Offset method in stress-strain relationship

Offset method: many materials (aluminium, high-strength steel, copper, cast iron) show no clear yield point, so their stress–strain curve bends gradually. In the offset method, a straight line is drawn parallel to the initial straight (elastic) part of the curve, starting from a chosen permanent strain on the strain axis (usually a 0.2% offset, i.e. $\varepsilon = 0.002$). The stress at which this line cuts the curve is taken as the proof stress (offset yield strength).

 stress
   |            ___------  curve
   |        _--'
   |      ,'  .  <- yield (proof) point
   |    ,' . /
   |   / . /   offset line, parallel to the
   |  / /      initial straight part
   | //
   |/_/____________________ strain
   O  0.002

Where it is required: for materials without a definite yield point, to define a practical yield strength for design (permissible stress = proof stress divided by the factor of safety).