Problem Sheet 4: Defects in materials and plasticity

The numbers in square brackets refer to the number of the problem in your textbook.

1. [E6.4] The lattice resistance of copper, like that of most FCC metals, is small. When 10% of nickel is dissolved in copper to make a solid solution, the strength of the alloy is 150 MPa. What would you expect the strength of an alloy with 20% nickel to be?
2. [E6.5] A metal-matrix composite consists of aluminium containing hard particles of silicon carbide (SiC) with a mean spacing of 3$\mu$m. The composite has a strength of 180 MPa. If a new grade of the composite with a particle spacing of 2$\mu$m were developed, what would you expect its strength to be?
3. [E6.6] Nanocrystalline materials have grain sizes in the range 0.01-0.1 $\mu$m. If the contribution of grain boundary strengthening in an alloy with grains of 0.1$\mu$m is 20 MPa, what would you expect it to be if the grain size were reduced to 0.01$\mu$m?
4. [E6.7] Polycarbonate, PC (yield strength 70 MPa) is blended with polyester (PET; yield strength 50 MPa) in the ratio 30:70. If the strength of the blend follows a rule of mixtures, what would you expect the yield strength of this blend to be?
5. Given the enthalpy of formation of vacancies in aluminium and nickel to be 68 and 168 kJ/mol, calculate the equilibrium concentration of vacancies in these two metals at 0, 300 and 900 K.
6. Given that the shear modulus of BCC iron is 80.2 GPa and the lattice parameter of BCC iron is 2.87 $\AA$, compute the line tension of dislocations. Note that the Burgers vector is of the (1/2) <111> type.
7. Consider a cylindrical single crystal of copper with the axis of the cylinder lying in the (111) plane. Let a tensile stress of $\sigma$ be applied along the axis of the crystal. What is the resolved shear stress in any direction on the (111) plane? Does your result imply that the crystal will not be sheared irrespective of the magnitude of the applied stress? Explain.
8. In a cold-worked copper crystal, having a dislocation density of 3 x 1014 m-2, the shear stress to move a dislocation is found to be 100 MPa. What is the shear stress needed to move a dislocation in a copper crystal cold worked to a dislocation density of 2 x 1012m-2.
page revision: 2, last edited: 29 Jan 2009 12:56