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Yield, strain hardening, stress-strain diagram

Short answer

Yield is the onset of plastic deformation without load increase; strain hardening is the subsequent rise in stress due to dislocation entanglement. For brittle materials, the yield point is determined by the 0.2% offset method: a line parallel to the elastic region from 0.2% strain intersects the curve at the proof stress.

Define 'yield' and 'strain hardening' related to the tensile strength test for steel. How is the yield point of a brittle material found out from the stress/strain diagram? Draw the stress/strain diagram for ductile and brittle materials.

Yield

Yield is the stage in a tensile test of steel at which the specimen begins to deform plastically without any noticeable increase in load. The stress at this point is the yield stress. Mild steel shows an upper and a lower yield point; after the upper yield point the stress drops slightly, and the strain then increases rapidly at nearly constant stress (the lower yield point).

Strain hardening

After yielding, the dislocations in the metal multiply and become tangled, so more stress is needed to produce further strain. The curve rises again until the ultimate stress is reached. This region is called strain hardening (work hardening). Cold working of steel bars (TOR steel) uses this effect to raise the yield strength.

Yield point of a brittle material

A brittle material has no clear yield point on its stress-strain diagram. The yield point is found by the offset (proof stress) method: from a strain of 0.2% on the strain axis, draw a line parallel to the initial straight portion of the curve. The stress at which this line cuts the curve is taken as the 0.2% proof stress (yield strength).

Stress-strain diagrams

 Ductile (mild steel)               Brittle (cast iron)
 stress                             stress
   |               U                  |
   |            .-'''-.               |           x F
   |   Yu      /       \              |         .'
   |   /\_Yl__/         \             |       .'
   |  /                  x F          |     .'
   | / E                              |   .'
   |/                                 | .'
   +------------------------- strain  +-------------- strain
 E: elastic limit, Yu/Yl: upper/lower yield point,
 U: ultimate stress, F: fracture

The ductile curve shows a long plastic region and necking before fracture, whereas the brittle curve is almost linear and ends suddenly at a small strain.

✓ Answer checked by Claude Opus 5.5 (high effort)

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