What happens to a metal sample after it reaches its yield stress?

When a metal sample reaches its yield stress, it transitions from elastic behavior to plastic behavior.12

In the elastic stage, the metal deforms proportionally to the applied load and returns to its original shape once the load is removed. However, once the yield stress is exceeded, the material undergoes permanent, nonreversible deformation. If the sample is unloaded after this point, it will retain a residual plastic strain or elongation.1324

As the stress increases further beyond the yield point, the following occurs:
* Plastic Flow: The material continues to change shape permanently.2
* Necking: In ductile metals, deformation becomes highly localized, leading to a visible reduction in the cross-sectional area known as necking.14
* Fracture: If the stress continues to increase, the metal eventually reaches its fracture point and breaks.12

While ductile metals can withstand significant plastic deformation before failing, brittle materials may fracture shortly after reaching the yield point.15