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Engineering

# Research project: Strain through the looking glass

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This projects aims at using an unusual but very powerful technique to image the surface deformation of mirror-like structures.

Video 1: shear strain on a thin panel of Perspex shaken at 100 Hz. This high-speed video captures the deformation during 0.050 s.

Most materials do not exhibit such a smooth mirror-like surface so coating procedures based on gel coats have been developed (the type of coating present on a composite component when it looks shiny, like boats or tennis rackets).

The principle of the technique (also called ‘deflectometry’) is to record images of a pattern as reflected off the surface of this mirror (Figure 1). When it deforms, the reflection deforms according to the local slope at the surface. The technique is able to detect slopes of the order of 0.5 mm per km! From the slopes, curvatures can be obtained. The radius of curvature is the radius of the sphere that would be tangent to the deformed surface at a particular point. The technique can measure radiuses of curvatures of the order of 1.5km! When curvatures are measured on thin plates deformed in bending, they are directly proportional to the surface strains and can be related to the stresses in the plate.

This technique has been used by my group for different problems over the years, as captured in the list of publications below. As an illustration, one of the latest studies we undertook with this tool, as part of the PhD thesis of Dr Cedric Devivier, is explained below.

The experimental set-up is that of Figure 1. Composite plates have been tested, first virgin of any damage and then, after having been submitted to mechanical impact, representative of a dropped tool during maintenance, for instance. The objective is to use the deformation maps measured by deflectometry to detect the presence and magnitude of the damage. Figure 2 below represent a deformation map for an undamaged plate. It compares very well with a numerical model of the test, even though the deformations are really small (scales in microstrains, see comment at the end of this document).

Can the technique really visualize the effect of damage? Here is a small quiz (Figure 3).

The large reddish area is where the load is introduced. The rest of the maps looks smoother but if you look carefully, you can see that there is a small disruption of the smoothness of the map towards the middle of the image.

Using a technique closely related to the Virtual Fields Method, we were able to decrypt these maps for the presence of damage. In a nutshell, the technique detects that the measurements violate the basic law of mechanical equilibrium. This leads to so-called ‘Equilibrium Gap’ maps in Figure 4. The lines seen on the map for panel 2 come from small defects in the coating. The result is spectacular in locating the defect. This is confirmed by an ultrasonic technique called C-Scan which can determine the extent of the damage, as seen on Figure 5.

Another example of the incredible sensitivity of this technique is shown in Video 1 (Videos forthcoming). A thin Perspex plate was drilled in its centre and bolted to a shaker vibrating at 100 Hz, slightly deforming the plate. The video shows the kind of deformation map that can be obtained (here, the shear strain). The scale showing 10-6 means that the deformation is such that two points located say 1 mm away from each other would deform by a relative movement of 1 nm (nanometer, one millionth of a mm). Such deformation maps can usually only be obtained by very expensive laser systems.