Materials for engineering, 3rd Edition - (Malestrom)

Determination of mechanical properties 41
2.2.2 The engineering stress–strain curve
The load–elongation curve of Fig. 2.3 may be converted into the engineering
stress–strain curve as shown in Fig. 2.4 The engineering, or conventional,
stress σ is given by dividing the load (L) by the original cross-sectional area
of the gauge length (A o ), and the strain (e) is as defined above, namely the
extension of the gauge length (l – l o ) divided by gauge length (l o ).
The maximum conventional stress in Fig. 2.3 known as the Ultimate
Tensile Stress (UTS) is defined as:
UTS = L max /A o
and this property is widely quoted to identify the strength of materials.
The tensile test also provides a measure of ductility. If the fractured testpiece
is reassembled, the final length (l f ) and final cross-section (A f ) of the
gauge length may be measured and the ductility expressed either as the
engineering strain at fracture:
e f = (l f – l o )/l o ,
or the reduction is cross-section at fracture, RA, where:
RA = (A o – A f )/A o
These quantities are usually expressed as percentages. Because much of
the plastic deformation will be concentrated in the necked region of the
gauge length, the value of e f will depend on the magnitude of the gauge
length – the smaller the gauge length the greater the contribution to e f from
the neck itself. The value of the gauge length should therefore be stated
when recording the value of e f .
2.2.3 True stress–strain curve
The fall in the engineering stress after the UTS is achieved, due to the
UTS
Engineering stress (σ)
Strain (e)
2.4 Engineering stress–strain curve.
e f