A plate under remote tension contains a central through crack of full length

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 plate under remote tension σ=90 MPa\sigma = 90\,\mathrm{MPa} contains a central through crack of full length 8 mm8\,\mathrm{mm}. Someone argues: "The geometry factor for a central crack is Y=1Y=1, so KI=σπa=90 MPa×π×0.008 m=90×0.1585 MPa m1/2=14.3 MPa m1/2K_I = \sigma\sqrt{\pi a} = 90\,\mathrm{MPa}\times\sqrt{\pi\times0.008\,\mathrm{m}} = 90\times0.1585\,\mathrm{MPa\,m^{1/2}} = 14.3\,\mathrm{MPa\,m^{1/2}}, using a=8 mma = 8\,\mathrm{mm}, the length of the crack." ((a)) Find the error in this working. ((b)) Give the correct value of KIK_I.

Browse the problem library