The coating stress is created by solving a Static Structural analysis that has special values of Isotropic Secant Coefficient of Thermal Expansion (CTE) and a Thermal Condition load that raises the temperature by 1 C. The substrate CTE is set to 0 so the temperature change has no effect on that. The coating CTE is set by an equation that results in the coating stress being developed by a temperature increase of 1 C.
CTEcoating = CoatingStress(1-Nu)/Ec
Where Nu is the Poisson's Ratio for the coating and Ec is the Young's Modulus of the coating. If you don't know Nu, you can set that to 0 to get the largest effect. The reference for this method is Integrated Optomechanical Analysis (2nd Ed), Keith B. Doyle, Victor L. Genberg, Gregory J. Michaels on page 140. Below is a reference on plasma coatings. https://www.researchgate.net/publication/257809497_Several_fundamental_researches_on_structural_integrity_of_plasma-sprayed_coating-based_systems/download
Just for a simple example, let's use a coating stress of 10 MPa in an aluminum coating. Using the equation above, the CTE value is -9.44E-5 /C
Let's apply that to a quarter model of a very thin sheet of glass (to make a mirror!) A rectangle of 0.5 mm thick glass is 80 mm long x 40 mm wide, but the model will be 40 mm x 20 mm long. The two cut faces that create the symmetry will each have a displacement support of 0 in the direction normal to the face. One vertex has a displacement support normal to the sheet of glass. Note that under the Mesh branch, a Method of Sweep has been used to get 4 elements through the thickness of the glass. The Element Order was set to Linear. Under the Structural branch, note that the Environment Temperature is 22 C.
Add a Thermal Condition of 23 C, which represents a 1 C temperature increase.
Under the Geometry branch, Insert a Surface Coating. Pick the top surface of the solid body and fill out the Thickness of the coating, select the Material and set the Stiffness Behavior to Membrane Only.
Now Solve the model and plot the deformation in the Y direction.
The 1 micron thick aluminum coating with a stress of 10 MPa has caused the pre-coated, perfectly flat 0.5 mm thick rectangle of glass to deform so the corner lifted 2.67 microns away from the flat plane.
You may think that is not exactly "scrolling up", but it's an example of a mirror, where 2.67 microns of deformation could be a big deal. If this was too much, then increasing the glass thickness to 1 mm will greatly reduce the deformation.
The above was a linear analysis, since the deformation was a small fraction of an element thickness. If you try this with a much larger coating stress to get a lot more curl, you will want to make it a nonlinear analysis. Under Analysis Settings, you will want Large Deflection turned On. My solution was accurate with that turned Off.
CTEcoating = CoatingStress(1-Nu)/Ec
Where Nu is the Poisson's Ratio for the coating and Ec is the Young's Modulus of the coating. If you don't know Nu, you can set that to 0 to get the largest effect. The reference for this method is Integrated Optomechanical Analysis (2nd Ed), Keith B. Doyle, Victor L. Genberg, Gregory J. Michaels on page 140. Below is a reference on plasma coatings. https://www.researchgate.net/publication/257809497_Several_fundamental_researches_on_structural_integrity_of_plasma-sprayed_coating-based_systems/download
Just for a simple example, let's use a coating stress of 10 MPa in an aluminum coating. Using the equation above, the CTE value is -9.44E-5 /C
Let's apply that to a quarter model of a very thin sheet of glass (to make a mirror!) A rectangle of 0.5 mm thick glass is 80 mm long x 40 mm wide, but the model will be 40 mm x 20 mm long. The two cut faces that create the symmetry will each have a displacement support of 0 in the direction normal to the face. One vertex has a displacement support normal to the sheet of glass. Note that under the Mesh branch, a Method of Sweep has been used to get 4 elements through the thickness of the glass. The Element Order was set to Linear. Under the Structural branch, note that the Environment Temperature is 22 C.
Add a Thermal Condition of 23 C, which represents a 1 C temperature increase.Under the Geometry branch, Insert a Surface Coating. Pick the top surface of the solid body and fill out the Thickness of the coating, select the Material and set the Stiffness Behavior to Membrane Only.Now Solve the model and plot the deformation in the Y direction.The 1 micron thick aluminum coating with a stress of 10 MPa has caused the pre-coated, perfectly flat 0.5 mm thick rectangle of glass to deform so the corner lifted 2.67 microns away from the flat plane. You may think that is not exactly "scrolling up", but it's an example of a mirror, where 2.67 microns of deformation could be a big deal. If this was too much, then increasing the glass thickness to 1 mm will greatly reduce the deformation.
The above was a linear analysis, since the deformation was a small fraction of an element thickness. If you try this with a much larger coating stress to get a lot more curl, you will want to make it a nonlinear analysis. Under Analysis Settings, you will want Large Deflection turned On. My solution was accurate with that turned Off.
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