Can Young's modulus be applied to slinky springs?

[hulk78]

Could somebody please tell me if we can apply young modulus theory to a slinky spring, or can only be applied to a rod when strenched?If possible to apply to the slinky spring, how can we calculate the elasticity of that slinky spring?by the way what is the process by which slinky springs are manufactured?(do they compress a thin metal wire in such a way that it always compresses)
Thanks in advanced

 

[Chestermiller]

Could somebody please tell me if we can apply young modulus theory to a slinky spring, or can only be applied to a rod when strenched?If possible to apply to the slinky spring, how can we calculate the elasticity of that slinky spring?by the way what is the process by which slinky springs are manufactured?(do they compress a thin metal wire in such a way that it always compresses)
Thanks in advanced

Yes. Hooke's law of stress and strain can be applied to express the spring constant of a spring in terms of Young's modulus, the Poisson ratio, and the helix angle in the undeformed state. The basic deformation kinematics is one of shear (twist) at each cross section of the wire. This problem can be analyzed using a strength of materials approach, and does not require a theory of elasticity solution.

 

[hulk78]

Yes. Hooke's law of stress and strain can be applied to express the spring constant of a spring in terms of Young's modulus, the Poisson ratio, and the helix angle in the undeformed state. The basic deformation kinematics is one of shear (twist) at each cross section of the wire. This problem can be analyzed using a strength of materials approach, and does not require a theory of elasticity solution.

So based on what you said, can I say that we can apply the Young's modulus to the material of the slinky spring itself and therefore we can see in this graph http://en.wikipedia.org/wiki/File:Metal_yield.svg
that as the limit E tends to 0 the spring gets damaged?

 

[Chestermiller]

So based on what you said, can I say that we can apply the Young's modulus to the material of the slinky spring itself and therefore we can see in this graph http://en.wikipedia.org/wiki/File:Metal_yield.svg
that as the limit E tends to 0 the spring gets damaged?

No. It's much more complicated than that. First of all, as I said, the basic deformation is not tensile. It is shear between adjacent cross sections of the wire. To figure this problem out, you need to go through an analysis of the kinematics of the deformation, and see how the shear of the cross sections translates geometrically into an axial extension of the helical spring. Then, you also need to go through a failure analysis to determine at what extension, the shear stress is high enough to cause failure of the wire. I've seen an analysis of this problem in a strength of materials book by a guy named Faupel, but I'm not sure whether the book is still in print. Try some Googles to see if you can find an analysis on line.

Chet