The best answer is to use a more robust extensometer which would not get damaged when the specimen breaks.  This is because only extensometers which are attached to the specimen over a known gauge length can correctly measure engineering strain (extension/original gauge length).   However, I guess that such a device is not available to you.  

Some test machines have a LVDT which measures the movement of the actuator if your machine has one of these then you could make use of this data.  Alternatively you could attached your own LVDT to measure the displacement of the grips or the cross head.  

Now you must remember that measuring displacement at some point of the rig is not the same as measuring extension on the specimen and there would be an error in any calculated engineering strain.   Much of this error comes from the fact that the displacement is the sum all displacements (and not only due to the strain in the specimen).  You should do your best to estimate all these other displacements and minimise this error.  For example, the extensometer measures

strain*gauge length.  

Whereas any remote measurement will measure;

strain*(effective gauge length) + (elastic displacement of load train)*length of load train.  

During elastic loading of the specimen strain is proportional to load.  

Also (elastic displacement of load train) is proportional to the same load.  

Therefore, it should be possible to estimate the

(elastic displacement of load train)*length of load train, and therefore it is possible to estimate strain*(effective gauge length).  

During elastic loading both strain estimates should be the same (after subtracting (elastic displacement of load train)*length of load train).  

Therefore, this gives you an estimate for the (effective gauge length) necessary to make your Modulus measurement from the extensometer equal to the  Modulus measurement from the remote displacement.  

Once, you know

1. The effective gauge length and

2. The (elastic displacement of load train)*length of load train

Then you can use the remote displacement to estimate strain after you have taken the extensometer off.  I would suggest you always use the extensometer to measure Modulus.  and to keep a check that your estimates of 1. & 2. are reasonable.  

Hi Michael thank you for your reply! I do have graph that shows displacement of the cross head and stress and also some successful samples that gives me the strain at failure (but most samples encountered slippage during test closer to failure).

I was wondering if its possible to use the stress vs displacement head to show the moudulus toughness difference for different sample. Though I know it will be inaccurate as there count be slippage and strain occurs across the sample.

In your answer, you mentioned load train several times. Do you mind explaining what is load train?

Dear Si

By load train I mean anything that experiences the same load as the specimen and which is between the (i) fixed point on the test rig and (ii) the measurement point at which the cross head displacement is being measured.   

Nevertheless, it does not matter too much since, all strain in the load path will be elastic and therefore all of the displacements are proportional to the load.  Therefore, since you know the load and you know the displacement you can work out the stiffness of the load train or load path, for the ELASTIC PORTION OF YOUR TEST.  

To write it as a pair of equations

Cross Head Displacement = 

Strain in specimen * length of minimum section of specimen

plus

load / stiffness of load path (everything except length of minimum section of specimen)

ALSO you know from elastic portion the extensometer: 

Extension as measured by the Extensometer = Strain in specimen * extensometer gauge length

ALSO (for linear elastic portion)

Strain in specimen = load/(area of minimum section of specimen) * Modulus

I think, you now have everything in this set of equations except for one thing only: 

"stiffness of load path (everything except length of minimum section of specimen)"

You can now find "stiffness of load path".  

And once you know this you can convert your cross head displacement data into and ESTIMATE OF Strain in specimen.  

You can check that you have it close by comparing your extensometer measurements with what you calculate from the cross head.  If the two are close for the elastic region, then you can use the strain that you calculate from the cross head to estimate what happens close to failure.  

Please remember these are only ESTIMATES of Strain.  They are not accurate and they won't be good enough for testing standards.  Nevertheless, they should give you a better understanding of what happens when your composite fails.  

Have fun with your research, publish your findings but don't make claims that can't be substantiated.