Thermoelastic stress analysis with SPATE 8000

TWI Bulletin, May/June 1988

The importance and value of experimental stress analysis are well known and accepted by designers and engineers, and there are many techniques available to provide this function, for example photoelastic and electrical resistance strain gauge methods. The appearance of a completely new technique on the engineering scene is a relatively rare event, but the introduction of SPATE 8000 to the commercial market five years ago was one such event.

Principle of operation

SPATE 8000 makes use of a physical property of materials known as the 'thermoelastic effect' in determination of stress. This phenomenon occurs as a change of temperature of a body subjected to adiabatic elastic deformation. It was first observed in vibrating wires by Weber ^[1] in 1830, and in 1853 the relevant theory was published by Kelvin. ^[2] This theory predicted that a linear relationship existed between change in the sum of the principal stresses and the change in temperature. Because the temperature changes involved were very small, of the order of 0.001°C, it was not until 1915 that the accuracy of Kelvin's theory was demonstrated, by Compton and Webster ^[3] using highly sensitive contacting resistance thermometers. By 1967, infrared radiometric technology was sufficiently advanced to allow the thermoelastic effect to be observed by non-contacting means. ^[4] It was not until some years later that advances in electro-optical and signal processing techniques permitted the full development of an infrared radiometric system with sensitivity and resolution capabilities required for quantitative assessment of stress in engineering structures and components. These developments eventually led to the production of SPATE 8000, the first commercially available stress analysis system using the thermoelastic effect.

where
Δ T = change in temperature
Km = thermoelastic constant for the material question
T = absolute temperature
σ = change in the sum of principal stresses.

The thermoelastic constant can be expressed in terms of material properties as follows:

α = coefficient of linear thermal expansion
ρ = density
C = specific heat at constant stress

Most common engineering materials experience a decrease in temperature when loaded in tension, and an increase in temperature when loaded in compression. Typical values of Km for common engineering materials are:

Epoxy resin 6.2 x 10 ^-11 Pa ^-1

The practical consequences of the above, in terms of its usefulness to the experimental stress analyst, can be more simply expressed. If an engineering structure or component can be subjected to a cyclic load, then every point on the surface of the structure will respond with a thermoelastically induced cyclic temperature change. If the loading frequency is sufficiently high to satisfy adiabatic conditions, then the amplitude of the induced cyclic temperature variation at any point is directly proportional to the amplitude of the sum of the principal stresses (created by the cyclic load) at that point, within the elastic limit. Therefore, a system that can accurately measure this temperature fluctuation, and isolate it from any other extraneous temperature variations, is capable of determining the stress state at any point on the surface of the structure.

The SPATE system

The heart of the SPATE system is the infrared radiometric detector, or scan head ( Fig.1). It is this part of the system that measures the thermoelastic temperature fluctuations. The detector is a highly sensitive lead/tin telluride cell, approximately 0.1mm in width, cooled by liquid nitrogen and operating over the 8.14µm waveband. Incoming radiation (from the specimen) is focused onto the detector through a germanium lens. The point of observation on the specimen is selected by operation of a pair of servo-controlled surface coated mirrors contained within the scan head. A visual light channel also operates through the mirrors, enabling the operator to see the point on the specimen sampled by the detector by looking through a built-in eyepiece. Alternatively a fibreoptic white light source can be connected to the eyepiece, projecting a spot of light onto the surface of the specimen corresponding to the sample point.

The remainder of the system, housed as a single unit, is shown schematically in component form in Fig.2. Operation of the system is controlled through the keyboard, with some operations being also remotely controllable by means of a separate handset connected directly to the scan head. The computer controls the operation of the scan head and post-processing of collected data, which can be displayed in various forms on the colour monitor. The ink jet printer can produce hard copy of data displayed on the colour monitor. Data can be stored separately on floppy disk.

In use, the computer controls the operation of the scan head, according to the requirements of the user. Basically, this involves sampling points on the surface of the cyclically loaded specimen, in one of three basic modes:

1. Single point scan;
2. Line scan (a row of points along a specified line);
3. Frame scan (a block of points within a specified rectangular area - essentially a 'stack' of line scans).

The operator also has control of the following parameters:

1. The number of points sampled along a line and within a frame.
2. The overall size of the line or frame.
3. The size of each sample point (effectively a circle of variable diameter).
4. The spacing between individual sample points.
5. The sampling rate.

