A new imaging technique for measuring the surface strains applied to dentine
Introduction
Experimental methods of stress/strain analysis are fundamental to the design and engineering of structures. The principal methods of stress investigation are the use of electronic strain gauge, brittle lacquer, and photoelastic techniques [1]. Strain methods using surface grids and lines have been used for a long time to study displacements in structures but the limitation has been the low level of accuracy compared to other methods [2]. If the grid is not measured before loading it is assumed to have a certain value. If measurements are made both before and after loading then the line spacing is not critical and even random scratch lines can be used as grid lines. For a complete strain analysis at a point in a two-dimensional (2D) problem, intervals in three directions are needed. The rosette equations can then be applied to obtain the principal stresses and directions [2]. Interferometric methods have been used to measure the small displacement of the cusps of teeth under an applied load [3]. However, measurements to investigate the strain behaviour of hard tissues such as enamel, dentine and bone are frequently undertaken by the attachment of a strain gauge to the sample surface. The strain due to an applied load is then registered as a change in potential, usually in the microvolt range, across the changing resistance of the gauge. The size of the strain gauge and the surface area of the sample where the strain gauge is to be attached limit this strain measurement technique. If strain is to be measured in a very small sample, difficulty arises with attaching a small strain gauge to make sufficiently accurate measurements.
The accuracy of the strain gauge is partly a function of its inherent size and how well adhered it is to the surface of specimens. Other sources of errors arise due to surface preparation, moisture contamination, thickness of the adhesive and its permeability into the sample, the type of backing material supporting the gauge and its thickness. The sample's strain value, calculated from the calibrated conversion of microvolts to micro-strain values, is then recorded only as the component of strain in the direction of the strain gauge unless multiple strain gauges (“rosette”) are used.
Another commonly used technique to measure strain on the surface of materials is the optical photoelastic method. Photoelastic studies have employed the construction of photoelastic models using 2D, 3D and “3D-frozen stress” techniques. Observations and measurements are then made with a polariscope to determine strain within the model from retained stress [4], [5].
Alternatively strain can be measured by an elaborate preparation of the specimen's surface with reflective materials and a uniform coating of a stress-free birefringent polymer. The strain fields formed on the specimen surface can readily be observed as colour fringes due to birefringent changes in the polymer coating the sample. This may be difficult if the sample is small relative to the thickness of the coating which is required to show small birefringent changes [6]. Further quantitative and directional analysis of these fringes can be undertaken with a null balance compensator. A good understanding of polarisation optics in required and errors such as the pre-stresses in the polymer coating and its non-uniformity in thickness must be accounted for.
The optical imaging technique reported in the present paper calculates the strain due to a load on the sample from the deformation of the grid pattern imprinted on the sample. Static or dynamic loading conditions can be used to capture a sequence of images for later analysis. The before and after images require sharpness, clarity and permanence of the grid markings [2].
Several applications are presented and some preliminary data are qualitatively and quantitatively analysed.
Section snippets
Dentine compression tests
Intact caries-free human permanent teeth were obtained from patients undergoing tooth extraction for unrelated reasons (orthodontics, oral surgery). The teeth were cleaned and stored at 4°C in sterile buffered saline with 0.05% sodium azide. The teeth were prepared and tested at room temperature within approximately four months.
Sample preparation
A longitudinal section 1 mm thick or greater was cut through the middle of the pulp chamber, using a Leitz water-cooled sawing microtome. The plane of the section ensured
Dentine compression tests
The stress and strain data gathered from 43 rectangular dentine blocks were similar. Graphs were plotted to determine the elastic modulus from the linear region of the stress strain plot determined from the load range 50–150 N with corresponding strains derived from grid measurements. The mean and standard deviation value for all samples tested was The value of elastic modulus for 0, 45 and 90° were 10.7±2.4, 7.7±0.7 and , respectively. There was no significant difference
Discussion
The new method reported allows for the determination of the precise strain in any direction by directly measuring the deformation of the grid line pattern silhouetted onto the surface of the sample. Different grid mesh sizes were tried with 300 mesh being found to be the most suitable for the particular magnification and the dimensions of the dentine samples being tested. Smaller (400 mesh) or larger (200 mesh) spacing between grid lines may be used or a different template pattern depending on
Conclusion
These preliminary compression tests show the elastic modulus of samples of dentine loaded parallel and perpendicular to the tubule direction to be similar to each other and to previously reported values in the literature [10]. However, both compressive and tensile ultimate strength values show anisotropic behaviour. With the further development of this imaging technique to greater precision, it is anticipated that subtle variation in the material properties of dentine, due for example to
Acknowledgements
We would like to thank Asso. Prof. J.G. Clement for the use of the hard tissue laboratory facilities, Messrs: E. Bernard and P.M. Barnes for their technical assistance, and Dr H Bione for her experimental work. This work was supported by the NH&MRC Australia grant # 34788
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