STEEL - Materials for Civil and Construction Engineers - page 115

160

1,000

Carbon 0.90%

0.64%

120

800

0.49%

600

80

0.19%

400

40

200

FIGURE 3.14 Tensile
stress-strain diagrams of hot-
rolled steel bars with different
carbon contents.

0 0

0 0.1 0.2 0.3

Strain

The large increase in length at the neck increases the true strain to a large
extent because the definition of true strain utilizes a ratio of the change in
length in an infinitesimal gauge length. By decreasing the gauge length
toward an infinitesimal size and increasing the length due to localization
in the neck, the numerator of an expression is increased while the denom-
inator stays small, resulting in a significant increase in the ratio of the two
numbers. Note that when calculating the true strain, a small gauge length
should be used at the neck, since the properties of the material (such as the
cross section) at the neck represent the true material properties. For vari-
ous practical applications, however, the engineering stresses and strains
are used, rather than the true stresses and strains.
Different carbon-content steels have different stress-strain relations.
Increasing the carbon content in the steel increases the yield stress and re-
duces the ductility. Figure 3.14 shows the tension stress-strain diagram
for hot-rolled steel bars containing carbons from 0.19% to 0.90%. In-
creasing the carbon content from 0.19% to 0.90% increases the yield
stress from 280 MPa to 620 MPa (40 ksi to 90 ksi). Also, this increase in
carbon content decreases the fracture strain from about 0.27 m/m to 0.09
m/m. Note that the increase in carbon content does not change the modu-
lus of elasticity.

Sample Problem 3.2

A steel alloy bar 100 mm long with a rectangular cross section of 10 mm * 40 mm is

subjected to tension with a load of 89 kN and experiences an increase in length of
0.1 mm. If the increase in length is entirely elastic, calculate the modulus of elasticity
of the steel alloy.