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# Material Choice Optimisation

## Material Choice Optimisation

(OP)
Hey,

I'm looking for someone who's come across this problem before:

The design of a lightweight flexure hinge.

Basically, I am trying to design a lightweight flexure hinge, (like those found on plastic shampoo bottle lids) I know already that I should look for materials which have a high specific strength to stiffness ratio.

The hinge should bend to a known radius - the strength constraint. It should also offer a resistance of an exact amount - the stiffness constraint. The hinge is constrained in width. The thickness is not constrained. I wish to know which would be the lightest material to use and the thickness required to make the hinge.

The thickness of the hinge is constrained for each material due to their ultimate strain - the elongation at which they break - regardless of the strength or stiffness. Since we are optimising, the hinge will break as soon as it passes it's design bend radius. At this radius, the upper and lower fibres of the hinge will be a certain percentage of the length of the neutral fibre - the breaking or ultimate strain.

Ideally, I am looking for the materials selection parameters, such as those used in the Cmabridge Materials selector and any equations that describe the problem.

So, can anyone offer any ideas about how to progress? I can post an example problem to clarify the issue if needed.

Many thanks!

PS this seems like a classroom problem!

### RE: Material Choice Optimisation

Since you are familiar with the Cambridge Materials selection process, I will give you the derivation for an elastic hinge from Materials Selection in Mechanical Design by M. F. Ashby:

Hinge is a thin ligament that flexes elastically, but does not carry an significant axial loads.  The best material is one which, for given ligament dimensions like length and width, can bend to the smallest radius (most strain capacity) without yielding or failing.

When a ligament of thickness t is bent elastically to a radius R, the surface strain is

epsilon = t / 2R

and since the hinge is elastic, the maximum stress is

sigma = E * (t / 2R) where E is the elastic modulus

This stress must not exceed the yield/failure strength, which will be called sigmaf.  Substituting into the initial equation, the radius can now be defined as follows:

R < (t / 2)(E / sigmaf)

The best material is the one that can be bent to the smallest radius; that is, the one with the greatest value of the index

M = sigmaf / E

Plastics and elastomers have the highest values for M, anywhere from 30-300, but are limited in modulus, temperature capability, etc.  Spring steel and titanium alloys are the best metallic candidates, with M indices of around 5 - 15.  Chrome-silicon steel alloys like SAE 9254 and all of the latest proprietary grades like SRS60, HDS-12, etc. are the best steel candidates.  Ti 3-8-6-4-4, also know as Beta-C is the high-strength titanium spring alloy.

If you need mechanical property information, you can find a lot of it for these grades on the web.  Do a search of Eng-Tips threads for links to various sites, as well as a google search of the web.  FYI, Formula 1 racing cars now use elastic hinges on the inboard side of the suspension arms (wishbones in racing parlance), and as far as I know, they are ALL made out of some type of titanium alloy.  Beta-C is most readily available in round bar and wire, so other high-strength grades like Ti 10-2-3 or Ti 6-4 may be used/considered.

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