The remaining major item in the system is the correlator. Into the correlator must be fed a reference signal, corresponding in phase and frequency to the loading waveform. This reference signal may be taken from a transducer such as a strain gauge bonded directly to the specimen, or from the load cell or function generator of the test machine. The correlator then filters out any extraneous temperature fluctuations detected by the scan head but not caused by the thermoelastic response of the specimen to the input load. It also serves the function of optimising the incoming data signal, such that resolution and accuracy are maximised.

The signal received from each point scanned is simultaneously digitised, stored and displayed on the colour monitor. For single point measurements, the output is displayed numerically in machine units, i.e. uncalibrated data. (Calibration into engineering units is discussed later). For line scans, the data are presented as a graph of machine units versus distance along the line. For frame scans, the data are presented as a two dimensional 16 colour stress contour map, again in machine units.

The more practical considerations concerning the use of SPATE are highlighted in the following example of its use.

Evaluation of stress distribution in a tubular T joint

The subject of this evaluation is a tubular T joint loaded in in-plane bending. The specimen and loading arrangement are shown schematically in Fig.3. The area of interest is the weld itself, and the chord and brace material immediately adjacent to it. Due to the symmetry of the test arrangement, only one quarter of the complete weld needs to be examined.

The SPATE equipment is assembled near the test rig and the component parts wired together as shown in Fig.4. The scan head is in the left foreground, mounted on an adjustable tripod, and pointed at the area of interest on the specimen. The remaining hardware is in the right foreground. The colour monitor sits above the keyboard on the right, whilst on the left are stacked from the base up; the computer, floppy disk unit, correlator and printer. This assembly is connected to the scan head by a pair of multiway cables, visible in the figure.

The specimen is then prepared for testing. With SPATE, surface preparation is minimal. Loose rust and scale should be removed by wire brushing from steel specimens. In theory, that is the minimum required preparation, since SPATE will work on reasonably clean bare or even painted surfaces. However, in practice the specimen is normally lightly sprayed with matt black paint. This serves two main purposes. Firstly, it provides a surface with uniform high thermal emissivity. High emissivity gives maximum resolution of measurement, and uniform emissivity ensures that the signal strength is constantly proportional to stress over the whole painted surface. The SPATE sensitivity when used with a high emissivity coating is as high as 1.0 N/mm ² in steel and 0.4 N/mm ² in aluminium. Secondly, it maximises the tolerance of the detector to oblique angles of view. With a painted surface, the angle of incidence of the line of sight of the detector can deviate as much as 50% from normal before signal attenuation will be seen.

In situations where the line of sight to a point of interest is directly obscured, the SPATE system can be used with mirrors to achieve the desired access and angle of viewing incidence. Viewing the inside wall of a tube from one end is an example. Also, mirrors can be used to accommodate lateral movement in the specimen, so that the scan head sees a stationary image.

A close up view of the area to be examined is shown in Fig.5. The specimen has been wire brushed and painted matt black. The paint coating thickness is not critical, except at very high test frequencies. Also shown is the border of the rectangular area to be examined. The wires visible in the bottom left hand corner terminate at a three element strain gauge rosette bonded onto the specimen in the field of view. This is for calibration, as will be explained later. Specimen preparation is now complete.

The next step is to position the scan head. A number of factors influence the exact positioning. The distance from the scan head to the specimen determines the maximum field of view, the depth of field and the spot size. The field of view is 25° x 25°. The depth of field is approximately 175mm at 2m range. At the minimum stand off distance of 250mm (the limit of focus) the size of each single measurement point is a circle of diameter 0.5mm. Ideally, the scan head will be positioned as close to the specimen as physical limitations allow, while ensuring that sufficient field of view and depth of field are available. This will provide the maximum resolution of spot size. The scan head should then be suitably angled so that the line of sight is predominantly normal to the specimen surface. Having positioned the scan head, the average stand off distance is measured and the focus adjusted accordingly. The detector can then be filled with liquid nitrogen.

The next stage is to adjust the correlator to maximum gain. At this stage, the cyclic load must be applied to the specimen, and a reference signal fed to the correlator. The cyclic load must be of constant amplitude. The SPATE system is not greatly sensitive to waveform, but frequency is important. The system can accommodate test frequencies in the range 0.5-20kHz, but in practice the lower limit is governed by the requirement for adiabatic conditions. At low frequencies, non-adiabatic local heat flow can attenuate the measured signal from high stress regions, especially when testing materials with high thermal conductivity and/or high stress gradients. In practice, this means that the minimum test frequency should be limited to about 2Hz for steels and 4Hz for aluminium alloys, for example. Once the correlator has been set, data collection can begin. The whole procedure up to this stage will typically take 20-30 minutes.

