Force vs. Displacement data for a Flat Spring

[jongyonkim]

Hi,

I'm running a simulation of unrolling a flat spring made of silicon to obtain the system's reaction force (spring force) vs. displacement graph.

See the picture at :

http://i102.photobucket.com/albums/m97/jongyonkim/flatspring.jpg

http://i102.photobucket.com/albums/m97/jongyonkim/flatspring3D.jpg

I am currently using the FEA solver ABAQUS/Explicit to run the stretching analysis. Basically, I apply a constant force on either end of the spiral and stretch it until it completely unwinds.

Before I can dive into postprocessing, I need to know how to calculate the (spring reaction) force vs. (spiral end) displacement of this particular structure.

Does anyone know how to do the calculation of my flat spring? Any recommendation on online sources / books regarding a similar spring structure?

Also, ABAQUS/Explicit can spit out a number of data including nodal displacement, External Work, Kinetic Energy, Internal Energy, etc.

I tried differentiating Internal Energy (of the entire structure) with respect to displacement to get force, but that seems wrong somehow...

Any FEA solver experience would also be helpful.

Thank you.

 

[israelkk]

When you say silicon do you mean silicon rubber or real silicon ceramic?

 

[jongyonkim]

Real silicon ceramic (stiff)

Young's Moduls : 112.4 GPa
Poisson's Ratio : 0.28

Thanks.

PS. The stress/strain data is of no interest to me for now, despite the obvious immminent fracture upon unrolling.

 

[israelkk]

If this is the case I do not believe you can completely unwind it because it probably will break. Silicon has no plasticity compared to metal. Just consider how much deflection the flat spring has to go from its natural radius to flat infinite radius). Secondly, the spring strip curvature is a stress raiser (Wahl constant) because you try to flatten the strip.

There is another issue, when you pull the spiral end the coils may touch each other and cause friction between coils and erratic inconsistent force-deflection behavior.

Basically you have two constant force springs (extension type) in parallel.

You can find the formulation for such a spring in: Design Handbook, Engineering Guide To Spring Design 1987 Edition printed by Associated Spring Barnes Group Inc. (SPEC) Page 92.

http://israelkk.googlepages.com/home

 

[jongyonkim]

Hi israelkk,

Thanks for replying.

I actually keep the silicon from breaking by coating the structure with a layer of ductile substance.

My interest is in extracting force vs. displacement data, and you suggested this book (which is quite expensive).

Is there another (free) online source where I can look it up?

 

[NickE]

Try this:

http://home.asbg.com/ASPortal/Pages/Handbook/default.htm

(note: I might have acess to this that you dont have, so it may not work.)

 

[kenvlach]

Most data is for compression of bulk crystalline material. E.g.,
COMPRESSIBILITY (VOL/VOL_o)
@ 25,000 kg/cm²: 0.978;
@ 100,000 kg/cm²: 0.940

"Small single-crystal filaments are very strong and exhibit breaking strengths of up to about 1.4 GPa (200,000 psi)...
Vapor deposition below about 500 deg C produces amorphous silicon; upon reheating to a somewhat higher temp, crystallization will occur."
From

http://www.speclab.com/elements/silicon.htm

I think that for your coil to work it must be thin, amorphous Si. Maybe make by CVD of amorphous Si onto an Al foil coil, which can later be removed by acid.

Amorphous Si nanorods can be bent further than bulk crystalline Si:
"...Various samples with different dimensions and inclination angles were tested in bending using an atomic force microscope. The material response was elastic up to large stresses/deflections. The Young’s modulus was calculated from the slope of the experimentally observed stiffness versus the geometrical factor common to all the samples and was found to be (94.14±10.21) GPa. No size effect of this parameter was observed within the accuracy of the present measurement..."
from
Mechanical Testing of Isolated Amorphous Silicon Slanted Nanorods, C. Gaire et al., Journal of
Nanoscience and Nanotechnology, Vol.5, 1893–1897, 2005.

http://www.rpi.edu/~wangg/publications/2005_4.pdf#search="amorphous silicon physical properties"

Nano-indentation & deformation modeling of Si, p. 32-50 in this presentation (note the change of structure):

http://wwwrsphysse.anu.edu.au/~jeb1...earch="amorphous silicon physical properties"

Maybe more info in this book; try a library:
Properties of Amorphous Silicon and Its Alloys,
440 pages, Tim Searle (ed.), ISBN: 0852969228 (1998), published by INSPEC, The Institution of Electrical Engineers, London, UK.
"This book represents a data collection of physical and chemical properties of amorphous Silicon..."
from book review at

http://www.crystalresearch.com/crt/ab34/828_a.pdf#search="amorphous silicon physical properties"