Engineering Stress (ES) is equivalent to the applied uniaxial tensile or compressive force at time, i, divided by the original cross sectional area of the specimen.
ESi = Pi / Ao
Where,
ESi = Engineering Stress at time, i
Pi = Applied Force at time, i
Ao = Original Cross Sectional Area of Specimen
True Stress (TS) is equivalent to the applied uniaxial tensile or compressive force at time, i divided by the cross sectional area of the specimen at time, i.
TSi = Pi/ Ai
Where,
TSi = True Stress at time, i
Pi = Applied Force at time, i
Ai = Cross Sectional Area of Specimen at time, i
Ductile materials undergo plastic deformation prior to rupture or break. When a ductile material is loaded beyond its Ultimate Tensile Strength, necking occurs and the cross sectional area and applied force both decrease. Thus, the Engineering Stress which is based on the original area decreases beyond the Ultimate Tensile Strength, whereas the True Stress increases, due to the necking or reduction of area that occurs to the specimen cross section.
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