... | ... | @@ -13,18 +13,18 @@ Using photoelasticity, we can measure internal stress. This measurement is best |
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Photoelasticity can be used to quantitatively measure local stress. Assuming that the relation between stress and refractive index is linear:
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$`n_1-n_2=C(\sigma_1-\sigma_2)`$
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\(n_1-n_2=C(\sigma_1-\sigma_2)\)
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where $`\sigma_i`$ is an eigenvalue of the local stress tensor, $`n_i`$ is the refractive index for polarized light in the corresponding direction, and $`C`$ is called the stress-optical coefficient. The relative phase shift of wave components in the eigen-directions of the local stress tensor can be calculated using:
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where \(\sigma_i\) is an eigenvalue of the local stress tensor, \(n_i\) is the refractive index for polarized light in the corresponding direction, and \(C\) is called the stress-optical coefficient. The relative phase shift of wave components in the eigen-directions of local stress tensor can be calculated using:
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$`\alpha=\frac{2\pi C d}{\lambda}(\sigma_1-\sigma_2)`$
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\(\alpha=\frac{2\pi C d}{\lambda}(\sigma_1-\sigma_2)\)
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where $`\lambda`$ is the wavelength of the light and $`d`$ is the distance traveled inside the material, which corresponds with the sample stiffness. Given this phase shift, the intensity of the emergent wave is:
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where \(\lambda\) is the wavelength of the light and \(d\) is the distance traveled inside the material, which corresponds with the sample stiffness. Given this phase shift, the intensity of the emergent wave is:
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$`I=I_0 sin^2(\frac{\alpha}{2})=sin^2(\frac{\pi C d}{\lambda}(\sigma_1-\sigma_2)) `$
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\(I=I_0 sin^2(\frac{\alpha}{2})=sin^2(\frac{\pi C d}{\lambda}(\sigma_1-\sigma_2)) \)
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This equation relates internal stress and intensity for a single wavelength. In most cases, both the light and camera channels cover a wide range of wavelengths. Stress calculation is less noisy using a narrow range of wavelengths and a single channel from the camera. However, it is still possible to retrieve stresses using white light.
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The last equation makes it possible to invert the mechanical problem and to get the full stress field (even if there is non-uniqueness of the solution). This is not a trivial problem but in this wiki, we show [how to do](/inverse-analysis) it in the specific case of loaded discs. Other more [qualitative possibilities](/method-analyze) exist to have an estimation of the stress field.
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The last equation makes it possible to invert the mechanical problem and to get the full stress field (even if there is non-uniqueness of the solution). This is not a trivial problem but in this wiki we show [how to do](/inverse-analysis) it in the specific case of loaded discs. Other more [qualitative possibilities](/method-analyze) exists to have an estimation of the stress field.
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[<go back to home](/home) |
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\ No newline at end of file |
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[<go back to home](/) |