Measurement of residual stress in thick section composite laminates using the deep-hole method
Introduction
Carbon fibre composites are used throughout the airframe of civil and military aircraft but recently very thick section laminates, perhaps up to 30 mm in thickness, have been proposed for the wing skins of large aircraft. One concern with the application of such thick section components is that substantial residual stresses may be introduced during manufacture. Such residual stresses could be detrimental to the integrity of the structure because the total stress, that is the stress resulting from the applied load added to the residual stress, may be higher than is allowed for in design. Clearly, a reliable method for measuring such stresses would be of benefit. This paper describes the application of the deep-hole technique to measure the residual stress in a 22 mm thick carbon/epoxy composite laminate. The deep-hole technique is a well-established residual stress measurement method for metallic materials and is particularly suitable for large, thick section components.
In the deep-hole method, a hole is first drilled through the thickness of the component. The diameter of the hole is measured accurately and then a core of material around the hole is trepanned out, relaxing the residual stresses in the core. The diameter of the hole is re-measured allowing finally the residual stresses to be calculated from the change in diameter of the hole. The deep-hole method is classified as a semi-destructive method of residual stress measurement since although a hole is left in the component, the diameter of the hole can be quite small and could coincide with a hole that needs to be machined subsequently.
Initial development of the deep-hole method was carried out by Zhandanov and Gonchar [1], Beaney [2], and Jesensky and Vargova [3]. Zhadanov and Gonchar used the deep-hole method to measure residual stresses in steel welds. They drilled 8 mm diameter holes and trepanned out a 40 mm diameter core. In their method, the trepanning was carried out incrementally. Beaney used a 3 mm gun-drill and an electro-chemical machining process to trepan the core. He measured the diameter of the hole using two strain gauged beams that were drawn along the sides of the hole. His methodology was later improved by Procter and Beaney [4] with the introduction of non-contacting capacitance gauges to measure the hole diameter. Jesensky and Vargova [3] again measured residual stresses in steel welds but used strain gauges attached to the sides of the hole to measure the strain relaxation following trepanning.
More recent improvements to the deep-hole method have been made by Smith and his co-workers [5], [6], [7], [8], [9], [10], [11], [12]. They have followed an approach of gun-drilling a hole of 3 mm nominal diameter and measuring the change in diameter of the hole using an air probe. The air probe works by calculating the clearance between the gauge and the hole from the pressure required to blow air from the gauge into the gap. Trepanning the core is carried out using an electro-discharge machining (EDM) operation.
The problem of measuring the residual stress in composite materials has attracted previous attention, although many techniques that have been attempted are not ideally suited to thick laminates. Sicot et al. [13] describe an application of the incremental hole-drilling method to measure residual stress in a unidirectional and a carbon/epoxy laminate with thicknesses of the order of 1 mm. In the hole-drilling method, a strain gauge rosette is bonded to the surface of the laminate and then a hole drilled progressively deeper perpendicular to the surface through the centre of the rosette. The residual stress is calculated from the strain changes measured by the rosette. Sicot et al. [13] measured tensile and compressive residual stresses in the fibre direction and transverse direction up to a magnitude of about 100 MPa. Residual stresses in the laminate were much higher than in the unidirectional laminate. The method is unsuitable for thick laminates because the strain change measured by the rosette becomes smaller and smaller as the depth of the hole increases.
An interesting application of Raman microscopy was made by Filiou and Galiotis [14] to measure the residual strain in individual fibres in carbon-fibre thermoplastic composite. They measured compressive residual fibre strains of the order . This work is, however, concerned with what Barnes and Byerly [15] term as ‘microstresses’: microscopic residual stress arising from the difference in thermal properties of the fibre and resin. Here it is rather the ‘macrostresses’ that are of concern, the macroscopic residual stresses arising from thermal differences between the plies making up a laminate.
Bragg grating fibre-optic sensors have been embedded in composite laminates as a method to measure longitudinal strain. Guemes and Menéndez [16] presented the result of attempts to measure residual stress using such sensors. They embedded two fibre Bragg gratings at right angles to each other in a 7.0 mm thick carbon/epoxy quasi-isotropic laminate. A hole was then drilled close to the point of intersection of the fibres, but so that fibres themselves were not damaged. Their results showed that stresses of the order of 50 MPa were released by the hole drilling.
Cowley and Beaumont [17] describe a technique to measure the residual stress in near surface plies of symmetric laminates. Their method involves machining away the near surface plies using a diamond-coated end mill and then measuring the resulting curvature of the remaining un-symmetric laminate. They present equations that calculate the residual stress that existed in the near surface plies from the measured curvature. Beam type specimens were used, 150 mm long by 25 mm wide and of thicknesses less than 1 mm. The orientation of the beam meant that the residual stresses transverse to the fibre direction of the near surface plies were released. Tensile residual stresses of the order 25 MPa were measured. Ersoy and Vardar [18] also used a layer removal technique to measure residual stress, except that they removed layers by forcing a knife blade between plies. They compare the results of the layer removal technique with an alternative method involving slitting plies rather than machining them away completely. For their work they used a specimen cured from 40 plies of APC-2 thermoplastic pre-preg with a layup of . They measured residual stresses of the order of 60 MPa.
