21-Mat-A5 Phase Transformations and Thermal Treatment · December 2015
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2015 — 10-Met-A5, Mechanical Behaviour and Fracture of Materials. Three hours, closed book, any non-communicating calculator permitted. Eight questions of 20 marks each; the rubric states that five questions constitute a complete paper and that only the first five appearing in the answer book are marked. All eight are answered here, because this set is a study resource rather than an exam script. Several questions ask explicitly for essay-format answers, and the marking scheme rewards clarity and organisation, so the answers below are written as structured prose rather than as note form.
The printed exam header reads 10-Met-A5, Mechanical Behaviour and Fracture of Materials. The paper has no phase-transformation or heat-treatment question in the classical (TTT/CCT diagram, hardenability, tempering-curve) sense; the syllabus actually examined is deformation, strengthening, creep, fatigue, fracture, toughening, deformation processing and environmental degradation.
Reference texts. The answers below are keyed to the works normally recommended for this syllabus code:
Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.
A single crystal of a pure metal is weak for exactly the reason it is useful in research: it contains almost nothing that a dislocation can be stopped by. Plastic flow begins as soon as the resolved shear stress on the most favourably oriented slip system reaches the critical resolved shear stress, $\tau_{\text{CRSS}} = \sigma\cos\phi\cos\lambda$, and in a pure face-centred-cubic metal that value is of the order of one megapascal — a thousandth of the theoretical shear strength. Every practical strengthening method is therefore a way of putting obstacles in the glide path of dislocations, and every one of them works by raising the stress needed to move a dislocation past, through, or around those obstacles.
The metal chosen here is wrought aluminium alloy AA2024 (Al–4.4Cu–1.5Mg–0.6Mn), a classic airframe sheet alloy, and the two methods described are precipitation hardening and grain-size refinement.
Method 1 — precipitation (age) hardening. The alloy is solution-treated near the top of the single-phase field (about 495 °C for 2024), so that the copper and magnesium dissolve into the aluminium lattice, then quenched to room temperature. The quench does not allow the equilibrium $\theta$ (Al$_2$Cu) and $S$ (Al$_2$CuMg) phases to form, so the alloy is left supersaturated in both solute and quenched-in vacancies. On subsequent ageing — naturally at room temperature to the T4 temper, or artificially near 190 °C to the T6/T851 tempers — the supersaturation decomposes through a sequence of metastable products (GP zones, then coherent and semi-coherent $S''$ and $S'$) before reaching the equilibrium phase. Peak strength occurs while the particles are still coherent and closely spaced: a dislocation must either cut through a particle, paying the cost of creating new particle–matrix interface and of shearing an ordered structure, or bow between particles. The bowing (Orowan) stress
$$\tau_{\text{Or}} \;=\; \frac{Gb}{L - 2r}$$rises as the interparticle spacing $L$ falls, which is why the fine, dense dispersion of an under-aged or peak-aged temper is stronger than the coarse, widely separated equilibrium precipitates of an over-aged one. The whole strength increment is therefore controlled by a heat-treatment schedule rather than by composition alone, and it can be reversed and re-applied by re-solutionising.
Method 2 — grain-size refinement. A polycrystal is stronger than the single crystal it was made from because grain boundaries are barriers to slip transmission: slip planes are misoriented across a boundary, and a dislocation pile-up in one grain must raise the stress in its neighbour sufficiently to activate a source there. The resulting size dependence is the Hall–Petch relation
$$\sigma_y \;=\; \sigma_0 + k_y\, d^{-1/2}$$where $d$ is the mean grain diameter, $\sigma_0$ the friction stress of the lattice and $k_y$ a constant characteristic of the alloy. In AA2024 the grain size is controlled by the manganese-bearing dispersoids (Al$_{20}$Cu$_2$Mn$_3$), which pin the boundaries during hot rolling and solution treatment and stop the recrystallised structure coarsening; the cold-rolled sheet then recrystallises to a fine grain size during solution treatment, and those dispersoids stop it coarsening. Grain refinement is the one strengthening mechanism that also improves toughness and lowers the ductile-to-brittle transition temperature, because the same boundaries that block slip also block cleavage crack propagation — every other mechanism on this list trades ductility for strength.
