I am not sure if there is an 'approved' or standard method to convert the cross head displacement to the actual strain on the sample. However, you can develop your own method.

For this, you have to have an extra tensile specimen of your material of investigation. Run a tensile test on a regular sample until failure and record the load Vs. cross head displacement. This displacement includes closing of the space between specimen holder and the loading pin, alignment of the loading train, etc. This will occur at ~ zero load. As the load increases you strain not only the specimen but also the specimen holder and loading arrangement. You have to subtract this value from the load-displacement plot. To do that you have to run another tensile test using a very thick cross section specimen (diameter = shoulder dia of your tensile sample) that will deform only elastically when you apply the maximum load you noted during the testing of your regular specimen. You record the load vs displacement using this larger dia specimen. Subtract this data from your original load-displacement data. The resultant data may give an actual load vs elongation data of the gauge length portion of your specimen.

I don't think it would be easy considering the fact that there are localized strains in the sample during testing.

Slipping of the sample would also be a problem...

Mikheyev P.V., Mostovoy G.E., Konyushenkov A.A.

METHODICAL FEATURES OF DEFINITION OF THE MODULE OF ELASTICITY OF HIGH-MODULAR CARBON FIBRES

Moscow

At static stretching of modern high-strength fibers the dependence of the module of elasticity on base of measurement is observed. Authors explain observed effect with the impact of deformation of fibers in clips of the testing equipmentr and offer simple model for accounting of amendments.

On the example of carbon VPR-19 fibers high-quality coincidence of the data obtained by different methods – static stretching taking into account the amendment, on the composite module by the return calculation and by measurement of acoustic speed in fiber is shown.

The received results can are applied to any fibers and complex threads with the high module of elasticity from 70 to 600 GPa

Keywords: carbon fibers, the elasticity module, deformation at stretching, acoustic speed

the problem is the strain measured from the cross head movement covers all parts of the frame including grips, and the various tensile dimensions each of which would stretch according to its own stiffness and the total movement would be all of these separate displacements added together. So unless you can separate out each component then it is not possible. You would need to strain gauge the section whose strain you want, or use a contactor none contact extensometer.

I don't think that you can correlate head displacement to the strain in the sample. You must be attentive to the slipping of the sample.

Dear Subrahmanyam Adabala

did you find a method to convert

There is no method. It cannot be converted.

You can find the answer in this publication: Article Experimental characterization of the compressive mechanical ...