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Materials Engineering Group

Materials Engineering

Departmental Staff - Dr. Salih Gungor

Moiré Interferometry for strain measurement


Moiré interferometry is a technique to study strains and deformations of structural elements with very high accuracy. It requires highly stable environment and therefore it is mainly a laboratory tool.

Moiré is the generic term for full field measurement techniques, which utilise the interference effect between some form of specimen grating and reference grating to magnify the surface deformations and create a contour map which is related to surface displacement – a moiré fringe pattern or interferogram. For relatively large displacements, mechanical moiré uses the interference of lined gratings to achieve sensitivity of measurement of up to 25 micron metre. Optical moiré, or moiré interferometry , in which a diffraction grating is illuminated by laser light, increases the sensitivity to sub-micron level, enabling measurement of elastic strains in engineering materials.

Fig.1 Formation of moiré fringes by superimposing two line patterns which vary in line spacing and rotation.

The moiré pattern is a full field representation of the relative displacement between the gratings. This property of moiré makes it an excellent tool for observing and quantifying the gradients in localized deformation. In practice, a grating is attached on the surface of the test piece. The grating deforms together with the test piece and when an undeformed (reference) grating superimposed onto it, a moiré pattern depicting the nature and the magnitude of the deformation field is obtained. Each moiré fringe represents a line of constant displacement in the direction perpendicular to the direction of the reference grating (Note that the fringes due to rotation in figure 1 do not give any displacement component). The displacement value ( u ) of a fringe is u = Np where N is the fringe number relative to a known zero displacement and p is the pitch of the reference grating, i.e. the perpendicular distance between the lines.

Moiré Interferometry

The moiré effect described above is termed mechanical moiré because the fringes are formed from the mechanical crossing of the two gratings. The mechanical moiré effect is limited by the frequency (inverse of pitch) of the grating employed. The typical upper limit for these type of gratings is 40 lines/mm above which diffraction effects dominate. This means, when 40 lines/mm gratings are used, a minimum deformation of 0.025 mm would be required to produce one fringe. This is quite adequate for large deformations, but in order to measure small elastic strains much higher grating densities, which would give higher deformation sensitivities, are required. Optical moiré commonly known as moiré interferometry provides higher sensitivity by employing the principles of light interference and diffraction.


Fig.2 Two-beam interference on a reflective diffraction grating.

Figure 2 shows a basic moiré interferometer with a specimen grating exposed to a two-beam interference system. The diffraction effect split the incoming light beams into multiple preferred rays on the grating. When the grating is undeformed, the -1 and +1 diffraction order from the beams emerge perpendicular to the grating without any interference. When the specimen is deformed, the -1 and +1 orders will exit the specimen grating warped and interfere with each other. The result is a moiré fringe pattern of the in-plane displacements. The interpretation of the pattern is identical to that of mechanical moiré.



Residual stresses in friction stir welded aluminium alloy plates

This example shows the use of moiré interferometry in an investigation of the structural integrity of a friction-stir welded aluminium alloy. Diffraction gratings were replicated onto the cross section of the specimens, covering whole of the weld and HAZ located at the centre of the specimens. With this arrangement, tensile force is applied normal to the weld line. The fringes in Figure 3b give the displacements in the direction of loading, where each fringe represents points of equal displacement. The displacement difference between each neighbouring fringe is determined by the optical set up, and it is 417 nanometre in this case. So, as expected, the fringes in Figure 3b are equally spaced in the direction of loading Figure 3c shows that the sample is plastically deforming and the deformation is confined to a region around HAZ where there was extensive material flow during the welding process. The information allowed inferences to be made about the magnitude and distribution of residual stresses in the region of the weld. Note that in the example given in Figure 3, the fringes were demodulated at 100 and 200 MPa (when the fringe density became too high so that they couldn't be resolved with the imaging system).

Fig.3 Plastic deformation at the weld joint.

Out-of-plane displacement at the tip of a mode I crack

The moiré interferometry is very effective in determining high gradients of strain. Figure 4b shows the fringe pattern around the tip of a 1mm long through crack in a four point bend titanium alloy specimen at a certain loading condition. Here, the fringes represent contours of equal displacements (very like height contours in terrestrial maps). With this particular set-up, each neighbouring fringe shows 417 nanometre height difference. By employing optical phase shifting methods, the displacement values in between fringes can also be determined. This increases the displacement sensitivity to better than 50 nm (Figure 4c).

Fig.4 (a) Central part of the 4-point bend specimen (essentially subjected to pure bending) (b) fringe pattern around the crack tip, and (c) surface plot of the displacement map.

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