A hard-drawn copper wire of unstretched gauge length and diameter hangs vertically…

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

A hard-drawn copper wire of unstretched gauge length

1.50\ \mathrm{m}

and diameter

0.80\ \mathrm{mm}

hangs vertically and a load of

60\ \mathrm{N}

is hung from its lower end. Take

E = 120\ \mathrm{GPa}

for copper. The wire is a uniform cylinder, its own weight is negligible, and the stress stays inside the straight part of its curve. Engineering stress and strain are used throughout. ((a)) Find the extension read on the vernier. ((b)) A piece of annealed copper, a much softer form of the same metal, with

E = 120\ \mathrm{GPa}

and yield stress

\sigma_Y = 70\ \mathrm{MPa}

, is pulled to a strain of

0.020

, far beyond yield, where the stress has risen to

100\ \mathrm{MPa}

, then unloaded completely along a line parallel to the original straight part. What permanent strain is left in it? ((c)) A glass rod with

E = 70\ \mathrm{GPa}

and surface energy

\gamma_s = 1.0\ \mathrm{J\ m^{-2}}

carries an internal crack of half-length

a = 0.10\ \mathrm{mm}

. Estimate the tensile stress at which it fractures.

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