The next step is to define the scan parameters. In this case an area, defined in Fig.5, is to be scanned. The limits of the area are entered into the computer by manually driving the visible light beam to the top left and bottom right corners of the frame. Points of interest within the frame can be marked in a similar fashion. The remaining scan parameters to set are the resolution and scanning speed. The resolution determines the number of points sampled within the frame, and the scanning speed determines how many load cycles are sampled at each point. Both these factors and the test frequency determine how long the full scan will take.

In this case, a high resolution is selected, giving 91 x 125 = 11 375 data points within the frame. Each point must be sampled for a minimum of one complete cycle, but sampling for two or more cycles per point improves the signal to noise ratio. Three cycles per point are selected. The test frequency is 3Hz, therefore the complete scan will require just over 34 000 cycles, which will take just over 3 hours. The computer obligingly tells you this. This example illustrates the relationship between data accumulated, test frequency, and time taken. Clearly, if the test frequency could be significantly increased, the total scanning time could be reduced (the maximum scanning speed of the system is 25 points/sec). Similarly, scanning for only one or two cycles per point, or reducing the resolution, i.e. number of data points, would also speed up the process. The maximum system resolution is 255 x 255 points.

Scanning is then initiated, and a sixteen colour stress contour map is built up on the colour monitor. The completed scan is illustrated in Fig.6, and can be compared with its visual equivalent in Fig.5. There are a number of colour scales to choose from, and the scaling factor is infinitely adjustable by the operator. In Fig.6 can be seen marker crosses established before scanning started. These identify the positions of the two weld toes and the strain gauge rosette. It can be seen that the weld toes coincide with the regions of maximum stress (red colours), the weld toe on the chord being the more highly stressed of the two. The purple colour indicates regions of negative stress. This results when the measured thermal signal is in antiphase with the reference signal.

Having produced such a visually attractive picture, the engineer then wants to extract some useful information from it. The first step is often calibration of the data into engineering units of stress. The scan shown in Fig.6 has already been calibrated.

Calibration

Three methods of calibration of SPATE data are available, identified as:

1. Theoretical
2. Indirect known stress
3. Direct known stress.

For theoretical calibration, we return to equations [1] and [2]. These can be combined as:

D = SPATE calibration factor, unique to each system
e = surface emissivity
V = measured SPATE signal

thus

The constant of proportionality in brackets in equation [4] consists only of 'known' properties. If these parameters can be accurately established, the calibration can be completed. In practice, this is not usually the preferred method of calibration.

The indirect known stress method is quasi experimental calibration procedure. A sample of test material with the same surface condition as the test specimen is subjected to a SPATE scan. The sample is loaded in simple bending or tension, such that the true stress state can easily be calculated. The SPATE output can then be calibrated directly using the calculated stress value. This method is rather cumbersome.

The direct known stress method involves the use of a strain gauge rosette bonded to the specimen under test, in the field of view of the SPATE system. The measured strain range is recorded during testing, and the relevant stress parameter calculated. This is then used to calibrate the scan by comparison with the SPATE data in the vicinity of the strain gauge, because the SPATE output from the gauge itself will not be representative of the output from the specimen surface. This is the preferred method of calibration at The Welding Institute, and arguably the most reliable. However, accuracy of this method is dependent on the siting of the strain gauge. For best results it needs to be positioned in a region of high stress but low stress gradient.

One important aspect of the SPATE system that has been glossed over so far is the significance of the stress parameter measured. This parameter is the principal stress sum. In a uniaxial stress field, when the minimum principal stress is zero, the SPATE system measures the maximum principal stress. However, in biaxial stress fields, if both principal stresses are positive, the SPATE output is greater than the maximum principal stress. If principal stresses are of opposite sign the SPATE output is less than the maximum principal stress. In pure shear, when the principal stresses are equal and opposite, SPATE output is zero.

