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Ductile and brittle stress-strain behaviour

Short answer

Ductile materials undergo large plastic strain before fracture with necking, while brittle materials fracture suddenly with little plasticity. For materials without a sharp yield point, yield strength is determined by the 0.2% offset method: draw a line parallel to the elastic portion from 0.002 strain on the axis, and the intersection stress is the yield strength.

Differentiate between ductile and brittle materials using their stress-strain curves. How is the yield strength determined for a material that has no clear yield point?

A ductile material undergoes large plastic deformation before fracture; a brittle material fractures with little or no plastic deformation.

 stress
   |    ductile           brittle
   |     ,--.              /
   |   ,'    `.           /
   |  /        x         /
   | /                  x
   |/                  /
   +------------------------> strain
BasisDuctile materialBrittle material
Plastic strain before fractureLarge (over 5% elongation)Very small (under 5%)
Yield pointPresent (or defined by offset)Usually absent
FracturePreceded by necking; cup-and-coneSudden, flat fracture, no necking
Area under curve (toughness)LargeSmall
ExamplesMild steel, copper, aluminiumCast iron, glass, ceramics, concrete
Strength in tension and compressionNearly equalCompression much higher
Failure warningGives warningNo warning

Offset yield strength

Aluminium, copper and high-strength steels show no sharp yield point. The yield strength is then taken by the 0.2% offset method:

  1. Mark a strain of 0.002 on the strain axis.
  2. Draw a line from this point parallel to the straight elastic portion.
  3. The stress at which this line cuts the curve is the 0.2% proof stress (yield strength).

✓ Answer checked by Claude Opus 5.5 (high effort)

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