A new petrochemical plant is being built. Pipes are required. The pipes are
• cylindrical in shape,
• 11.75 m long,
• have mean diameter of 300 mm,
• have a wall thickness of 12.0 mm, and
• are subject to a maximum internal pressure of 4.5 MPa
It has been proposed by a junior engineer that the pipes should be constructed out of heat
treated aluminium 7075-T651 alloy. This alloy has the following physical and mechanical
properties:
Density 2.80 g cm$^{-3}$
Yield strength 500 MPa
Tensile strength 572 MPa
Young's modulus 71 GPa
Fracture toughness 25.0 MPa m$^{1/2}$
During service, thermal cycling may lead to the formation of small surface cracks.
Laboratory experiments have revealed the radius of curvature of the tips of typical cracks to
be 0.20 mm.
(a) After sufficient crack growth, failure will occur. Use the information provided above
for the aluminium 7075-T651 alloy pipe to determine whether the mode of failure is
by yielding or by fast fracture. Show any calculations you make. For a cylinder,
$\sigma_{hoop} = \frac{Pr}{t}$, where $r$ is the mean radius, $P$ is the internal pressure and $t$ is the wall
thickness. You may assume $Y = 1.$
