Finite element modelling and analysis of crack shape evolution in mode-I fatigue Middle Cracked Tension specimens

Abstract

A numerical procedure was employed to study the shape evolution of fatigue cracks in Middle Cracked Tension specimens. This iterative procedure consists of a 3D finite element analysis to obtain the displacement field in the cracked body, calculation of stress intensity factors along crack front and definition of local crack advances considering the Paris law. Numerical predictions were compared with experimental crack shapes with a good agreement. The evolution of crack shape was analysed for different propagation conditions considering robust dependent parameters. Two main propagation stages were identified: an initial transient stage highly dependent on initial crack shape and a stable stage where the crack follows preferred paths. Mathematical models were proposed for transient and stable stages consisting of exponential and polynomial functions, respectively. The transition between both stages was defined considering two criteria: the rate of shape variation and the distance to stable shape. Finally, the crack shape change was linked with the distribution of stress intensity factor along crack front.

Determination of Paris law constants with a reverse engineering technique

“…These coordinates were directly used to define the initial crack on the FEM model. All numerical variables were fixed taking into consideration previous optimization studies [7,8]. A set of independent numerical propagations was carried out, with values of m between 1 and 5, with constant increments of 0.25.…”

“…Two main groups of parameters can be distinguished: global parameters which quantify the shape of all crack and local parameters which study the behaviour of few specific nodes [7,8]. Herein, it was used a global parameter (Z) given by the ratio A 1 /A 2 , where A 1 and A 2 are, respectively, the light and dark areas shown in Fig.…”

“…Numerical errors must be minimized to obtain feasible predictions; therefore the parameters affecting the accuracy must be identified and optimized. A detailed identification and optimization of these parameters can be found elsewhere [7,8].…”

“…An exhaustive analysis of both types of variables lies beyond the scope of our present study and it would be extensive. Thus, critical variables were identified considering author's experience [7,8]: x i and y i coordinates, Poisson's ratio and number of fatigue cycles. In relation to the numerical parameters, following similar criterion, the most important are: radial size of crack front elements L 1 , K values and the crack increment Da.…”

Stress intensity factor analysis of through thickness effects

“…Lee and Lee [20] investigated fatigue crack growth in single side repairs aluminium plate. Branco et al [21] used these techniques to evaluate the curvature of the crack front. They found that and stable crack curvature was achieved independently from the starting shape.…”