Materials for engineering, 3rd Edition - (Malestrom)

Determination of mechanical properties 39
departure from elastic behaviour (as defined above) at progressively lower
stresses, due to the presence of microstrains.
Departure from elasticity is therefore defined in an empirical way by
means of a proof stress, the value of which is independent of the accuracy of
the strain-measuring device. Having constructed a stress–strain curve as in
Fig. 2.1, an arbitrary small strain is chosen, say 0.1 or 0.2%, and a line
parallel to Young’s modulus is constructed at this strain. The point of intersection
of this line with the stress–strain curve defines the 0.1 or 0.2% proof stress
and values of this stress for different materials are available in books of
reference, since they provide an empirical measure of the limit of elastic
behaviour. In the USA this stress is known as the offset yield strength.
The Bauschinger Effect
If a metallic specimen is deformed plastically in tension up to a tensile stress
of +σ t (Fig. 2.2) and is then subjected to a compressive strain (as indicated
by the arrows in Fig. 2.2), it will first contract elastically and then, instead
of yielding plastically in compression at a stress of –σ t as might have been
expected, it is found that plastic compression starts at a lower stress (–σ c ) –
a phenomenon known as the Bauschinger Effect (BE). The BE arises because,
during the initial tensile plastic straining, internal stresses accumulate in the
test-piece and oppose the applied strain. When the direction of straining is
reversed these internal stresses now assist the applied strain, so that plastic
yielding commences at a lower stress than that operating in tension.
+ σ t
Tensile stress
–Strain
+Strain
Compressive
stress
– σ c
– σ t
2.2 Illustration of the Bauschinger Effect when the direction of
straining is reversed as indicated by the arrowed dotted line.