http://www.engineersedge.com/material_science/heat_treatment.htm

http://www.thefabricator.com/article/metalsmaterials/making-steels-stronger

2. Strengthening mechanisms in metals

2.1 Work hardening

2.2 Solid solution strengthening and alloying

2.3 Precipitation hardening

2.4 Grain boundary strengthening

2.5 Transformation hardening

I'm agree whit the suggestions of Mr Gopikrishna Nidigonda, and I´ll invite you to think about this:

1) Can you reduce the hardness of the elements that works with the cable?

2) Can you reduce the friction (using a lubricant)?

Regards

I'm following the opinion of Enrique Isaza (the antifrictional coatings may be useful) and also propose to assume the possibility of optimization of twisting angle of strings (wires) in the cable .

All the best, Serge  

Keep in mind that increasing the strength of your steel may not help if failure occurs by fatigue since most higher-strength steels have less ductility.

@ Martin, thanks for your reply.

In this case what are the other methods for reduce the failure rates?

cf.

M. Ch. Schmidmeier: Fatigue of locked coil ropes due to bending

Fundamental investigations concerning the use of ropes in tied arch bridges

https://mediatum.ub.tum.de/doc/1239430/1239430.pdf

In your case , the following variables are there

1. Wire diameter

2. No of stands

3. Angle of twisting of steel wires

4. Type of load acting on wire. May be tensile at end or lateral load 

5. Coating or sleeve may consider on its out surface.

All these are contributing the cable wire strength. If you vary this parameter , you can have different strength of wire. 

Normally aluminum based material being used as cable wire and material selection also depends on the temperature raise.

If you go for the composite material aluminum matrix with boron may gives you good wear resistance property.