In some ductile materials such as Aluminium, Copper, Mild Steel, the yield point cannot be clearly defined during tension test, therefore yield stress is Unknown. For such metals design stress called PROOF stress is calculated using offset method.
An offset of strain equal to given permissible plastic strain, eg at 0.2% for Al, is marked on the x axis of the stress-strain curve, and a straight line is drawn through this point which is parallel to the initial stress-strain curve. The intersection of straight line with the stress strain curve gives design stress called PROOF STRESS.
Some materials like High Strength Deformed (HSD) steel, brass, duralumin etc., do not show anywell defined yield point. For these materials, proof stress serves as analogous to yield stress. Proof stress is the stress that is just sufficient to produce under load, a defined amount of permanent residual strain, which a material can have without appreciable structural damage. This arbitrary value will be different for different material or different uses of same material.
It is determined from the stress-strain curve by drawing a line parallel to initial straight part or tangent of the curve and at a distance from the origin by an amount representing the defined residual strain (normally 0.1% or 0.2%) thus determining the stress at which the line cuts the curve. In specifying proof stress, the amount of permanent strain considered, should be mentioned,
i.e.,0.1% proof stress, 0.2% proof stress etc.