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I.

INTRODUCTION

FATIGUED surfaces are often rough due to the presence of slip extrusions formed on metal surfaces subjected to cyclic loading.[1,2] The roughened surfaces[1,3] can lead to fatigue crack initiation, regardless of the surface condition.[4] Thus, the surface roughness induced by cyclic slip has been considered a fatigue damage precursor to crack initiation and used in fatigue crack prognostics. For example, Buckner et al.[5] have applied a laser scattering technique to measure the surface roughness of a fatigued surface. Such a technique can potentially be used as a structural health monitoring system if the surface roughness can be directly related to fatigue life.[5] The processes responsible for the formation of persistent slipbands, extrusions, and fatigue cracks in surface grains are well established, as described in several reviews.[1,2,6] A number of mechanistic models have been proposed to describe the initiation of fatigue cracks at slipbands or extrusions.[1,2,7–12] The crack initiation model of Tanaka and Mura[8,9] was based on a dislocation dipole mechanism operating in a surface grain. During fatigue loading, irreversible slip occurs on parallel slip planes in a favorably oriented surface grain, producing dislocation dipoles at the ends of double pileups whose coalescence ultimately leads to crack nucleation. Tanaka and Mura’s model[8,9] was K.S. CHAN, Institute Scientist, is with the Materials Engineering Department, Southwest Research Institute, San Antonio, TX 78238. Contact e-mail: [email protected] J.W. TIAN, Postdoctoral Research Associate, and P.K. LIAW, Professor, are with the Department of Materials Science and Engineering, University of Tennessee, Knoxville, TN 37996. B. YANG, formerly Postdoctoral Research Associate, Materials Science and Engineering Department, University of Tennessee, is Materials Engineer, with Shell Global Solution, Houston, TX 77082. Manuscript submitted January 11, 2009. Article published online September 1, 2009 METALLURGICAL AND MATERIALS TRANSACTIONS A

subsequently extended by Chan[12] to explicitly incorporate the microstructural unit length, crack size, and other pertinent material parameters in the response equation by considering the energetics of the fatigue crack initiation process. Specifically, the length of the incipient crack was obtained by equating the elastic strain energy released by dislocation coalescence and crack opening to the fracture energy, consisting of elastic and plastic components, required to form the crack surfaces. This formulation leads one to a stress-life relation given by[12]  1=2    8Ml2 h a 1=2 a ðDr
2MkÞNi ¼ ½1 D D kpð1
mÞ where Dr is the stress range, M is the Taylor factor, k is the friction stress, Ni is the cycles to initiation, m is Poisson’s ratio, l is the shear modulus, and k (=0.005) is a universal constant.[10] Equation [1] relates the crack initiation life, Ni, to the grain size, D, the slipband width, h, and the dislocation pileup length or crack depth, a. The exponent to Ni has been generalized