When initially being [[Stress|stressed]], a ductile material will undergo [[Elastic|elastic]] (reversible) elongation. Once the [[Yielding|yield stress]], $\sigma_y$​, is reached the material will undergo [[Plastic|plastic]] (permanent) deformation. [[Strain]] loading or strain hardening occurs after yielding and will increase the strength of the material. Once the [[Ultimate Stress|ultimate stress]], $\sigma_u$, is reached, the ductile material will begin necking, experiencing a rapid decrease in it’s cross-section until it breaks. Brittle materials undergo the same initial elastic and plastic deformations as a ductile material but will abruptly break without necking. ![[fracture.png]]