Localization of stress in tensile test specimen I'm studying the mechanical (tensile) properties of metals, and my textbook (Introduction to Materials Science for Engineers by James Shackelford) says this:

The smallest area region, referred to as the gage length, experiences the largest stress concentration so that any significant deformation at high stresses is localized there.

I then learnt about necking, and again it seems that when the cross sectional area of a section decreases, more and more stress becomes localized there.
Why does stress become localized in regions with lower cross sectional areas? My textbooks seem to present this almost axiomatically, but I am in search of a physical explanation.
 A: It is a simple matter of the force required to break molecular bonds. When the cross sectional area decreases, the number of molecular bonds that must be broken decreases. In tensile tests the gage section is inserted to insure that separation occurs in a region that is easiest to study.
A: If the acceleration of points inside the specimen is small (if at all it is straining), then net force inside the specimen must be close to zero everywhere (it will be exactly zero if there is no acceleration). This means that when tension is applied to the specimen, this force must be roughly constant at all cross-sections. Now stress on a cross-section being force on it divided by its area, cross-section with smaller area must have greater stress on it. @Lewis Miller has already stated this point from molecular perspective.
A: In tensile testing, a constant tensile force is applied to a material, pulling it apart. Stress is then calculated by this general equation:
Stress = Force/Area

Force is felt evenly throughout the entire material, but stress is maximized at planes in the sample that have the smallest cross sectional area. The places where the largest stresses are found are generally where the material fails.
So, the stress is not localized, but rather maximized at the smallest cross section. The deformation that occurs is what is localized to this area.
