21-Mat-A4 Deformation Behaviour and Properties of Materials · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2017 — 12-Mtl-A4, Mechanical Behaviour and Fracture of Materials. Three hours, closed book, one approved non-communicating calculator. Eight questions of 20 marks each; the rubric marks only the first five questions as they appear in the answer book. All eight are solved here. This sitting's own printed content is fracture mechanics, fatigue crack growth, creep, toughness, strengthening, composites and plastic instability.
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.
Take aluminum (a soft, low-strength single-crystal metal on its own) as the metal of choice, strengthened as an Al–Cu wrought alloy (e.g. the 2xxx series).
Mechanism 1 — Precipitation (age) hardening. The alloy is solution heat-treated above the solvus to dissolve Cu into a single-phase $\alpha$ solid solution, quenched to trap the Cu in a supersaturated solid solution, then aged at a moderate temperature. Aging nucleates fine, coherent or semi-coherent Cu-rich zones/precipitates (GP zones, then $\theta''$, $\theta'$) throughout the matrix. A moving dislocation must either shear through a coherent precipitate (raising the stress needed to cut the ordered/strained particle) or, once precipitates coarsen and become incoherent, bow around them by the Orowan mechanism, leaving a dislocation loop behind and requiring extra stress to bulge between closely spaced particles. Both routes raise the yield stress substantially above that of the pure metal or the as-quenched solid solution.
Mechanism 2 — Grain-size refinement (Hall–Petch strengthening). Because a single crystal has no grain boundaries at all, converting it to a fine-grained polycrystal (by controlled casting/recrystallization, or by adding a grain-refining inoculant such as Al–Ti–B) introduces boundaries that block dislocation glide: a dislocation pile-up against a grain boundary raises the local stress until it is large enough to activate a source in the neighbouring grain, so smaller grains (more boundaries per unit volume) require a higher applied stress to propagate slip across the material, $\sigma_y=\sigma_0+k_yd^{-1/2}$.
Conventionally cast (equiaxed, polycrystalline) turbine blades operate at homologous temperatures around $0.8$–$0.9\,T_m$, where grain boundaries are the weakest microstructural feature: they are preferred paths for diffusional (Coble/Nabarro–Herring) creep and grain-boundary sliding, they concentrate lower-melting-point carbide/eutectic films that can locally melt or soften, and they act as easy paths for creep-cavity nucleation and intergranular fracture. Directional solidification, followed by the fully single-crystal (no-grain-boundary) casting process, removes every one of these weak paths entirely — there is no grain boundary anywhere in the blade to nucleate a creep cavity or to slide.
Because the process also grows the columnar/single-crystal structure along the low-elastic-modulus $\langle001\rangle$ direction, and the casting is oriented so that $\langle001\rangle$ lies along the blade's primary (centrifugal) stress axis, the blade combines the lowest stiffness (hence lowest thermal-fatigue stress for a given thermal strain range) with its highest creep-resistant orientation in the direction that matters most. The resulting two-phase $\gamma/\gamma'$ microstructure (coherent, ordered $\mathrm{Ni_3(Al,Ti)}$ $\gamma'$ precipitates in a $\gamma$ matrix) then provides the bulk of the high-temperature strength through precipitate/dislocation interactions, without needing any grain-boundary-strengthening additions (e.g. boron, carbon, hafnium, zirconium) that would otherwise be required in an equiaxed casting — and which themselves tend to lower the incipient-melting temperature, reducing the usable service temperature. The net result is a large improvement in creep life and thermal-fatigue resistance at the highest practical operating temperature.
