Hi, probably the instron machine that you use gives you the whole history of your testing. Then the slope of first part of your curve which is essentially linear for hookean solids, gives you the young's modulus of your material. In composite materials, yield occurs together with damage; i.e. the so-called yield stress is generally the maximum stress of your curve and generally called as failure stress actually, then both ultimate tensile stress (actually this definition is a generic definition for strain hardening ductile-necking materials) and yield stress must be found the same as maximum stress. Sincerely.

Hi, hope the few statement below  that can be of some help.

1) Any mechanical test requires a valid method to measure the strain.

2) if you use the nominal strain coming from the crosshead displacement this gives rise to strong errors. Extensometers or optical methods should be used.

3) Since the strain measuremens are difficult on thin fibers I suggest performing the tests at different fiber length in order to appreciate the error due to the machine compliance.

4) In ordinary materials the yield point has nothing to do with the elastic modulus. For example at room temperature the elastic modulus of steel is always around 200GPa, while the strength of steel may vary from 250 to 2000 MPa!

5) in ordinary materials  the elastic modulus depends only on  bond energy at molecular level 

6) the elastic modulus of polymer fibers may depend strongly on the strain rate adopted to stretch the sample. Thus whatever the method you use for the determination of the Young modulus,  the chrosshead speed should be specified.

7) The elastic modulus of fiber or any other materials is determined in the linear portion of the stress-strain curve provided the strain is correctly determined, otherwise you will get wrong results.  

Modulus is an independent property. It does not depend on  strength and ultimate strain. 

First of all, Niranjan K. Naik is right.

Sure, you can calculate Young's modulus from any linear portion of stress/strain curve (as Ali Kara had written, instron machine should give you the whole history of your testing).

If to choose between tensile stress and strain at maximum load, tensile stress and strain at yield, tensile stress and strain at break then better to select pair with minimal values.

Finally, carefully read the remarks of Bradley Dodd and Alberto D'Amore, they could help to improve your investigation and gain better and more accurate results.

I suppose you are using a software that gives a tabulated test results readily (Blue Hill for eg in Instron. BYW if you are using BlueHill, it also will give the elastic modulus automatically, you may have to select the parameters to be reported prior to starting the test ). Do not go by those numbers. Get the raw test data (test history as mentioned in other posts), plot separately in a spread sheet to decide up on the elastic region. The software (neither one who writes the software) would not have studied materials science or strength of materials. All that it will do is to construct a linear line to a set of data of points as defined by the software engineer, irrespective of the scatter in the data or non-linearity. Who knows if your material (fibre) exhibits a linear or non-linear elasticity? Plot the data yourself and judge accordingly.

BYW, Elastic Modulus is related to atomic bonds and unless the parameters that alter the bond strength are changed, it is not expected to vary. What you are measuring as a slope from the elastic portion of the stress-strain curve is basically the stiffness of the material. Though in engineering sense we loosely term this as "elastic modulus" actually it is the measure of effective modulus or the stiffness of the material.