As we stretch a ductile material, does the x section area decrease

[theBEAST]

...in the elastic region? Or does the x section area decrease only after the yield point?

 

[PhanthomJay]

There is some small reduction in cross section in the elastic region due to poisson's ratio, but it is very small compared to the reduction in cross section area beyond the yield point, and such reduction becomes greatest well after the yield point, in the area beyond the strain hardening portion (for steel) of the stress-strain curve, where localized 'necking' significantly decreases the cross section area prior to failure.