I could not find the attachment (May be you forgot it). You are not mentioning how the strain was measured (strain gauge, DIC, etc). Compression test are not the preferable method to measure the elstic modulus, because there are many challenges in the test. First, You should guaranted a complete unixal stress state in the zone where the strain is measured. Second, the specimen should be large enoguh to avoid local efects of the load points. Third, if the load is not perfectly uniform, you will get some asymetric bending, and you will need to discard this effect, then you probably need to measuring the strain in four points of the specimen.  

Dear Chirag,

There are low modulus Ti alloys, especially those used in bioimplants that have elastic moduli in the range you mentioned. So possibly your results are not far off the mark.

In general, compression tests are not ideal for modulus measurements because specimens are not usually gripped, so errors due to imperfect lubrication and slipping can cause measurements at low deformation to be error-prone, in addition to the errors mentioned by Richard Moran. Nevertheless, a compression test should still give you a reasonable estimate.

If you are not using extensometer it is not possible to obtain correct value of Young's modulus (or it is very hard). The machine is not perfectly stiff so when you are applying pressure on sample the anvils and every part of machine bends as well a little and it is enough to decrease the measured value of Young's modulus. You can use strain gauges glued to the sample, these are not very expensive and should give you good results.

https://www.hbm.com/en/4561/ly-linear-strain-gauges-with-1-measurement-grid/

Thank you very much Richard Moran, Aashranth B and Mr Cios for your valuable suggestions. I am sending the stress strain curve of my samples.

I have to add that I have not used any strain gauge or DIC. I just tested my samples without strain gauges but load cells of instron machine are very accurate. So, will the extension given by Instron Bluehill be accurate?

At this moment, I do not have strain gauges. This plot is made without strain gage and extensometer.

The problem with extensometer in compression test is the length of my clip on extensometer end is 25 mm and my sample length is 15 mm. So, when we go for compression, the compression crosshead wheels will touch extensometer and so how it can be used?

Please give your suggestion. How can I measure Young's modulus without strain gauge or using clip on-extensometer?

Make compression test without sample, just compress the anvils together without putting sample. You will see that the anvils and machine bends a little bit and if you record the curve of machine "bending" you can then subtract it from your samples' compression curves (force vs displacement) and check the Young modulus. You can also test several samples of different materials (Cu, Al, Fe,) with known Young modulus (with exactly the same machine configuration and sample size) and you will be able to estimate the modulus +-15 GPa probably.

Thanks a lot for your valuable answer. I was looking for the same.

I have a doubt that if I will start compression test without putting my sample to record bending, the software will give too many points of load and extension..

Then how to get machine Bending from these datas. Please suggest.

Thanks

Recalculate the stress from compression tests to force move anvils to position when they touch each other (for example with force of 10 N) and run compression test up to maximum force of the compression experiment (the one with your titanium sample). Paste the compression data and "bending" data to excel (displacement vs force) and subtract bending from compression test and calculate the Young's modulus again.

As your interest is in correcting the machine compliances and getting more accurate values, please also have a look at this paper: 

https://www.researchgate.net/publication/226271361_Accurate_Characterization_of_Machine_Compliance_for_Simple_Compression_Testing/amp

It compares three methods of doing the correction, including the one that Grzegorz elucidated.

Article Accurate Characterization of Machine Compliance for Simple C...

Dear colleague, I may add the simple technique:

Try to aggregate two specimens in axial direction to obtain their total length about "the length of my clip on extensometer end is 25 mm". This allows you to apply available extensometer and satisfy requirement of uniaxial compression better. Some error (underestimation of Young modulus of tested material) will be expected due to contact deformation between these specimens and increasing of bending factor, but I hope this error will be small because you have mentioned  "... polished its surfaces and made completely flat".

Thanks a ton Aashranth B and Serge V. Shil’ko

Dear Sir,

I think the ASTM E111 - 04 (2010) and related standards may be useful in your work. In my opinion, the ultrasonic technique is better.

greetings

M. Wrobel

Thank you very much Aashranth B.

I read the paper you sent me related to machine compliance.

It is really a good technique. Thanks for your answer

Thanks Wrobel for your answer. i will go through ASTM E111-04.

Unfortunately, we dont have Ultrasonic measuring instrument for elastic modulus.

What about the results using extensometer or strain gages?

As far as I know, without extensometer errors can be made up to 20%.

I also recommend to use one small electrical strain gauge. Normally it can be used over 0.2% strain. 

But compliance of ASTM E111 - 04 is mandatory.

Additionally, it is advisable to grease the two ends of specimen in contact with testing machine (where friction occurs - because of this for ductile materials the specimen has the shape of a barrel at the end of test). 

Of course, some materials do not have the same Young's modulus in tension and compression.

Greetings,

Paul

you can use

ASTM E111 - 17 to calculate Young"s modulus