how does breaking stress of wire depend on material of wire

To find the stress -strain of any material the material is tested with increasing amounts of stresses and tabulated.Then a graph is made to show the stress-strain curve for the given material which is linear for small deformations.As the strain is increased the stress is not proportional to the strain , and the wire exhibits plastic behaviour where permanent deformation occurs in the wire.If the deformation is increased further the wire breaks at a point called as the fracture point, the stress corresponding to this point is called the breaking stress .This stress depends only on the material of the wire and can be estimated by the bond energy of the material atoms E, the Young's modulus Y, and the spacing between atoms r.

To break a bond between two atoms,energy that is needed per unit volume is appoximately =E/2r^3.Again assuming that breaking point is not further from the region of proportionality, then energy per unit volume given to wire =Stress^2 /2Y = E /2r^3,therefore breaking stress can be approximated as =(YE/r^3)^1/2. The actual breaking stress is tabulated experimentally and depends only on the material of wire.