A moiré technique has been used by Chai et al. [19] to determine the magnitude of residual stresses by measuring the distortion of fringe patterns on the surface of a laminate after a perpendicular hole is drilled into the laminate. This technique is therefore similar to the incremental hole drilling-method of Sicot et al. [13] except that a moiré method is used to measure the release of strain rather than a strain gauge. The same group have also measured interlaminar strain again using a moiré method [20].
X-ray diffraction is a standard method to measure residual stress in metals. Fenn, Jones and Wells [21] describe a variation of the method which may allow residual stress to be measured in a composite. Essentially, they use nickel particles introduced into the resin and then carry out X-ray diffraction on these particles. Results are provided for nickel particles within cured resin rather than a fibre composite.
In addition to experimental work to measure the residual stress in composites, a number of attempts have been made to predict the residual stress from theoretical models of the manufacturing process. Bogetti and Gillespie [22] used a method based on laminate theory to predict residual stresses arising from shrinkage of the resin during cure and mismatch of thermal expansion coefficients between plies. More recent work (Jounston, Vaziri and Poursartip [23]) has used the finite element method to predict residual stress. Such analyses are not straightforward because the thermal and mechanical properties of the resin change as the cure process progresses, demanding an incremental approach.
The application of the deep-hole method to measure the residual stresses in a 22 mm thick carbon fibre-epoxy composite laminate will now be described. First, the analytical basis of the deep-hole method is revised and then methods developed to allow measurements of residual stresses in orthotropic materials. A proving experiment is described to demonstrate the correct functioning of the method. Finally, the measured residual stresses in the 22 mm laminate are presented.
Section snippets
Deep-hole method for isotropic materials
For the case of an isotropic material, the calculation of the residual stress from the distortion of the hole is based on the solution presented in Timoshenko and Goodier [24] for the radial and tangential displacements around a hole in an infinite plate subjected to a far-field applied stress under plane stress conditions (Fig. 1).where is the far-field applied stress, a is the radius of the hole, E is Young's
Extension to orthotropic materials
Eq. (4) relating far-field direct stresses and shear stress for an isotropic material is an exact, closed form relationship. No such equation has been found for an orthotropic material, although Lekhnitskii [26] presents an approximation for the distortion of a circular hole in an orthotropic material when far-field stress is applied in the principle material direction. In Lekhnitskii's analysis the distortion of the hole is characterised by the change in diameter in the loading direction and
Experimental validation
In Section 5, the deep-hole method will be used to measure the residual stress in a thick composite laminate. Before this, a proving experiment will be described that will demonstrate the correct functioning of the method. The experiment is conducted on a rectangular specimen of uni-directional carbon fibre epoxy composite. A central hole is drilled through the specimen and the diameter of the hole measured using the air probe. The specimen is then loaded in a test machine at a high enough load
Experimental measurements
The methods of measuring residual stress developed above will now be applied to the case of a 22 mm thick by 200 mm square carbon fibre epoxy composite laminate. Such thicknesses of composite are being considered for the wing skins and other substantial structural elements of large civil and military aircraft.
The composite laminate was manufactured using a resin film infusion process. Carbon fibre non-crimped fabric (NCF) plies were interspersed with resin film and cured in an auto-clave to
Discussion
No attempt has been made to compare the measurements of residual stress in this work with predictions of a numerical model of the manufacturing process. Such predictions are complex and rely on the knowledge of many experimentally measured parameters. Nevertheless, a simple prediction of the magnitude of residual stress can be made by assuming a zero coefficient of thermal expansion in the fibre direction and making the simplification that the strain in the fibre direction is zero since the
Conclusions
The deep-hole method has become a standard technique for the measurement of residual stress in isotropic materials. The method is particularly suited to thick components. The work described here is an extension to the method to allow the measurement of residual stress in orthotropic materials such as thick laminated composite components. The deep-hole method relies in its formulation on a calculation of the distortion of a hole in a plate subject to remote loading. Suitable closed-form
Acknowledgements
We are grateful to Airbus UK Ltd. for the provision of the carbon fibre non-crimped fabric used in this work. Mr. C.E.P. Breen is sponsored by the Needham Cooper Trust. The measurements on the uni-directional tensile specimen were carried out by Ms. J.E. Kingsnorth and Ms. M. Wilson. The diamond encrusted hole saw was provided by Polymeric Composites.
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