A lamp of weight hangs from a straight steel wire of unstretched gauge length and diameter

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 lamp of weight

180\ \mathrm{N}

hangs from a straight steel wire of unstretched gauge length

2.50\ \mathrm{m}

and diameter

1.20\ \mathrm{mm}

. Take

E = 200\ \mathrm{GPa}

for the steel, and treat the wire as a uniform cylinder whose own weight is negligible and whose stress stays inside the straight (Hooke's law) part of its curve. Engineering stress and strain, referred to the unloaded dimensions, are to be used throughout. ((a)) Find the extension of the wire. ((b)) A second specimen of the same mild steel (with

E = 200\ \mathrm{GPa}

and yield stress

\sigma_Y = 250\ \mathrm{MPa}

) is pulled to a strain of

0.0150

, well past yield but still on its flat yield plateau, where the stress stays at

\sigma_Y

, and the load is then removed completely. Unloading follows a line parallel to the original straight part. What permanent strain is left? ((c)) A sheet of window glass with

E = 70\ \mathrm{GPa}

and surface energy

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

contains an internal crack of half-length

a = 0.20\ \mathrm{mm}

. Estimate the tensile stress at which the crack runs.

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