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The problem of a cylinder moving on a semi-plane, carrying an oblique edge crack is studiedby the Weight Function (WF) method. A general formulation of the WF is proposed, fromwhich the Green’s Function (GF) giving the crack opening displacement (COD), is deduced.An iterative procedure is adopted for studying the conditions of partial crack closure. Themethod is applied to evaluate the influence exerted on the crack loading by the non uniformcontact compliance when the cylinder crosses the crack mouth. In particular, the errorinduced by assuming the theoretical Hertzian nominal stress distribution is discussed bycomparison with correct WF solutions and with accurate Finite Element analyses. Aparametric study accounting for different friction conditions between the crack surfaces anddifferent contact conditions between the moving cylinder and the cracked semi-plane isperformed and typical K I and K II histories produced by the cylinder movement are evaluated.IntroductionMany mechanical components (e.g. gears, bearings, rail wheels,…) suffer surface damagedue to contact fatigue. In many cases, the contact between the moving bodies producesglobally elastic strain that locally varies as a consequence of the relative movement of thebodies in contact. The corresponding loading cycle can promote initiation and growth ofoblique edge cracks, initially loaded in mixed fracture mode (I+II) [1-3].The lack of symmetry of the fracture problem makes the analysis of the fatigue crackgrowth not so simple, as many evaluations of fracture parameters (K I and K II ) have to beperformed for complex stress distributions. Indeed, the local high stress gradients areproduced not only by the travelling contact but also by possible surface treatments, thatusually induce compressive residual stresses near the surface[4]. Moreover, the possibility forthe lubricant to be entrapped or pumped into the crack increases the complexity of theproblem [5,6].During a loading cycle, conditions of partial closure are usually experienced by the crack.In this case, the problem is no more linear [6,7] and the mutual forces between the crackfaces strongly influence the crack configuration and the Stress Intensity Factor (SIF) values.The Weight Function (WF) method was verified to be a very useful tool for solving thiskind of problem [8-10]. The authors have recently proposed a general matrix formulation ofthe WF for an inclined edge crack in a semi-infinite body [10]. On this basis, an analyticalformulation of the Green Function (GF) has been obtained [11], thus allowing the CODcomponents to be determined by direct integration under a completely general loadingcondition. Based on the WF and GF, an iterative procedure was developed to obtain the