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

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When stretching a ductile material, the cross-sectional area decreases slightly in the elastic region due to Poisson's ratio, but this reduction is minimal. A more significant decrease in cross-sectional area occurs after the yield point, particularly during the strain hardening phase. The greatest reduction is observed during localized necking, which happens well beyond the yield point. This necking leads to a substantial decrease in cross-sectional area before the material ultimately fails. Understanding these behaviors is crucial for predicting material performance under stress.
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...in the elastic region? Or does the x section area decrease only after the yield point?
 
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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.
 

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