Why does a neck form in a metal sample during a tensile test?

In a tensile test, a neck forms in a ductile metal sample when the material is stretched beyond its yield stress and continues to undergo plastic deformation.12

As the test progresses past the point of yielding, the load applied to the sample reaches a maximum value. At this stage, the strain begins to localize in a specific region of the material rather than being distributed uniformly across the entire length of the sample. This localization causes the cross-sectional area in that particular region to constrict, creating a visible "neck". Once this constricted region develops, the material continues to flow plastically within the neck until it eventually reaches its limit and fractures.21

This phenomenon is a characteristic behavior of ductile metals, which are capable of significant plastic deformation before failure, as opposed to brittle materials that typically fail suddenly without such localized thinning.12