# Calculating force required for specific strain

• scott_alexsk
In summary: Al are connected at one point, I was able to come up with an equation for the stress. Stress = Force/Area. Stress = (Force)/(Area of Nitinol+Area of Al) Stress = (8200 N/m2+28 GPa)*(4.45 m2) = 22300 N/m2
scott_alexsk
How would I approach the problem of calculating the amount of force necessary to enduce a certain flexural strain on a piece of alumnium? Would I use Young's Modulus and if so how would I use it?

Thanks,
-scott

scott_alexsk said:
How would I approach the problem of calculating the amount of force necessary to enduce a certain flexural strain on a piece of alumnium? Would I use Young's Modulus and if so how would I use it?

Thanks,
-scott
You'd have to know a lot of things. Like
Flex Stress = (Young's Modulus)*(Flex Strain), where
Flex Stress = Bending Moment/Section Modulus, where
Section Modulus is a geometric property of the member. I think aluminum has a Young Modulus of E = 10*10^6 psi, I don't use it much (steel has an E of 30*10^6 psi, making it a lot more stiff and with less strain and deflection than aluminum for a given loading).

scott_alexsk said:
How would I approach the problem of calculating the amount of force necessary to enduce a certain flexural strain on a piece of alumnium? Would I use Young's Modulus and if so how would I use it?

Thanks,
-scott
How are you going to apply the force?

(eg: cantilevered piece with one fixed end and a single point load at the other end)

This is not an easy calculation, but can be done trivially, using a beam analysis package of your choice (here's a fairly basic one that's free: http://research.et.byu.edu/llhwww/538/class.html )

You might see it as a cantilevered peice, but the force is not pushing straight down on one end of the alumnium sheet. A curve-annealed piece of Nitinol will be bonded to the alumnium and as it transforms, it will force the alumnium with it.

Thanks,
-scott

scott_alexsk said:
You might see it as a cantilevered peice, but the force is not pushing straight down on one end of the alumnium sheet. A curve-annealed piece of Nitinol will be bonded to the alumnium and as it transforms, it will force the alumnium with it.

Thanks,
-scott
If you're talking 2 metals bonded together,the plot thickens. Yoy have to do a composite material stress analysis that takes into account the different modulus of both materials.

Thanks guys, I'll get back to you if I come into any problems.
-scott

Mechanical properties of materials

Dear Scott_alexsk,

I learned a bit of materials science in my first year of mechanical engineering. U induce a certain flexural strain onto a piece of aluminium.
Let e be the amount of flexural strain and E be the Young's modulus of aluminium.
From Hooke's law for materials, we know that stress = Ee.
U need to know the cross-sectional area of aluminium in your calculation. It is better if u can roll the aluminium into a thin cylinder so that u can measure the diameter of the cross-section and use area = pi (d/2)².
After that u use the equation, applied stress = force/area. Manipulate it u get Force = applied stress x area = Young's modulus x strain x pi (d/2)² for cylindrical aluminium sheet.

Hope that helps u more in the calculation part.
Pls correct me if I'm wrong as I'm still new to this.

PhanthomJay said:
If you're talking 2 metals bonded together,the plot thickens. Yoy have to do a composite material stress analysis that takes into account the different modulus of both materials.
Not only that, but since they are bonded, you now have to deal with the adhesive layer that will not behave as the two metallic layers will. It will, most likely, play havoc with the boundary conditions between the two metals. Honestly, depending on how accurate you need to be, follow Gokul's advice and get someone to do a numerical analysis on this problem. This is not a simple beam calculation.

I'd echo what FredGarvin and PhanthomJay, and add that the answer for which one is looking will depend on the bonding (e.g. metallurgical bond) and how the stress is distrbuted. A composite beam model would give an approximate answer, if the Nitinol-Al are mated together relatively uniformly.

Does the Nitinol basically impose a shear force on the Al? Is the Nitinol bonded to all or part of the Al surface? The distribution of the load is important.

The nitinol should basically make up a composite sheet, with Al, or some other material, and should completely be bonded to that material, in order to produce a uniform change on the curve.

In the situation I am looking at the nitinol is set in a flat of strait position, while the Al is set in a curved position. When I heat the nitinol the Young's modulus of the material changes from 28 GPa to 82 GPa resulting in a change of the curve.

I found that by assuming the nitinol and the Al, each have the same thickness when bonded, ignoring the bond material, I could calculate the curve of the composite cross section (bit of a tongue twister) with a changing Young's Modulus of nitinol. However when I tried to figure in the varying thickness of the two materials in a real case, I was unable to calculate it. I mathematically determined at what strain the Al and Nitinol will reside, by simply calculating how much strain on each material, produces the same force on each other, but this only works with the same thickness to my understanding (i.e. I just starred at a piece of paper for a while to figure it out for a cross section of the material, using the Young's modulus, and flexural strain equation to figure it out).

Thanks,
-scott

## What is the formula for calculating force required for specific strain?

The formula for calculating force required for specific strain is F = k * ΔL, where F represents the force, k is the spring constant, and ΔL is the change in length or strain.

## What is the unit of measurement for force required for specific strain?

The unit of measurement for force required for specific strain is Newton (N), which is the SI unit for force.

## How do you determine the spring constant for calculating force required for specific strain?

The spring constant can be determined by dividing the applied force by the change in length or strain. This is represented by the equation k = F/ΔL.

## What factors can affect the accuracy of calculating force required for specific strain?

The accuracy of calculating force required for specific strain can be affected by factors such as the accuracy of measuring tools, variations in material properties, and external factors like temperature and humidity.

## Can force required for specific strain be negative?

Yes, force required for specific strain can be negative if the applied force causes the material to compress, resulting in a negative change in length or strain. This can occur with certain types of materials or under specific conditions.

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