Hi Raffaele,

Based on the curve you can find the elastic region. The best thing is to fit a line to your data and look into R-square. R-square higher than 95% can be assumed as linear. Using this method, when the R-square falls below 95%, it is end of elastic limit.

ASTM stated

"Offset yield strength is the stress at which the stress-strain curve deviates by a given strain (offset) from the tangent to the initial straight line portion of the stress-strain curve. The value of the offset must be given whenever this property is calculated"

Consequently, the same procedures used in tensile test can be used in flexural test, i.e. 0.2% strain  

Hi Raffaele,

The yield strength point, σy, represents the limit of the elastic region of a material, that means that, within the correspondent strain range, the sample shows an elastic behavior.  

The yield strength point can be  determined calculating the polynomial curve that better approximates the experimental points of the stress–strain curve and studying the second derivative behavior. The yield strain represents the ε value for which the second derivative nullifies.

Dear Raffaele,

Bending is not 'the best type' of tests for determining the elastic limit. During the test plastic part of the strain occur only at the outer layer of material. Because of the small plastified region of the cross-section the moment of occurring of it is difficult to observe. Moreover, if you perform bending then remember that the outer fibers are subjected to tensile and other compression. If your material behave different in tension and compression then you will get some kind of mean value (or first value) of the proportional limit. If you can I propose to use pure tension or compression and the ASTM procedure mentioned by Nawras H Mostafa.

By the way, if you apply ASTM procedure for bending stress-strain curve then your 0.2% yield strength will not be equal to 0.2% yield strength obtained from tension stress-strain.

Good luck.

From what Ive learnt, Modulus of elasticity is applicable when there is elastic deformation. A maximum of 0.2% deformation. Proportional limit is the stress limit where any stress above, will not follow Hooke's law. Stress above proportional limit will will plastic deformation and thus modulus of elasticity will not be applicable.

From what Ive learnt, Modulus of elasticity is applicable when there is elastic deformation. A maximum of 0.2% deformation. Proportional limit is the stress limit where any stress above, will not follow Hooke's law. Stress above proportional limit will will plastic deformation and thus modulus of elasticity will not be applicable.

Dear Raffaele,

The elastic behavior of a material, in general, is defined by the reversibility of the strains and stresses. In other words the plastic strains should be zero anywhere in your specimen and also residual stresses should not exist, when it is unloaded. The linear-elastic behavior is a special case of elasticity where the elastic strains (which coincide with the total strains) are in linear analogy to the stresses developed and  consequently the imposed load/displacement. This relation is defined by the elastic modulus (E) such as: σel=E*ε.

In this framework the proportional limit σο (until which the relation σel=E*ε, holds) differs from the yielding point σy (which is the onset of plastic deformations), in general. To my knowledge the proportional limit could be specified by the examination of the stress-strain relation - up to the point it remains linear-, while for the yielding point loading and unloading should be necessary to measure residual strains. 

I hope my answer is of some help to you.