Two further points make the answer complete. First, the two mechanisms superimpose approximately additively in this alloy, so a fine-grained, naturally aged 2024-T351 sheet reaches a yield strength roughly two orders of magnitude above the pure aluminium single crystal it started from. Second, the same argument explains why single crystals are used where creep, not yield, is the limiting mode — which is exactly the subject of part (b).
A high-pressure turbine blade does not fail by yielding. It operates at metal temperatures of the order of 1000 °C under a steady centrifugal stress of a few hundred megapascals for thousands of hours, so its life is set by creep, by thermo-mechanical fatigue as the engine is throttled, and by oxidation. Grain boundaries, which were an asset in part (a), become the dominant liability in every one of those three modes.
Grain boundaries are the weak link at high homologous temperature. Above roughly $0.4\,T_m$ the boundaries themselves become the fast diffusion path and the sliding plane. Coble creep carries matter along the boundaries with a rate varying as $d^{-3}$; grain-boundary sliding accommodates the shape change; and where sliding is blocked at a triple point, cavities nucleate, link, and produce the intergranular fracture that ends a blade's life. Removing the boundaries entirely removes the mechanism. In a directionally solidified columnar blade the boundaries that remain are all parallel to the blade axis, so no boundary lies transverse to the centrifugal load; in a true single-crystal blade, grown by adding a helical grain selector or a seed above the chill plate, there are no high-angle boundaries at all.
Removing the boundaries also unlocks the chemistry and the heat treatment. Conventional equiaxed superalloys must carry carbon, boron, zirconium and hafnium to strengthen their grain boundaries. Those elements form carbides and borides that melt at relatively low temperature, which caps the solution-treatment temperature below the $\gamma'$ solvus. A single crystal needs none of them, so they are removed; the incipient-melting temperature rises, the alloy can be fully solutioned above the $\gamma'$ solvus, and the $\gamma'$ (ordered L1$_2$ Ni$_3$(Al,Ti)) can be re-precipitated as a uniform array of coherent cuboids occupying some 65–70 per cent of the volume. That cuboidal $\gamma/\gamma'$ structure, with narrow $\gamma$ matrix channels between the particles, is what actually carries the creep load: a dislocation is confined to the channels, and shearing the ordered $\gamma'$ requires the creation of an antiphase boundary. Under load the cuboids progressively coalesce into rafts normal to the stress axis, which further impedes channel glide.
Crystallographic orientation is a design variable. Directional solidification grows the blade with its $\langle 001\rangle$ direction along the blade axis, because $\langle 001\rangle$ is the elastically softest direction in a cubic nickel superalloy — its Young's modulus is well under half that of $\langle 111\rangle$ (about 125 against 300 GPa). Thermal fatigue damage during start–stop cycling is strain-controlled, not stress-controlled, so a lower modulus means a lower stress for the same imposed thermal strain and a longer thermo-mechanical fatigue life. The same orientation also presents a favourable set of octahedral slip systems to the axial load.
Secondary benefits. Boundaries are preferential sites for oxidation and hot-corrosion attack and for the diffusion of aluminium out of the coating; with no transverse boundaries, coating life and sulphidation resistance both improve. The absence of boundaries also removes the intergranular path along which a casting defect could grow.
The cost of all this is real — a single-crystal blade is cast one at a time under a controlled thermal gradient, is highly anisotropic, and must have its internal cooling passages formed by ceramic cores that survive the slow withdrawal — but the payoff is an allowable metal temperature perhaps 50 °C above an equiaxed casting, which in turn translates directly into turbine entry temperature and thermodynamic efficiency.
