Estimation of Stress Intensity Factors for Embedded Irregular Cracks Subjected to Arbitrary Normal Stress Fields

Abstract

An integral is developed for calculating opening mode stress intensity factor at any point on the front of an irregular planar crack embedded in an infinite solid and subjected to an arbitrary normal stress field. No other solutions are available for irregular cracks, therefore the integral is first used to analyze three-dimensional regular cracks for which there are solutions. An embedded square crack is used to illustrate the integral procedure for an irregular shape. The integral is also used to explain qualitatively how irregular fatigue cracks will grow.

A precise computation of stress intensity factor on the front of a convex planar crack

“…Denoting the approximate value of the integral obtained with the jth mesh by K j we deÿne the corresponding relative error as and compute the convergence rate of the numerical approximation using the expression R j = log 2 E j E j+1 ; j= 1; : : : ; 4…”

“…Other numerical techniques have been described in Reference [3] and more recently in Reference [4]. However in References [2][3][4], a priori estimates of the error between the value of the K-integral and the numerical quadrature formula were not given.…”

“…Several values of the K-integral in the case of the ellipse have been computed numerically using a quadrature formula on a cartesian grid in Reference [2]. Other numerical techniques have been described in Reference [3] and more recently in Reference [4].…”

“…An analytic approximation of stress intensity factor for elliptic surface cracks was ÿrst given in Reference [1]. A more general expression for mode I stress intensity factor for embedded crack in an inÿnite elastic isotropic solid under normal traction distribution has been introduced as integral approximation by Ore and Burns in Reference [2].…”

Autofrettage innendruckbelasteter Bauteile

“…Eine genauere Bestimmung der K-Werte -in der Anwendung allerdings beschränkt auf die Kreuzbohrungsprobegelingt in [28] durch die Verwendung der dreidimensionalen Gewichtsfunktion von Oore und Burns [40] in der Form nach Glinka und Reinhardt [41,42]. Mit dieser können unregelmä-ßig berandete ebene Innenrisse unter reiner Modus I Belastung bewertet werden.…”