Past exam of the materials science course of the University of Cambridge 2016 Paper 1 5 a Solution 2026-10-20
The alloy shear yield stress can be roughly 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 .
- 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 .
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.
Past exam of the materials science course of the University of Cambridge 2017 Paper 1 7 d Solution 2026-10-20
The main strengthening architecture is a high volume fraction of fine, thermally stable ordered gamma prime phase precipitates in the ductile nickel-rich matrix. Their nearly matching crystal parameters allow coherent crystal interfaces, but coherence does not make them transparent to a moving dislocation: cutting disrupts chemical order and costs antiphase-boundary energy. Pairing of cutting dislocations and their interactions with narrow matrix channels raise the stress needed for deformation. For particles that are bypassed, bowing and high-temperature climb are also impeded by the precipitate spacing and interface dislocation structures.
coherency strain and differences in elastic response provide additional obstacles. Refractory substitutional solutes contribute solid-solution strengthening and can slow diffusion-controlled deformation. Single-crystal manufacture suppresses grain-boundary creep and grain-boundary cavitation. Together these mechanisms permit useful strength at temperatures where an unstrengthened nickel matrix would deform much faster. Protective oxide scales and coatings preserve load-bearing material against environmental attack; they complement, rather than replace, the internal strengthening mechanisms.
A concrete microscopic observation is the paired dislocation loops around fine precipitates in the Cambridge C263 creep micrograph: the observed defect structure supports the importance of precipitate–dislocation interactions, though one image does not by itself separate every strengthening contribution.[ref]
Nickel based superalloy: dislocation structure by H. K. D. H. Bhadeshia. creep-tested C263 micrograph and accompanying paired-loop interpretation
In-situ diffraction during stress-jump tests of a rafted AM1 single crystal also resolves evolving load partition and deformation in matrix channels, demonstrating why channel width and interface interactions matter.[ref]Dislocation Densities and Velocities within the γ Channels of an SX Superalloy during In Situ High-Temperature Creep Tests by T. Schenk and others. abstract, Sections 2–4: transmission diffraction, loading transients and channel-deformation analysis
Long exposure can coarsen or change the precipitate morphology and alter channel widths, so high strength is conditional on temperature, time and microstructural stability.