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Incoming links: Precipitation hardening
Heat treatment 2026-10-20
Controlled heating, holding and cooling to change a material's microstructure and properties. Precipitation hardening and steel tempering are examples.
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.
Irradiation softening occurs when irradiation removes pre-existing strengthening obstacles faster than it creates new ones. It is particularly plausible in an initially hardened alloy, rather than an initially soft annealed reference.
In a material strengthened by cold working, the starting dislocation density is high. Irradiation-generated point defects can assist dislocation climb, rearrangement and annihilation, reducing the contribution of work hardening. A schematic estimate iswhere is the shear modulus, the magnitude of the Burgers vector, the dislocation density, and the last two terms represent precipitate and irradiation-obstacle strengthening. It is an illustrative decomposition, not an exact additive law for every alloy. A sufficiently large decrease in the pre-existing contributions can exceed the increase in .
In a material strengthened by precipitation hardening, ballistic mixing can dissolve or disorder the original obstacles. Radiation-enhanced diffusion can change their composition or accelerate coarsening; increasing obstacle spacing can reduce strength. In an ordered alloy, irradiation-induced loss of order can also remove a strengthening contribution. None of these outcomes is inevitable: irradiation can instead create new strengthening precipitates.
The required conditions therefore include an appropriate initial microstructure, enough displacement dose to modify it, and a temperature and displacement dose rate at which obstacle removal or recovery can compete with new defect accumulation. Compare with an unirradiated specimen held for the same time at the same temperature to separate ordinary thermal aging from an irradiation effect.
A drop in yield strength or hardness need not restore ductility: cavities, helium embrittlement or localization of dislocation glide can coexist with softening. Conversely, an initially annealed steel may show strong irradiation hardening under the same exposure conditions.