5003 Lectures - Faculty of Engineering and Applied Science

E5003 - Ship Structures I 25
© C.G. Daley
large strain behaviors
σ 2 = σ − r
At low strains steel is a linear elastic material.
However, when steel is strained to large levels, the
linear behaviour ends. Typical ship steels will
follow a stress-strain curve as shown at the left.
After yielding the stress plateaus while the strains
increase significantly. At larger strains the stress
begins to rise again, in a phenomenon called
'strain hardening'. At even larger strains the
material starts to 'neck' and eventually ruptures.
Typical yield stresses are in the range 225 to 400
MPa. Typical ultimate stresses are in the 350 to
550 MPa range.
The initial slope is the Young's modulus which is
about 200,000 MPa (200 GPa). So the strain at
yield is about 1200 to 2000 x10 -6 strain (µ-strain).
Rupture occurs at around 25% strain (300,000 µstrain).
yield criteria and equivalent stresses
In ships structures, made almost entirely of plate
steel, most stress states are essentially biaxial. In
this case we need to have a criteria for any 2D
state of stress.
The 2D von Mises criteria is plotted at left. The
curve is normally represented in terms of principal
stresses and forms an oval. The oval crosses the
axes ay the uniaxial yield stress