At first this seems to be a major drawback, although in practice it does not create a great amount of difficulty, provided engineering judgement is used in the assessment of data. Often the relative magnitudes of the principal stresses can be estimated with some accuracy from a basic understanding of the specimen geometry and loading. For more accurate assessment, a few suitably positioned strain gauges can provide the necessary information. Also, a numerical method for separating the principal stress sum has been postulated, and The Welding Institute is currently developing a computer program to investigate this.

Data manipulation

Having produced a calibrated frame scan such as that in Fig.6, the data can be further analysed at leisure. Any point on the stress contour map can be identified and its numerical value displayed. If the scan unit has not been moved, the visual light channel can identify the same point on the specimen itself. A more useful facility is the development of a stress profile. Any two points on the frame scan can be identified, and the computer will sample all data points lying beneath a straight line between the points, and plot them graphically on the screen. For example, a vertical line scan extracted from the frame scan in Fig.6, and passing through the strain gauge, is shown in Fig.7. The position of the two weld toes and the strain gauge are marked with dotted lines. The profile clearly shows the stress peaks at the two weld toes, and the signal attenuation at the strain gauge. The uneven stress distribution across the weld is caused by the ripples in the weld profile itself.

This stress profile, extracted from a frame scan, is very similar to a line scan that could be measured directly from the specimen with the SPATE system. Indeed, in theory the two would be exactly the same. The advantages of recording a frame scan initially are that a) it gives a clearer overall picture of what is happening in the area of interest, and b) any number of line scans of any orientation can be extracted from it at a later date. The disadvantage is only that the frame scan takes longer to record.

Figure 7 also serves to illustrate a graphical method of calibration. If the attenuation of the signal at the strain gauge is smoothed out, the intersection of the stress profile with the strain gauge marking line gives a stress value to use for calibration. For further accuracy, other line scans of different orientations but passing through the gauge could be generated, and an average calibration value derived from them.

Other examples

The SPATE system has been used extensively for study of crack tip stress fields and crack growth parameters in cracked bodies ^[5,6] The frame scan in Fig.8 shows the measured stress field at a crack tip in a centre-cracked plate. From such data it is possible to determine by graphical methods the mode I stress intensity factor. For propagating cracks, the crack propagation rates and the Paris law parameters can also be determined.

The majority of work with SPATE at The Welding Institute has involved, not surprisingly, the study of welded joints. Figure 9 shows one such simple example. The specimen was designed to model a misaligned butt joint, and was loaded in pulsating tension in a fatigue testing machine. The oblique SPATE scan clearly shows the physical features of the specimen. It is interesting to note that the secondary bending induced by misalignment is greater than the nominal applied stress, creating net compressive stress under load (the purple regions of the scan). The scan also shows the stress concentration at the weld toe, and the distinct stress gradient across the width of the specimen (something not predicted by theoretical analysis). 

Figure 10 shows a schematic arrangement of another tubular joint, in which a growing crack was monitored ( Fig.11). In this test, a fatigue crack was generated in the weld toe on the chord, in the position marked in Fig.10. Figure 11a shows a scan of the uncracked joint. The stress concentrations at the two weld toes are clearly visible, and reasonably uniform along their length. In Fig.11b the crack has formed, causing a reduction in stress in the region along its length, but stress concentration at its two ends. Figures 11c and d show how the stress field is modified as the crack continues to grow in length.

Other work has included studies of machined components, complex welded structures and detailed analysis of welded joints. Some work has been carried out on the application of SPATE for determination of residual stress. The system has also been used for non-destructive testing of carbon fibre and metal/epoxy composites, for detection of subsurface impact damage and disbonds. The SPATE system can be used effectively on nearly all engineering materials, including non-metallic materials. However, interpretation of the results, especially in non-homogeneous composite materials, can be difficult.

Future work

Apart from general stress analysis of welded and unwelded joints and structures, it is intended to develop the use of the SPATE technique in a number of specific areas, including:

1. Determination of stress intensity factors in cracked bodies of complex geometry, and especially at welded joints.
2. Stress analysis of plastic, ceramic and composite materials.
3. Non-destructive testing of welded and bonded joints in metals and composite materials.
4. Measurement of residual stress.
5. Separation of principal stress sum.

Summary

The SPATE 8000 system has proved its effectiveness as a quantitative non-contacting full field stress analysis system. It has been found to be capable of providing large quantities of detailed stress data in a very short time, which perhaps represents its greatest advantage. Its full potential is possibly yet to be realised, and studies are continuing to identify new areas of application for the system.

References