An aluminium tie rod of unstretched length and uniform cross-sectional area carries a…

PHYSICS · Multi-part · Fermi University Physics · Fluids & Continuum Physics · Solid continuum mechanics and complex fluids · Solid continuum mechanics and complex fluids

Fluids and Continuum Physics, Ch Mechanical properties of materials: the Young modulus, plasticity and fracture

Problem

An aluminium tie rod of unstretched length

1.80\ \mathrm{m}

and uniform cross-sectional area

25\ \mathrm{mm^{2}}

carries a steady axial pull of

1.40\ \mathrm{kN}

. Take

E = 70\ \mathrm{GPa}

for the aluminium; the rod's own weight is negligible and the stress stays inside the straight part of its curve. Use engineering stress and strain throughout. ((a)) Find the extension of the rod. ((b)) A test piece of an aluminium alloy with

E = 70\ \mathrm{GPa}

and yield stress

\sigma_Y = 95\ \mathrm{MPa}

is pulled to a strain of

0.0080

, past yield, where the stress has risen to

110\ \mathrm{MPa}

, and then unloaded completely along a line parallel to the original straight part. What permanent strain remains? ((c)) A brittle ceramic with

E = 300\ \mathrm{GPa}

and surface energy

\gamma_s = 2.0\ \mathrm{J\ m^{-2}}

contains an internal crack of half-length

a = 50\ \mathrm{\mu m}

. Estimate its fracture stress.

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