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The fracture strength of glass may be increased by etching away a thin surface e layer. It is believed that the etching may alter the surface crack geometry (i.e.reduce crack length and increase the tip radius). Calculate the ratio of the original and etched crack tip radii for a five-fold increase in fracture strength ifone third of the crack length is removed.
For this problem use the approximation that σ_{m}= 2σ_{o}√(a/ρ_{t})
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