The contour technique is a destructive, mechanical strain release technique that is capable of measuring residual stresses in a single direction, in a two dimensional plane through a specimen.
The technique is based on a variation of Bueckner's elastic principle of superposition  and consists of three main stages. The first of these stages involves using wire-EDM to cut a free surface within the specimen containing residual stresses. The wire-EDM cut made in the material can be assumed to be perfectly flat. However, stresses in the material released by the creation of the ‘free’ surface cause the surface to exhibit distortions. It is then the forces needed to restore the surface to its perfectly ‘flat’ state that are equivalent to the stresses originally constrained within the specimen material .
An illustration of the principal used to calculate residual stresses from the cut surface distortions .
The second stage of the technique involves measuring the surface contours on the cut section, created by the slight distortions. These are typically measured using co-ordinate measurement machines (CMM) with either a touch trigger probe, or a laser attachment. In principal any technique for measuring the surface profile can be used that gives appropriate accuracies for the expected surface displacement. The measurement stage was until recently the most time consuming stage in the contour technique until recent improvements in laser scanning accuracies.
Figure 1: A reconstruction of the smoothed surface plot across a butt weld measured by CMM and probe 
The third stage of the technique is data analysis. This is the methodology used to convert a three dimensional surface contour into a two dimensional stress field, namely the filtering of the raw data array and the superposition of the surface contour in a FE model. The raw data measured by CMM gives a combination of the distortions due to the stress release and ‘noise’ inputs such as the surface roughness from EDM as well as stochastic noise from the measurement system. For this reason the data array must be filtered and smoothed before it can be applied to the model. There is no single ‘correct’ way of doing this as it is dependent on the measuring system and its specific signal-noise ratio. However, a good approach is to use smoothing splines, or piecewise defined and smoothly joined polynomials . After both sides of the cut have been processed and averaged, the inverse (as the surface will be returned to ‘flat’) is applied to the surface of a simple 3D FE model. The model does not have to be the same as the specimen, but the appropriate boundary conditions should be applied to stop rigid body motion. As the surface displacements are small, the reverse displacements need only be applied to the flat model surface to generate the required stresses.
Figure 2: An example of a FE model onto which the measured surface contours are superimposed for two butt-weld specimens to give residual stress results a) as-welded and b) with laser peening .
In summary the contour method is a simple technique in principal, which uses FE to keep the analytical skill required by the user to a minimum. This combined with rapid, accurate laser scanning allows the time taken for a measurement to be kept to a minimum, whilst output is maximised providing full 2D residual stress field across a section.
Procedure of the Contour Technique:
The basic experimental/analytical procedure is as follows:
- Mount the specimen using clamps/fixtures to ensure there will be no movement as the stresses are relaxed during the wire-EDM.
- Use a fine 0.1-0.25mm EDM wire to cut the specimen with the machine set to skim cut (or fine cut settings).
- Remove specimen from clamps/fixtures for cut surface measurement.
- Measure the surface contour using a probe or laser.
- Filter the measured data to remove noise and surface roughness, leaving only the stress relieved contours.
- ‘Reverse’ the contour and apply it to the surface of an elastic 3D FE model surface, deforming the surface into the inverse of the measured contour requires the original stresses in the specimen, which are output by the FE software.
Advantages of the Contour Technique:
- Depth of measurement is only limited by the wire EDM and CMM axis ranges;
- A full field 2D stress map is produced;
- Accuracy is not compromised by increasing the cut depth;
- A simple process that relies on ‘off the shelf’ hardware and software with minimal user computation;
- Price competitive with respect to the amount of stress data produced;
- Indifferent to grain structure/texture of component material;
- ‘Clean’ EDM surface allows further research such as etching, x-ray and even contour measurements;
- Still under development.
Disadvantages of the Contour Technique
- Laboratory based measurements;
- Uni-axial residual stress measurements;
- Difficult to apply to complex shaped components;
- Least accurate at specimen surfaces;
- Reliant on good contour measurement data, smoothing and filtering can reduce stress accuracy.
References & Further Reading:
- Bueckner, H. F., “The Propagation of Cracks and the Energy of Elastic Deformation”, Trans. ASME, 80, pp. 1225–1230, 1958.
- Prime, M. B., “Cross-Sectional Mapping of Residual Stresses by Measuring the Surface Contour After a Cut”, Journal of Engineering Materials and Technology, 123, pp. 162-168, 2001.
- Pagliaro, P. et al., “Measuring Inaccessible Residual Stresses Using Multiple Methods and Superposition”, Experimental Mechanics, Volume 51, No. 7, pp. 1123-1134, 2011.
- DeWald, A. T. et al, “Assessment of Tensile Residual Stress Mitigation in Alloy 22 Welds Due to Laser Peening”, Journal of Engineering Materials and Technology Volume 126, Issue 4, pp. 465-473
- Prime, M. B., 1999, “Laser Surface Contouring and Spline Data Smoothing for Residual Stress Measurement”, Experimental Mechanics, April 2004, Volume 44, Number 2, pp. 176-184.
A good source of literature for further reading can be found at www.lanl.gov/contour listing publications by Dr. Mike Prime, the inventor of the technique, who lists Greg Johnson’s PhD Thesis providing a very thorough breakdown of the technique. Other important researchers are Prof. Mike Hill, who also has a webpage at mae.ucdavis.edu/~mhill/.