A thin glaze on a thick stoneware tile becomes rigid and stress-free at

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 Hooke's law for an isotropic solid

Problem

A thin glaze on a thick stoneware tile becomes rigid and stress-free at 520∘C520^\circ\mathrm{C}, then cools with the tile to 20∘C20^\circ\mathrm{C}. The glaze has E=70 GPaE = 70\,\mathrm{GPa}, ν=0.25\nu = 0.25 and αg=7.0×10−6 K−1\alpha_g = 7.0\times10^{-6}\,\mathrm{K^{-1}}. The tile has αt=5.0×10−6 K−1\alpha_t = 5.0\times10^{-6}\,\mathrm{K^{-1}} and is thick enough that the glaze cannot alter its contraction. ((a)) The tile forces the glaze's in-plane strains to equal its own free thermal strain, ε11=ε22=αtΔT\varepsilon_{11} = \varepsilon_{22} = \alpha_t\Delta T, while the glaze's free surface keeps σ33=0\sigma_{33} = 0. Find the equal in-plane stress in the glaze, and say whether it is tensile or compressive. ((b)) A glaze left in tension crazes, cracking into a fine network. Which way must αg\alpha_g differ from αt\alpha_t for the glaze to finish in compression instead?

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