This is a very basic mechanical engineering question. As long as the material is tested in linear elastic regime (and it is isotropic), yes, you can use a tensile test with a circular cross section to calculate the Poisson ratio µ. Just measure the strain in the transverse direction Δεtrans and the strain in the axial direction Δεaxial , and divide:
µ = - Δεtrans /Δεaxial
Poisson's ratio is a parameter, intrinsic property of the material, which can easily be determined experimentally by measuring the longitudinal relative elongations. S you can do a longitudinal tensile test on your specimen.This traction is the result of a force exerted per unit of surface ( sigma11 = F/S)
This tension naturally leads to other distortions that should be explicit by applying Hooke's law: T = lambda* theta*identity matrix + 2*µ*Young's modulus (E).
where Lambda and µ are two Lamé coefficients,
by simplifying you find that £12 = £13 = £23 = 0
£11 = £22 = - [ (Lmbda + 2* µ -E) / 2*Lambda] * £11
which give £22 / £11 = £33 / £11 = poisson's ratio
where poisson's ratio = [ (Lmbda + 2* µ -E) / 2*Lambda] > 0
I hope that helps you
Thanks all. I know it is a very basic question, but I wanted to have opinions from real researchers like you.
Yes, you can use a tensile test with a circular cross section to calculate the Poisson ratio µ. Poisson's ratio is defined as the negative of the ratio of the lateral strain to the axial strain for a uniaxial stress state.For a perfectly isotropic elastic material, Poisson's Ratio is 0.25, but for most materials the value lies in the range of 0.28 to 0.33. Generally for steels, Poisson’s ratio will have a value of approximately 0.3.
Dear Chetankumar Patel, the useful information of previous answers, particularly given by Maria Fabiola Leyva-Mendivil, may be added with some practical propositions: 1) using widespread tensile specimen of rectangular cross-section; 2) along with tension test, to aply three-point bending setup with beam-type specimen which is convenient in case of high stiffness of specimen (high elastic modulus of tested material).
These techniques presumes the application of electrotensometry method and corresponding electrical resistance sensors as well as video extensiometers for longitudional and transverse strains (or displacements) registration.
At last I should like recommend enough old but a very exact optical methods of Poisson's ratio determination which thorough described in well-known book "Encyclopedia of Physics, Vol. VI Mechanics of Solids I: 1973, by J. F. Bell (Author), C. Truesdell (Editor). All the best
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