Shadow moire for experimental deformation analysis
EMA 611 class, Rod Lakes
Determination of out of plane deformation
Illuminate an object with a spotlight. The light beam makes an angle α with respect to the normal to the surface. An observer or camera receives the reflected light at an angle β with respect to the normal to the surface. Place a grating of pitch p (the distance between grid lines) near the illuminated surface. The grating casts a shadow on the surface. View or photograph the shadow grid through the actual grid. A pattern of fringes is formed, representing contours of equal depth from the grating plane. If the surface is initially flat and is then deformed, the fringes represent out of plane deformation.
The deformation wz(x,y) is given by the following. See, e.g. Manual of engineering stress analysis, third edition, ed. A. Kobayashi, SESA, Prentice Hall.
wz(x,y) = N(x,y) p [tan α + tan β]-1
The finer the grid, the closer it must be to the object to prevent blurring of the shadow grid. Blur can also occur if the object is translucent. Local heterogeneity of deformation can give rise to a grainy image.
The moire method is no more difficult if real time or dynamic measurements are called for. Capture sequential photographs or a video.
Sensitivity with this method can be increased by using a finer grid: if spacing p is made smaller, the fringe order N for a given displacement becomes larger. For shadow casting by geometrical optics to occur, the grid spacing must be much larger than the wavelength of visible light (400 nm to 700 nm). If yet more sensitivity is required, holographic methods may be appropriate.
In-plane deformation in the x and y directions may measured using in-plane moire in which a grid of lines is applied to the surface of the specimen. Holographic methods are capable of determining full three dimensional deformation fields without putting anything on the surface.