Problems for Chapter 9
Modeling Material Failure
9.6. Plastic Fracture Mechanics
9.6.1. Calculate values for the elastic constants , and the crack tip singularity parameter for the following bi-material interfaces:
(a) Aluminum on glass (b) A glass fiber in a PVC matrix
(c) Nickel on titanium carbide (d) Copper on Silicon
9.6.2. A center-cracked bi-material specimen is made by bonding Al to . It contains a crack with length 10mm, and is loaded to failure in uniaxial tension. It is found to fail at a stress level MPa.
188.8.131.52. Calculate the fracture toughness and the corresponding phase angle of loading, using a characteristic length
184.108.40.206. Calculate the fracture phase angle if is chosen as the characteristic length.
220.127.116.11. Calculate the distance behind the crack tip where (according to the asymptotic solution) the crack faces first overlap
9.6.3. A bi-material interface is made by bonding two materials together. The material above the interface has shear modulus and Poisson’s ratio ; the material below the crack has shear modulus and Poisson’s ratio Due to roughness, a residual stress distribution
acts on the bi-material interface. Suppose that the interface contains a long (semi-infinite) crack, with crack tip located at . Calculate the crack tip stress intensity factors as a function of the elastic mismatch parameter and other relevant parameters. Deduce expressions for the energy release rate and the phase angle.
(c) A.F. Bower, 2008