. For cyclic loading, In most cases, the bulk mechanical behavior of a number of experimental studies have investigated the contacting system is characterized by a macro- adhesion in a variety of materials Ð metals [7, 8], scopic continuum level analysis that evaluates the glasses [9], and polymers [10], for dierent surface uncoupled mechanics response [1]. However, a more and environmental conditions [11, 12], temperatures complete analysis requires a consideration of the [13], hardness [8], and fatigue cycles [14]. microscopic or atomic structure where coupled in- Theoretical work has demonstrated that under teractions at the contact interface become signi®- monotonic compressive loading of the contact inter- cant. These are typically analyzed within the face, adhesion induces tensile square-root singular framework of surface thermodynamics by recogniz- stress ®elds at the contact edges [2, 3]. However, ing that contacting surfaces are subject to short- connections to contact fatigue experiments speci®- range interatomic forces such as the van der Waals cally aimed at correlations between adhesion and forces. Consequently, spontaneous adhesion leading fatigue crack initiation have not been established. to the formation of a low energy interface reduces The objectives of the present work are, therefore, to develop and experimentally validate a general continuum level mechanics model that incorporates {Permanent address: Department of Materials, Imperial work of adhesion, material elastic properties, and College of Science, Technology and Medicine, Prince Consort Road, London SW7 2BP, U.K. contact loads, for predicting key features of contact {To whom all correspondence should be addressed. fatigue crack initiation (thresholds for the onset of 4653 4654 GIANNAKOPOULOS et al.: ADHESION IN CONTACT FATIGUE cracking, location of cracking, and initial orien- arising from the contact loads, leads to a novel tation of the crack plane with respect to the contact classi®cation whereby cases of strong and weak ad- surface) for a variety of loading conditions (cyclic hesion are recognized unambiguously{. Thus, the mode I or steady mode I with cyclic mode II or crack initiation location (contact perimeter for cyclic mode III) and contact geometry (sphere or strong adhesion and the stick±slip boundary for cylinder on a planar substrate). weak adhesion) can be predicted without uncer- This paper addresses the following key issues of tainty. contact mechanics and contact fatigue. Fifth, the present methodology conceptually fa- First, the present work extends the crack ana- cilitates the incorporation of known eects of sur- logue methodology developed earlier [15] for the face conditions, environment, hardness, and contact between a sharp-edged pad and a planar temperature on adhesion, through a simple modi®- substrate, where stress singularities are introduced cation of the work of adhesion. by the sharp cornered geometry. We now investi- The paper is arranged in the following sequence. gate the more general case of rounded contacts The mechanics of adhesive contacts for a variety of where stress singularities are induced by adhesion{ monotonic loading conditions are reviewed in and thus present a universal methodology that Section 2. The contact mechanics of cyclic loading enables analysis of a variety of contact problems for three-dimensional, spherical, adhesive contacts from those due to fretting fatigue in large-scale are analyzed in Section 3. The results of the ad- structures to contact fatigue in micro-scale devices, hesion model for cyclic loading for two-dimen- with adhesive or non-adhesive, sharp or rounded sional, cylindrical contacts are presented in Section geometries. 4. The range of applicability of the adhesion model Second, as the adhesion-induced, square-root as well as its signi®cance and limitations are dis- singular stress ®elds are amenable for analysis cussed in Section 5. Available experimental results within the framework of a ``crack analogue'' [15], for dierent material systems and loading con®gur- ations are compared to model predictions in the pre-existing long crack introduced by the con- Section 6. Finally, the paper concludes with a sum- tact circumvents ``length scale'' problems inherent mary of results and potential palliatives for contact in the modeling of crack initiation based on conven- fatigue from the perspective of the adhesion model tional fracture mechanics [16], or small crack in Section 7. growth based on initial dislocation distributions [17]. Third, under conditions of small-scale yielding, 2. MECHANICS OF STATIC ADHESIVE CONTACT the eects of static and/or oscillatory bulk stresses (i.e. residual stresses induced by surface treatments Consider a sphere of diameter, D, elastic mod- such as shot-peening or laser shock-peening, or far- ulus, E, and Poisson ratio, n, contacting the planar ®eld applied stresses acting parallel to the contact surface of a large substrate of similar material, Fig. surface) on contact fatigue crack initiation can also 1(a), with r and z being the global radial and depth be analyzed by recognizing that these are analogous coordinates attached to the center of the contact to the T-stresses present in a simple linear elastic circle. Three loading conditions are considered as fatigue±fracture formulation. follows. Fourth, all previous analyses which are based on 2.1. Normal loading stress-based approaches to fatigue at critical points (such as those using elastic stress ®elds of a sphere For elastic, monotonic loading from zero to Pmax on a ¯at plane [18] in combination with a variety of (>0), under non-adhesive conditions, the contact fatigue strain-based, multiaxial criteria for endur- stress ®eld is non-singular [Fig. 1(b)] and the maxi- ance limits [19±22], predict contact fatigue cracking mum contact radius, a0, is given as [1] to initiate at the contact perimeter. This prediction 1=3 3D 1 n2 is contrary to many experimental results which a0 Pmax : 1 clearly indicate that cracking could initiate at either 4E the contact perimeter or the stick±slip boundary. Under adhesive conditions, when two surfaces with The present analysis, though an examination of the surface energies g1 and g2 adhere to form a new work of adhesion via-aÂ-vis the crack driving force interface of lower energy, g12, the corresponding work of adhesion is de®ned as, w=(g1+g2g12)r0. {The adhesion induced
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