13th International Conference on Fracture June 16–21, 2013, Beijing, China -1- Fatigue Cracking Paths and Compliance Analysis in Round Bars under Tension and Bending Jesús Toribio1,*, Juan-Carlos Matos2, Beatriz González1, José Escuadra2 1 Department of Materials Engineering, University of Salamanca, E.P.S. Zamora, Spain 2 Department of Computing Engineering, University of Salamanca, E.P.S. Zamora, Spain * Corresponding author: toribio@usal.es Abstract The aim of this paper is to calculate how the surface crack front and the dimensionless compliance evolve in cracked cylindrical bars subjected to cyclic tension or bending with different initial crack geometries (crack depths and aspect ratios). To this end, a computer application (in the Java programming language) that calculates the crack front’s geometric evolution and the dimensionless compliance was made by discretizing the crack front (characterized with elliptical shape) and assuming that every point advances perpendicularly to the crack front according to the Paris law, and using a three-parameter stress intensity factor (SIF). The results show that in fatigue crack propagation, relative crack depth influences more on dimensionless compliance than the aspect ratio, because the crack front tends to converge when the crack propagates from different initial geometries, the compliance showing greater values for tension than for bending. Furthermore, during fatigue crack growth, materials with higher values of the exponent of the Paris law produce slightly greater dimensionless compliance and a better convergence between the results for straight-fronted and circular initial cracks. Keywords Numerical modelling, Cracked round bar, Fatigue crack growth, Dimensionless compliance 1. Introduction The problem of fatigue crack propagation in round bars is of great interest in fracture mechanics, applied to linear structural elements. These components, usually subjected to oscillating load, may fracture after surface fatigue crack growth, frequently with semi-elliptical flaws contained in a plane perpendicular to the loading axis. Several criteria have been stated in the past to characterize fatigue crack growth in these geometries, e.g., prediction of the 90º intersecting angle of the crack with the surface or the iso-K criterion along the crack front [1]. The most used are those based on the Paris-Erdogan law [2-7], requiring the knowledge of the dimensionless stress intensity factor (SIF), Y, along the crack front in the round cracked bar. It has been deducted by several authors following different procedures: compliance methods, finite element analysis, boundary integral equation methods, experimental techniques, etc. [1, 8-11]. Dimensionless compliance in round cracked bars under tension or bending depends on the crack geometry. If the crack is characterized by an elliptical shape, there are two factors exerting influence: the relative crack depth (crack depth divided by the diameter), which causes an increase of its value, and the aspect ratio (ratio of the crack depth to the other semiaxis of the ellipse), which causes a decrease of its value [3, 12]. Thus, there is a relation between the change in compliance during fatigue crack growth and the crack geometry evolution, depending on the specimen material, the initial crack geometry and the type of applied load [11, 13]. The aim of the present paper is the numerical modelling of crack front evolution for semielliptical surface cracks (under the hypothesis that every point at the crack front advances according to a Paris-Erdogan law), as well as analyzing how dimensionless compliance evolves during fatigue of round bars of different materials (Paris coefficient m of 2, 3 and 4), with different initial crack geometries (circular and quasi-straight, both crack shapes linked with initial relative depth (a/D)0 of 0.1, 0.3 and 0.5) and applying tensile load or bending moment.
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