A double-cantilever-beam specimen of a brittle ceramic is opened at its mouth by…
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 double-cantilever-beam specimen of a brittle ceramic is opened at its mouth by turning a screw wedged into the crack, which fixes the crack-opening displacement δ at each turn; the screw does not relax as the crack advances. The two arms have Young's modulus E=300GPa and second moment of area I=4.0×10−12m4, the specimen width (into the page) is B=10mm, and the crack currently has length a=40mm, at which the energy release rate happens to equal the fracture energy of the ceramic, G=Gc=20Jm−2, with the screw held fixed.
((a)) Using the fixed-opening result G=9EIδ2/4Ba4, predict whether the crack will run away or arrest if it advances by a small amount without the screw being turned further, and justify the prediction from dG/da.
((b)) Suppose instead the same initial opening at a=40mm had been produced instead by hanging from the arms a dead weight chosen to give that opening, and the weight is then left hanging. Would the prediction in part (a) change? Explain in terms of load control against displacement control.