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I.

INTRODUCTION

THE modification of the stress intensity factor based on crack closure has been universally applied to explain the experimental observations of fatigue crack growth behavior under various mechanical loading conditions and in various metallic alloys. For an overview of the topic, the reader is referred to the textbook by Suresh[1] and the overview by Sehitoglu et al.[2] However, to develop a better understanding of the intrinsic mechanisms of crack growth in various materials due to mechanical and microstructural factors, it is particularly important to determine the individual influences of crack closure due to plasticity, roughness, and oxide effects. Then, the effect of each of these mechanisms can be isolated to develop more advanced models for crack advance. Since a quantitative description of crack roughness effects has not been previously derived, the present work has undertaken this task. In many materials, when the crack advance is influenced by crystallographic slip or when the crack encounters microstructural barriers, the crack paths are nonflat and the crack can deviate from the normal mode I growth plane. The nonflatness of crack surfaces has been known to enhance the resistance of a material to fatigue crack growth. This resistance can develop in cases when the crack surfaces are viewed as nominally flat at the macrolevel, but there could be many periodic deviations from a smooth crack surface in the forms of asperities at the microlevel. These asperities could interlock at very low loads, or slide and crush in the presence of sufficient loading, resulting in an alteration of the crack surface profile as the crack advances. Combining the interaction of many asperities results in stresses in the crack wake which, in turn, have to HUSEYIN SEHITOGLU, Professor and Associate Head, and ANA MARI´A GARCI´A, Research Assistant, are with the Department of Mechanical and Industrial Engineering, University of Illinois, Urbana, IL 61801. Manuscript submitted March 5, 1997. METALLURGICAL AND MATERIALS TRANSACTIONS A

be overcome before the crack can move forward. Therefore, the calculation of the driving force on the crack in the presence of complex crack surface interaction represents one of the present challenges to fatigue crack propagation analyses. As will be discussed subsequently, almost all classes of materials, with suitable heat treatment or processing, can be made to exhibit nonflat crack surfaces which will undergo contact due to the presence of asperities. Due to the significance of the problem, many experimental studies from the materials science community have documented the role of crack roughness effects in the literature. On the other hand, the modeling of the crack surface interference via asperity sliding and crack closure has received much less consideration. The few models forwarded to capture the crack deflection on crack growth rates can be divided into two categories: those that consider isolated cases of periodic tilting and those that consider discrete asperity locking. I