Stress measurements on D1A: a new high precision strain-scanner

T. Pirling and R. Wimpory (ILL).

The neutron strain-scanning method has become more and more important as a non-destructive method for measuring stresses in all kinds of materials with crystalline phases, such as metals, alloys, ceramics and composite materials. These materials are of industrial relevance as well as of interest for the materials scientist. As neutrons can penetrate materials up to several centimetres the method is applicable to real components as well as to small mock-ups or just samples of a material. The applications range from analysing stresses during manufacturing at different stages of production - extrusion, rolling, machining, welding, heat-treatment - and causes of failure of used components to the development of new materials and the verification of computer models. It is also a good method to calibrate other measuring techniques and determine elastic constants of materials.

The high penetrating power of neutrons means that this is the only non-destructive method that gives space-resolved information about stress deep within materials. The probe for stress is the d-spacing of the crystalline phases in the sample. Their variation must be measured with high accuracy, typically d/d = 10^-4. From the shift of the corresponding Bragg-peak one gets information about the (elastic) stress state whereas analysis of the peak shape can give information about plastic deformation.

The common set-up of a strain scanner is shown in Fig. 1 (left). It consists of a high-resolution (neutron) diffractometer with an xyz-translation table for sample positioning and a pair of slits that defines the measuring or gauge volume. The gauge volume is at a fixed position in the centre of the diffractometer and the sample is moved to scan its properties.

The size and shape of the primary beam is defined by an aperture close to the sample. A vertical slit is positioned in front of the detector and as close to the sample as possible. (Fig. 1, left). These two apertures define the gauge volume. But this is an oversimplification and it is not only the divergence of the neutron beam that leads to inaccuracies as we will see later. What are the requirements on a high-precision strain scanner?

There are two types of resolution to be considered: lateral and angular resolution. The latter means the accuracy with which the peak positions can be determined. As the peak-shifts are much smaller than the peak width this is a question of how well the peaks can be fitted. High counting rates and many measuring points in the peak are needed. The strain scanning set-up at D1A includes a highly efficient two-dimensional position-sensitive detector, developed at the ILL. With this detector high counting-rates in a reasonable time with angular resolution of better than 0.05° in 2 are possible. Measuring the true peak-shape is also important for a good fit and, of course, for the analysis of plastic deformation. This is a question of the performance of the optical components. They are also responsible for the lateral resolution because they define the gauge volume.

We have developed a computer simulation program to determine the accuracy of the experiment. The program calculates the image of the peak on the detector while scanning the sample through the gauge volume, performs a fit and plots the resultant peak parameters. This leads to some surprising results concerning the slit set-up.

The computer model of the slit set-up shows that the size of the gauge volume is not well defined. Apart from beam divergence it is not sharp edged, its size depends strongly on the peak width, the detected peak shape becomes asymmetric at interfaces and along stress gradients which leads to misinterpretation of the peak position and makes peak-shape analysis impossible. Fig. 2 shows the result of the simulation of a scan through an artificial sample that contains a stress gradient as well as an unstressed surface region to see the consequences of the surface effect itself. The surface effect occurs at interfaces and surfaces and means that the centre of gravity of the emitted radiation is shifted when the gauge volume is only partially filled. This leads to a shift of the peak position on the detector. In case of a slit system the peak also becomes asymmetric which complicates peak fitting.

The yellow and green curves show the result using a conventional slit for peak widths of 1° and 0.4° respectively: there is a strong dependence of the measured position on the peak width. As these errors depend on the sample it is impossible or at least very difficult to correct them properly. But simulations show also that there are conditions under which precise measurements can be performed with the slit set-up. These are roughly: the peak-width should be smaller than 0.3° and the distance of the secondary slit to the gauge volume should be less than 20 mm. This allows only measurements near the surface or in small samples. But it is the big advantage of the neutron method to penetrate right through thick samples. So the slit does not then meet the requirements for accuracy.

The solution to these problems is to use a radial collimator positioned between sample and detector (Fig. 1 right). The results of the simulation for this set-up are also shown in Fig. 2 (blue curves). The collimator defines the secondary component of the gauge volume as nearly ideally sharp and independent of the properties of the sample. There is no additional peak-shift near stress gradients nor any dependence on the peak width. Only the surface effect remains but it is much smaller because of the good definition of the volume, and, more importantly, it is an instrumental constant which can be corrected. In all measuring conditions, including the surface, the detector sees the true peak shape of the reflection so that peak-shape analysis is now possible.

In August 1997 the strain scanner at the D1A high-resolution powder diffractometer, was equipped with a radial collimator and a 2-dimensional position-sensitive detector. The collimator is 450 mm long and has 22 channels each with an input aperture of only 0.42 mm and a divergence of 0.19°! It was specially made by Euro-Collimators (U.K.) and shows excellent performance. The focal length of the collimator is 150 mm and it leaves enough space for many applications. By installing different slit masks at the end of the collimator - next to the detector - the gauge volume can be defined between 0.5 and 1.1 mm.

The angular resolution of the detector depends on its distance from the gauge volume and is typically 0.05° per channel.

A first experiment to verify the performance of the collimator is shown in Fig. 3. It focuses on the problem of the surface effect that results in what are called pseudo-strains when analysing data, because measured peak-shifts are caused by instrumental errors and not by the sample. To be able to measure the surface effect without additional complications we used for the measurements a rectangular shaped thin-walled aluminium container filled with Ni-powder, so that the sample has no strain gradient. The reflection measured was the (111) which occurs at 94.7° in 2 at a wavelength of 2.99 Å. Two scans were performed: one with the scattering vector perpendicular to the surface (arrow in Fig. 3) and the other with the scattering vector parallel to it. The sample was scanned perpendicular to the surface. From the fitted peak positions the strain was calculated and is plotted in Fig. 3. One can see that using the collimator the surface effect starts at less than 0.5 mm in the sample, whereas it starts already more than 1 mm below the surface for the slit geometry, which is in good agreement with the simulations.

The simulations and measurements described above show that the diffraction peak-shape is not distorted when using the collimator which is therefore important for the accurate determination of peak shapes. Fig. 4 shows an example: the results of a measurement of the 110 reflection of an iron tube, bent so as to have 10% plastic deformation in the tensile and compressed regions. The object of the experiments is to relate the microscopic behaviour as revealed in the diffraction peak-positions and widths to the macroscopic properties important to the engineer.

Data were obtained for both the radial and axial direction for which the results for the broadening were almost identical. The peak broadening is related to the plastic deformation and this relation has to be established by calibration experiments specific to the sample material being measured.

By comparing peak shapes with known deformations (tensile, compressive and a combination of the two) as well as microscopic modelling of plastic deformation, the information obtained in a diffraction peak can be interpreted with more accuracy.

Conclusion

The ILL now has available a high-precision strain scanner equipped with a radial collimator which has been shown to be essential for accurate measurements. Examples of experiments already performed are plastic strain in metals and residual stress in wear-resistant new generation coatings in synchronisers for automotive gears.