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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.
9.6.2.1.
Calculate the
fracture toughness and the corresponding phase angle of loading, using a
characteristic length
9.6.2.2.
Calculate the
fracture phase angle if is chosen as the characteristic length.
9.6.2.3.
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.
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