Stability revisited for a straight-fronted edge crack in a three-point loaded round bend bar

Abstract

Stable crack extension is difficult to realize for very brittle materials in many loading geometries for which the crack extends into an increasing stress intensity field. Stable crack extension is necessary for fracture experiments that need to be well controlled, such as in the determination of: fracture toughness, R-curve data and fatigue crack growth data. The prediction of stability is necessary in the guidance of such experiments. Theoretical calculation of the stability parameter includes: the knowledge of specimen compliance, the second derivative and the squaring of the first derivative of compliance with respect to the crack area, see (1). If the compliance is not accurately known, then it must be attained through the integral of strain energy (G) and its squared relationship with stress intensity (K~) and Young's modulus of elasticity (E), [1]. Therefore, any slight change in K~ as a function of crack length can cause considerable variation in compliance and the resulting calculation of stability. Because compliance was not accurately known, this mathematical process was applied to the straight-fronted edge crack in a three-point loaded round bend bar, [2][3][4]. In these works the stress intensity factors (SIF) presented by [5] were employed to obtain stability factors for the round bar configuration. Reference [5] was the best available at that time; the SIF's were estimated for a three-point loaded beam of several span-to-diameter ratios (S/D) based on the experimental work by [6] and the constant moment beam results using a finite element analysis by Daoud and Cartwright [7]. Therefore, the stability results given in [2-4] await further improvement either by employing a more accurate description of K~ or a direct determination of compliance. Now the latter case can be realized for the straight-fronted edge crack in a three-point loaded round bend bar by not having to utilize the integral of strain energy release rate to obtain compliance, but by directly employing the most accurate to date wide range compliance results of [8]. This is the path taken for the round beam, shown in Fig. 1, and in the approach that follows.The basis for general stability analyses are well presented elsewhere, see [9][10][11]. Therefore, these analyses are not repeated here. However, some comments are appropriate: The general stability equation used here, which was taken from [10], presumes that an idealized testing system is utilized, which infers that constant crosshead displacement is employed, and that rigid body motion occurs between the crosshead of the testing machine and the point of load application to the specimen; i.e., the deflection of the load cell is ignored. Most experimenters choose 'stroke control' during testing because it is a convenient option when using a closed loop hydraulic testing machine. Such a testing system is designed so that a transducer senses the displacement of the specimen, which is then fed Int Journ of Fracture 62 (1993)