Stress intensity factors for V-notched strip under tension or in-plane bending

Abstract

The singular stress field around a sharp notch tip is expressed as a sum of two independent fields: a symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaigdaaeqaaaaaaaa!3CC3!\[1/r^{1 - \lambda _1 } \]and a skew-symmetric field with a stress singularity % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaGymaiaac+% cacaWGYbWaaWbaaSqabeaacaaIXaGaeyOeI0Iaeq4UdW2aaSbaaWqa% aiaaikdaaeqaaaaaaaa!3CC4!\[1/r^{1 - \lambda _2 } \]. The intensities of the symmetric and skew-symmetric singular stress fields are defined in terms of constants K _I and K _II, respectively. In this study, a plane problem of a strip with single or double edge notches under tension or in-plane bending is considered. The bisector of the notch may be inclined to the edge, so that the two singular stress fields with different singularities may be created simultaneously at the notch tip. The body force method is used to calculate the stress intensity factors K _I and K _II. In numerical analysis, basic density functions of the body forces are introduced to characterize the stress singularity at the notch tip. The advantages of this technique are the high accuracy of results, due to the smoothness of the unknown weight functions, and the presence of the direct relation between the values of K _I and K _II and the values of unknown weight functions. The stress intensity factors are systematically calculated for the various geometrical conditions.