# Imprinting Stamp Force

Hi

I have a problem I'm trying to figure out, but no idea where to start. Essentially I am trying to calculate the amount of force required to imprint 'photoresist' (a very viscous fluid sensitive to light) of some known density, $$\rho$$ and viscosity, $$\mu$$, with a ridid stamp, given a certain amount of time, t, and a certain depth, d.

Since I've never taken a fluid dynamics course, and am not sure if concepts from basic fluid dynamics are even relevant at these scales (lets say the stamp features are just an array of walls 100 nm wide and 1 micron depth, resembling a stripe pattern).

Is it harder to break through the surface of the fluid? Will the sides of the stamp 'walls' cause extra (non-negligable) resistance as opposed to a stamp with just a single feature (lets say a square) with the same surface area of all the walls in the first stamp? Is there a difference whether or not this is done in vacuum?

I've also attached a picture I created to help visualize the situation. Thank you for any help you can provide.

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This is a difficult calculation. I would set up a simple experiment and directly measure the force required to deform the material. Generally the force drops significantly after failure occurs. You might be able to set up a simple lever system with spring scale to measure a force. I don't think having a vaccuum makes much difference.

Andy Resnick
I agree, you are better off measuring the force (actually, the pressure) as a function of time and depth. The photoresist is likely not a simple fluid.

This is an odd problem to solve- what is the application?

The 'desired' application is a SAW (surface acoustic wave) transducer, which in reality looks like this: http://www.sp.phy.cam.ac.uk/SPWeb/research/HFSET/Research/Background/content_files/schematic_transducer.jpeg" [Broken]

This is actually for a thesis-like project where no experimentation is allowed, so I am kind of stuck there. Would there be any way to 'simplify' the calculation with some type of approximations or idealizations so that I could obtain a 'ballpark' answer? The reason I'd like to know the force required is to attempt to figure out whether it is feasible to have the stamp deform the resist under gravity rather than have stepper motors.

Thanks for the help so far.

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This problem is similar to metal stamping. I am enclosing a formula for calculating the maximum Blanking force needed to punch a blank from a material. You will need to find or estimate the Ultimate Tensile Strength of the material you are working with. A web search might help for example the Ultimate Tensile Strength of polyethylene,HDPE is 15 MPa.

P=t*L*K*ts

Where P is Blanking force(kgf)
t= thickness of stamped piece (mm)
L= TOTAL length of all cuts (mm)
K= correction factor (0.8-1) allows for sheared profile, finish of cutting edge etc.
ts= tensile strength (kgf/mm^2)

You are really more interested on stamping or embossing than blanking but it is a place to start.