Stress intensity factors for elliptical and semi-elliptical cracks subjected to an arbitrary mode l loading
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Fatigue durability, damage tolerance and strength evaluations of cracked structural components require accurate determination of stress intensity factors (SIF). Most practical crack configurations are embedded and surface breaking planar cracks subjected to complex two-dimensional stress fields. The only cracked body configuration which has been studied analytically for all types of applied stress fields is a circular crack in an infinite elastic solid. However, this model is suitable only for a narrow class of practical applications. Much wider class of practical problems can be solved using the model of an elliptical crack. The exact analytical SIF solutions for an elliptical crack were obtained only for some particular cases of polynomial applied stress fields. In the present work the exact analytical SIF solution has been obtained for an elliptical crack embedded in an infinite elastic body and subjected to an arbitrary applied normal stress field (Mode I). The most effective method of evaluating the stress intensity factor induced by an applied stress field is by using the weight function for a given cracked body. The weight function represents the SIF induced by a unit concentrated load. The only exact analytical weight function for a planar crack was obtained for a circular one. In the present research the exact analytical weight function has been derived for an elliptical crack embedded in an infinite elastic solid. The weight function for an elliptical crack was subsequently employed in the alternating method to obtain the unique SIF solution for a surface breaking semi-elliptical crack in a semi-infinite body subjected to an arbitrary applied stress field. The solutions obtained in the present work can be used in various practical applications, such as cracks in pressure vessels, welded structures and mechanical engineering components subjected to cyclic loading.