You may want to reconsider the specimen mounting technique ― not mentioned at the query enunciate. I would suggest to (previously) embed the titanium wire specimen in clear transparent acrylic resin, so that you can inspect the specimen trough the embedding resin. That may help with flexible wire.

Dear Hassan Saleem,

there are many types[1,2] of Tungsten wires (and filaments).  So, what do you know about the specifications of your (as received) Tungsten wire(s) ?

1.  http://www.made-in-china.com/products-search/hot-china-products/High_Purity_Tungsten_Wire.html

2.  https://www.alibaba.com/showroom/tungsten-wire.html

Dear Carlos,

thanks for your efforts. I appreciate that.

Yes, the wires are embedded into epoxy resin with hardening agent. Wires are prepared in shape of spiral/coil. The problem is when it comes to mechanical grinding and polishing, it seems that grinding is inducing damages especially damaging the edges of the wire cross-section. I also have reduced the grit size and forces so not to wear the wire deliberately.

Dear Ioannis,

As recieved spec: 99.95% tungsten wire.

Thanks for your response.

Dear Mr. Hassan ,

I wish you best of luck. I am confident with your intellect, this project would turn out to be great success with a bench mark findings for industry.

Regards