Hi Karolina,

Single-crystal silicon can be considered a brittle material at room
temperature, but at elevated temperatures it flows plastically at stresses
much lower than its room-temperature yield stress.  This is important if
your structure will see elevated temperatures.  I think you can safely
assume that silicon behaves linearly as long as the applied stresses are
several percent below the yield/fracture stress (the linear elastic/plastic
transition is not always sharply defined).  As for calculating your working
stress, 3) is correct - take the fracture or yield stress of silicon (to be
on the safe side you could take whichever value is lower) and divide it by
your desired factor of safety.  Safety factors vary depending on the
application, and no one value can be quoted as being correct.  If you
require higher reliability or if your device might be subjected to loads in
excess of the design load, you might want a higher safety factor - it all
depends on your application.

Good luck,

Brian Stahl

--
Brian C. Stahl
Graduate Student Researcher
UCSB Materials Research Laboratory
brian.stahl@gmail.com / bstahl@mrl.ucsb.edu
Cell: (805) 748-5839
Office: MRL 3117A


On Tue, Nov 10, 2009 at 12:38 AM, Karolina psychowlosy  wrote:

> Hello,
>
>  I am not specialist in mechanics, so I would like to consult with you on
> the follow subject.  It concerns straight and very long beams (i.e.
> lenght/height ratio is around 100) with rectangular cross-section, where
> the
> height of a beam is larger than its width.
>
> What I have found about Single Cristal Silicon I would like to ask you to
> comment the points mentioned below. I would be very grateful for any
> comment.
>
>
> 1. It is a brittle material. For the brittle materials the characteristics
> is linear in the elastic region until the yield point and the SI is
> fractured, so linear stress-strain curve.
>
> 2. From the point 1 and the fact that the straight beam during the bending
> doesn't change its shape I assume it is a linear material.
>
> 3. Accroding to Gere and Timoshenko "Mechanics of Materials", 3rd SI
> Edition, 1991, pp.34-35,  the allowable stress is obtained from the
> relation
> ultimate stress divided par safety factor.
>
> 4. Petersen in his article " Silicon as a mechanical material" pointed only
> yield strength of Silicon, however some group of researcher pointed the
> fracture strength e.g., *"Due to its brittleness at room temperature, SCS
> fractures before it deforms plastically. Fracture strength, instead of
> yield
> stress which is used for most metals, becomes the design parameter that
> limits the maximum load a silicon structural member can bear"
> * (Yi T. et al, Sensors and Actuators 83 (2000), pp. 172-188)
>
> And here are some questions:
>
> a)  For brittle materials in the room temp., what strength then should be
> considered concerning MEMS components like beams - fracture strength or
> yield strength to calculate teh allowable stress - I mean tension and
> compresion stresses?
>
>  b) Have you ever seen in the literature what the safety factor is for the
> Si?
>
> Best regards.
>
> Karolina