yield strength
Yield strength marks the moment a material stops springing back and starts to bend for keeps. Below it, load the part and it returns to shape; above it, some deformation stays behind forever. It is the single most important number for most designs, because engineers almost always want a part to keep its shape — a bent bracket or a stretched bolt has failed its job even though it has not broken.
On the stress-strain curve, yield is where the straight elastic line bends over into the curving plastic region. Many metals have no sharp corner there, so a practical definition is used: the 0.2 percent offset yield strength is found by drawing a line parallel to the elastic slope but starting from 0.2 percent strain (0.002), and reading the stress where it crosses the curve. That 0.2 percent is the small permanent set the engineer is willing to accept as the marker of yielding. Some low-carbon steels do show a distinct upper and lower yield point with a little jump.
Yield strength is hugely tunable — unlike stiffness. Alloying, cold work, heat treatment, and grain refinement can multiply it several times over (a mild steel might yield near 250 MPa, a quenched-and-tempered alloy steel above 1500 MPa), all because these make it harder for dislocations to move. The honest trade-off: raising yield strength this way almost always costs ductility, so a stronger metal is usually a less forgiving one.
A steel with no sharp yield knee is graded by its 0.2 percent offset: slide the elastic line over by 0.002 strain, and where it cuts the curve reads, say, 350 MPa — that is the yield strength the designer keeps stresses below.
The 0.2 percent offset is a practical marker for the start of permanent deformation.
Yield strength is where permanent deformation begins, well below the fracture stress — a part can 'fail' by yielding without ever breaking. It is highly changeable by processing, but raising it usually lowers ductility.