A drawn silica-glass fibre

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

Bending, Ringing, Breaking and Flowing, Ch Fracture: stress concentration, cracks and toughness

Problem

A drawn silica-glass fibre, thin enough that plane stress applies, has E=70 GPaE=70\,\mathrm{GPa} and surface energy γs=1 J m−2\gamma_s=1\,\mathrm{J\,m^{-2}}, and behaves as an ideally brittle solid. Handling leaves a surface scratch that acts as a crack of depth a=0.1 μma=0.1\,\mathrm{\mu m}; treat it, as the text treats the scratched rod, with the through-crack result, aa being its depth. ((a)) Setting G=2γs\mathcal{G}=2\gamma_s, find the fracture stress of the fibre. ((b)) Find the scratch depth that would bring its strength down to 50 MPa50\,\mathrm{MPa}.

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