 Solution

ID: past-exam-of-the-materials-science-course-of-the-university-of-cambridge/2016/paper-1/5/a/solution

The alloy shear yield stress can be roughly

70/0.78 ≃ 90

times the stated pure-aluminium critical resolved shear stress. Strengthening raises the stress required for dislocation glide rather than requiring homogeneous shearing of a perfect crystal.

Solid-solution strengthening: substitutional solutes create elastic and chemical disturbances that interact with dislocations. A moving dislocation must escape or drag these disturbances.
Precipitation hardening: suitably spaced second-phase particles obstruct glide. Small shearable precipitates resist cutting; larger nonshearable obstacles require dislocation bowing and bypass. Particle spacing and coherency matter, so overaging can reduce strength.
Work hardening: prior plastic deformation increases dislocation density. Intersections, junctions and forest dislocations impede subsequent glide; a common scaling is $Δ τ \sim α G b ρ_{d}$ .
Grain boundary strengthening: smaller grains shorten the distance over which dislocations can pile up and make slip transfer across differently oriented grains more difficult. In its ordinary regime, the Hall-Petch relation is $σ_{y} = σ_{0} + k_{y} d^{- 1/2}$ .

These mechanisms can coexist. The numerical comparison is an order-of-magnitude comparison of shear strengths; it is not a conversion of the alloy's shear yield stress directly into a tensile yield stress.

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