C O M P E T I T I O N Young Stress Analyst Final Young Stress Analyst Poster Competition Investigation of Thickness Effects in Plasticity‐induced Fatigue Crack Closure Motivation and General Description of the Work

The effect of the specimen (or component) thickness has been shown to have a significant effect on closure behaviour and this seems to be related to the relative size of the plastic zone. Real cracks are inherently three-dimensional; plane stress-like behaviour is found close to the region where the crack front intersects the free surface, whereas most of the crack front will experience something close to plane strain. The aim of the present work is to investigate the influence of specimen thickness on closure behaviour (both close to and remote from the surface) and on fatigue crack propagation. Results from a simple experimental program, which consists of fatigue testing CT specimens with different thicknesses are presented. Fatigue crack propagation is measured optically; crack closure is assessed using traditional compliance techniques (clip gauge and back face strain gauge) and Digital Image Correlation methods. Experimental results are compared with two and three-dimensional finite element simulations of plasticity-induced fatigue crack closure. The implications of thickness effects for predicting the propagation of three-dimensional fatigue cracks are discussed. MOTIVATION AND GENERAL DESCRIPTION OF THE WORK The prediction of the fatigue life of engineering components and structures is of primary concern for designers in a wide range of applications. Major advances in this area have, of course, been made over the last 50 years. However, major challenges still remain. In particular, it can often be difficult to predict the life of structure or component subject to a practical loading cycle, starting from available materials data, which is very often for the case of uniaxial loading at constant amplitude. Elber's discovery of fatigue crack closure, nearly 40 years ago, held out the prospect of significant advances in this area. Closure can be difficult to measure experimentally, and different measurement techniques can give apparently different results. Modelling of crack closure is computationally demanding and models frequently have to be simplified with respect to the experimental conditions. Focusing more specifically on plasticity induced closure, which is thought to be the most significant effect over the majority of the propagation life, some useful progress might be made by combining high quality experimental measurements with detailed finite element modelling. A particularly promising technique is that of image correlation. This offers the advantages of sophisticated techniques such as moiré interferometry without the requirement for complex specimen preparation and specialised optical equipment. In the current work the application of full field digital image correlation to the measurement of plasticity induced crack closure will be described. A range of experiments are undertaken, using different thickness compact tension specimens. These enable an evaluation of crack closure, which is often thought to be a surface phenomenon, in determining the crack propagation rate. The experimental results will be compared to three-dimensional finite element models of the experimental configuration. The material chosen for the investigation was the aluminium alloy 6082 T6, which is widely used in the aerospace industry. Compact tension specimens with three different specimen thicknesses, t, of 3, 10, and 25 mm were fatigue tested. The main pieces of instrumentation employed were a load cell, a ‘back face’ strain gauge, a crack mouth opening displacement (CMOD) and a ‘Questar’ QM 1 long distance microscope, mounted on a translational stage with digital readout. This could be used for observing the specimen, both to measure the crack growth rate optically and to capture sequences of images during load cycles, which could be used for Digital Image Correlation (DIC). In order to restrict the amount of data processing required, displacement measurements were taken at five locations along the crack, corresponding to different distances, Li, from the crack tip (see Figure 1a). Figure 1 b) shows a typical variation of this quantity with frame number (i.e. time). Also shown on this plot is the variation of load with time. It can be seen that whilst the load varies sinusoidally, the relative displacement does not. The flat region at the bottom of the displacement cycle corresponds to crack closure, where the relative displacement is constant even though the load is varying. a) b) Figure 1 – Digital Image Correlation: a) Points on surface of a fatigue crack; b) Relative displacement between two points and load 3 load cycles. As well as digital image correlation, closure was also assessed using conventional compliance approaches, a back face strain gauge and a crack mouth opening displacement gauge. Figures 2 a) and b) show crack opening load data obtained for constant amplitude loading in specimens with different thicknesses. It will be seen that the opening load obtained with the compliance gauges are very similar to those found using the digital image correlation approach for thin specimens (t=3mm). A different picture emerges when data from the thick (25 mm) specimens is considered. Figure 2 – Opening stresses: a) Digital image correlation; b) Back face strain gauge. These results therefore suggest that surface closure levels are almost independent of specimen thickness, whereas measurements obtained by the compliance technique, which effectively average over the thickness, do vary. This is probably because relatively high levels of closure exist at the surface, with lower levels close to the centre of the specimen. The lower proportion of the specimen affected by surface closure leads to lower overall closure levels in the thick specimens, as measured by the compliance technique. A key practical question is which of these closure measurements is more appropriate for determining crack growth rate. Figures 3 a) and b) show the rate of crack propagation as a function of effective stress intensity factor range, ΔKeff, calculated using DIC and back face strain gauge. These results suggest that an average closure measurement, such as that obtained by compliance technique, may be more appropriate for determining crack growth rate and a pure surface measurement, such as that obtained by DIC. Figure 3 – Fatigue crack growth rate for CT specimens with different thicknesses: a) FCG rate as a function of ΔKeff (DIC); b) FCG rate as a function of ΔKeff (Back face strain gauge). a) b)