Full Field Deformation Measurements
EM517
Bastawros 3/1/05
1. Two dimensional grid methods
a) Over a two dimensional grid on the specimen surface and follow its coordinate movements via
video imaging of the parallel lines as they change and follow the deformation.
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Reference (undeformed) configuration
Deformed configuration
b) Analysis of grid points:
1. Locate a reference point on the deformed and undeformed configuration.
2. Find the grid coordinate relative to local axis
3. Find the displacement vector at each grid point (i,j) on the deformed configuration according to:
u (i, j) = x (i, j) – X(i, j)
4. Remesh the displacement vector onto an even grid (through three point interpolation)
5. Use central difference to get the spatial displacement derivatives on the deformed configuration
Deformed grid
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Evenly spaced grid for
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Full Field Deformation Measurements
EM517
Bastawros 3/1/05
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c) Digital image processing to evaluate u:
1. The deformed image has to be binarized, ie. The full gray scale of the image is switched to
two levels; either black or white.
2. Perform edge tracing of the grid to locate the corners of the grid.
Original-full gray scale image
Binarized-two level image
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Gray Scale
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Gray Scale
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Pixel
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d) Gray scale, gage length and strain sensitivity:
If we use a mapping of 10 pixel per line periodicity, the minimum detectable strain will be
εmin=∆L/L = 1/(10xDynamic range)
For 1-bit camera
εmin= 1/(10x1)= 10%
For 8-bit camera
εmin= 1/(10x256)= 0.04%
For 16-bit camera
εmin= 1/(10x65536)= 0.0001%
- By using a bigger camera array, you can increase the mapping of the gage length and thereby increase
your strain sensitivity.
- Using bigger camera array with the same optical magnification will give bigger field of view with
the same strain resolution.