110 lines
4.9 KiB
Markdown
110 lines
4.9 KiB
Markdown
#SMMS
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Objective : Measure displacement field, and obtain the strain field.
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Need markings, but is often kind to the material, and the measure itself does not need any physical contact with the material. => Useful for hostile environments.
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However light is not always reliable (for example heat can bend the path of the light)
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In addition to that, they are multi-scale methods. Depending on the optic tools, measures can be taken at the micron or tens of kilometers scale.
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## Vocabulary
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The **test body** *(corp d'épreuve)* is the body being tested.
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The **resolution** is the smallest change detected that is not considered "noise", the detection threshold.
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The **sensitivity** *(sensibilité)* is how much the response of the sensor change when the measured physical quantity changes.
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**Accuracy** *(précision)* is banned (ISO 5725-1), and are preferred **trueness** *(justesse)* and **precision** *(fidélité)*.
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![[Trueness vs Precision]]
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## Sensing light
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Light sensors measure the photon flux, and therefore work only with grayscale.
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They cannot measure it on the full surface of the sensor, with the upper bound being 95% of photosensitive surface
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To measure color, a filter is applied and the photon flux assessed for this color specifically. But doing this for R, G, and B you can get a full color image, at the cost of the information (discontinuities in the red light between to R sensors are not measured for example).
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![[Bayer_pattern_on_sensor.svg]]
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(image of a Bayer matrix)
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You can also use mirrors to not lose so much informations, but it is rarely used in practice.
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Whatever the architecture, one of two types of sensor is used :
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#### CCD : the ol' reliable
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Used to be the only viable option, and is very precise, but slow and power-hungry.
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#### CMOS : quick and dirty
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The newcomer, faster and energy-efficient but less precise.
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# Philosophy
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Care needs to be taken regarding what you measure :
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you cannot measure force directly, so if you want force you have to take hypothesis for a method to get the force.
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In calculus, often everything is assumed to be continuous, but it often lacks real meaning, and continuity cannot be measured. Each sensor has its own **resolution**.
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---
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# Local Approach (2d)
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Difference in the sense of least squares :
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$$C(\overline{x,y},\overline{u,v})=\sum_{i,j=-n/2}^{n/2}[I\overline{(x+i,y+j)}-I^*\overline{(x+u+i,y+v+j)}]^2$$
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$I$ Image before displacement, $I^*$ Image after displacement
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$i$,$j$ coordinate within the subset
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Other coefficients can be calculated, for example the correlation product, which is roughly a [convolution](https://www.youtube.com/watch?v=KuXjwB4LzSA&pp=ygULY29udm9sdXRpb24%3D). It is the coefficient used in fluid mechanics because it can be efficiently computed with the FFT.
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The subset size is always a compromise : a small subset allows for more local information with more noise, while a large subset allows for global informations with less noise.
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## A word of caution
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The study body's surface must be plane, and the camera axis normal to this plane. And any out-of-plane displacement causes errors.
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---
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# Volumetric Correlation
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The goal is to be able to see the heterogeneity of the material, and get the structural architecture. (even get architecture gradients)
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### Tomography
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aka volumetric scan, like IRM, X ray scan, ultrasonic scans
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-> sinogram
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To get the image of the internal structure, the inverse transform of Radon is used.
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**Issue** : when you need to load the study body : loading equipment may be bulky and not fit in the tomograph.
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The texture used for the process is often the microstructure itself, so it is impossible to access to the behavior of the microstructure (since 2 colors are 2 different materials).
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---
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# Computing parameters
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Usually to fully characterize a material, a lot of test need to be conducted. One of the goals of Photomechanics it to find a reliable way of finding a lot of parameters from a few tests (even if more complicated).
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### FEMU
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It is an iterative parameter tweaking. An intuitive method, a bit rustic but works in most cases.
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(another field but perfectly describes the method : [video](https://www.youtube.com/watch?v=IHZwWFHWa-w)*20min*)
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### Other methods
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Can need some conditions to work :
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##### Kinematic admissibility :
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$$\varepsilon = \frac{\nabla U+\nabla U^T}{2},\ x \in B$$
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(see [video](https://www.youtube.com/watch?v=X-H3Fwdm-kI) *10min*)
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$$U=U_d,\ x\in\delta B $$
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($\delta B$ is the boundary of the body $B$)
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##### Static admissibility
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$$\nabla \cdot \sigma + f = \rho \gamma$$
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*(I may be wrong but I see a generalization of $F=ma$)
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$$\sigma n=T$$
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(for other definitions of admissibility see [article](https://en.wikiversity.org/wiki/Elasticity/Kinematic_admissibility))
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## A word of caution
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$\varepsilon$ is computed from deriving $U$, adding a lot of noise to the measures. To have better result it is more rigorous to use $U$, even if it means struggling with boundary conditions.
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