21-Mat-A5 Phase Transformations and Thermal Treatment · December 2014
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2014 — 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 discursive 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 examines fracture mechanics and fatigue-crack-growth life, strengthening and toughening of engineering materials, creep and fatigue testing, deformation processing selection, and elastic–plastic forming behaviour; it has no classical phase-transformation or heat-treatment (TTT/CCT diagram, hardenability, tempering-curve) questions. The answers below are written to the printed subject.
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.
The material chosen is a wrought, precipitation-hardened nickel-based superalloy (e.g. Inconel 718) used for a gas-turbine compressor/turbine disc, a component that must be qualified against both damage modes simultaneously in service.
Creep test procedure (ASTM E139). A cylindrical specimen with a reduced gauge section is suspended in a furnace held at a fixed elevated service-representative temperature (for this alloy, a qualification test might run at 550–650 °C), loaded in axial tension by a constant dead-weight or lever-arm system that produces a fixed nominal stress well below the alloy's room-temperature yield strength. A precision extensometer records gauge elongation continuously, often for thousands of hours, and the test either runs to rupture (a creep-rupture test, also recording time-to-rupture and reduction-in-area) or is terminated once the minimum (secondary) creep rate is well established, since that rate is what design life calculations actually use.
Fatigue test procedure (ASTM E466 / E606 for strain-controlled low-cycle work). A smooth, polished specimen (or, for a disc, a representative notched coupon) is subjected to a cyclic axial or rotating-bending load at fixed amplitude and mean stress — low-cycle fatigue (LCF) testing is strain-controlled to represent the large thermal/mechanical strains of an engine start–stop cycle, while high-cycle fatigue (HCF) testing is stress-controlled to represent the many small vibratory cycles at steady operating speed. The number of cycles to failure, $N_f$, is recorded at each stress or strain amplitude, and several nominally identical specimens are tested at different amplitudes to build a stress–(or strain–) life curve.
The two curves plot fundamentally different variables because the two damage clocks accumulate differently: creep is a continuous, time-driven process at fixed stress, so strain vs. time is the natural axis pair, with the classical primary (decelerating, as dislocation substructure builds up), secondary (near-constant minimum-rate, the stage that dominates design life) and tertiary (accelerating, as internal cavitation or necking reduces load-bearing area) stages ending in rupture. Fatigue is a discrete, cycle-driven process, so stress (or strain) amplitude vs. $\log N_f$ is the natural representation; unlike a plain-carbon steel, this nickel superalloy shows no sharp fatigue (endurance) limit — the S–N curve continues a gradual decline rather than flattening — so design practice instead quotes an endurance strength at a stated reference life (commonly $10^7$–$10^8$ cycles).
All three definitions describe the same underlying idea — the energy a material can absorb before it fails — but each is measured over a different regime of the loading history, and the numbers are not interchangeable.
(i) Toughness for purely elastic deformation — the modulus of resilience. When a material is loaded only up to its elastic limit and unloaded again with no permanent set, the "toughness" available is the elastic strain energy stored per unit volume, the modulus of resilience: $U_r=\int_0^{\sigma_y}\sigma\,d\epsilon=\sigma_y^2/2E$ for a linear-elastic material (or, for a nonlinear elastic material, the actual area under the elastic portion of the curve up to $\sigma_y$). This is the area under the stress–strain curve up to the elastic limit only, and it is the relevant "toughness" for components that must absorb energy and then spring back completely — springs, snap-fit fasteners, elastic seals.
(ii) Toughness for elastic + plastic deformation — the modulus of toughness. When permanent (plastic) deformation is acceptable up to the point of fracture, toughness is instead the total area under the entire nominal stress–strain curve from zero strain to the fracture strain, $U_t=\int_0^{\epsilon_f}\sigma\,d\epsilon$, commonly approximated for ductile metals as $U_t\approx\left(\dfrac{\sigma_y+\sigma_{UTS}}{2}\right)\epsilon_f$. This "modulus of toughness" captures both the elastic energy and, far more significantly for a ductile material, the much larger energy absorbed during plastic flow up to fracture — it is why a low-strength but highly ductile material (large $\epsilon_f$) can have a larger modulus of toughness than a much stronger but more brittle one, and is the relevant measure for crash structures, impact-resistant fittings, and any part meant to deform substantially and absorb energy without fully separating.
(iii) Toughness at fast fracture — fracture toughness. When a component already contains a crack or crack-like flaw, neither of the two smooth-specimen areas above is the governing quantity: the relevant "toughness" instead becomes the critical value of the crack-tip stress-intensity factor at the onset of unstable crack propagation, the fracture toughness $K_{Ic}=Y\sigma\sqrt{\pi a}$ evaluated at fracture (or, energetically, the critical strain-energy release rate $G_{Ic}=K_{Ic}^2/E$ for plane strain). This is the toughness definition used throughout Questions 1, 3 and 5 of this paper: it governs whether a cracked component fails catastrophically at a nominal stress far below either $\sigma_y$ or $\sigma_{UTS}$, and it is measured on a fatigue-precracked fracture-mechanics specimen (ASTM E399/E1820), not on the smooth tensile bar used for (i) and (ii).
