21-Mat-A5 Phase Transformations and Thermal Treatment · December 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, December 2017 — 10-Met-A5, Mechanical Behaviour and Fracture of Materials. Three hours, closed book, any Casio- or Sharp-approved 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 sub-parts explicitly call for an essay-format answer, and the rubric rewards clarity and organisation, so those answers are written as structured prose rather than as note form.
Nothing on the paper is a phase-transformation or heat-treatment question in the TTT/CCT, hardenability or tempering sense; the syllabus actually examined is dislocation theory, slip and twinning, strengthening mechanisms, creep, fatigue, toughness and fracture mechanics, and deformation processing.
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 Cr-Mo low-alloy steel (e.g. ASTM A387 Grade 22), a standard power-plant piping alloy exposed to both elevated-temperature sustained load and cyclic thermal/pressure loading in service.
Creep test (ASTM E139). A cylindrical specimen is held at a fixed elevated temperature in a furnace and loaded with a constant dead-weight axial load through a lever arm, giving a constant nominal stress. Extensometers record axial strain continuously as a function of time, from load application until rupture (a creep-rupture test) or until a target strain/time is reached (a creep test proper). Multiple specimens are run at several stress/temperature combinations to build a family of curves.
Fatigue test (ASTM E466). A polished, notch-free specimen is subjected to a fully-reversed or constant-mean cyclic stress (or strain) at a fixed frequency, and the number of cycles to failure $N_f$ is recorded. Repeating the test at several stress amplitudes and plotting amplitude against $\log N_f$ builds the S-N curve. Unlike the creep test, temperature is normally ambient and each individual data point is a single number (cycles to failure), not a continuous history.
The two curves plot fundamentally different variables against different axes because the two failure modes accumulate damage differently: creep is a rate process, so strain accumulates continuously and is plotted against real time at one fixed stress; fatigue damage per cycle is nominally constant, so the natural summary statistic is the total cycle count to failure, plotted against the stress amplitude that produced it, one data point per specimen rather than one continuous trace.
“Toughness” names three different energy-absorption quantities depending on how much of the deformation is elastic, plastic or confined to a crack tip.
(i) Elastic deformation — the modulus of resilience. If deformation stays elastic, the only energy stored is recoverable strain energy, equal to the area under the stress-strain curve up to yield:
$$U_r=\int_0^{\varepsilon_y}\sigma\,d\varepsilon=\frac{\sigma_y^2}{2E}\quad(\text{J/m}^3)$$This is what matters for a spring: a good spring material combines high $\sigma_y$ with low $E$.
(ii) Plastic deformation — tensile toughness. Once the material yields, the relevant quantity is the total area under the nominal stress-strain curve to fracture,
$$U_T=\int_0^{\varepsilon_f}\sigma\,d\varepsilon\approx\left(\frac{\sigma_y+\sigma_{UTS}}{2}\right)\varepsilon_f\quad(\text{J/m}^3)$$which is one to two orders of magnitude larger than resilience because $\varepsilon_f\gg\varepsilon_y$; it is dominated by ductility. This is the energy a Charpy/Izod impact test estimates (reported in joules for a fixed specimen volume), and the everyday sense of “tough” — a material that deforms and warns rather than shattering.
(iii) Fast fracture — fracture toughness. With a sharp crack present, almost all of the surrounding material stays elastic and only a small process zone at the tip does plastic work, so the relevant measure is energy per unit area of new crack surface, $G_c$ (J/m$^2$), with stress-based equivalent
$$K=Y\sigma\sqrt{\pi a},\qquad K=K_{Ic}\text{ at fracture},\qquad G_c=\frac{K_{Ic}^2}{E'}$$The plane-strain value $K_{Ic}$ (units MPa$\sqrt{\text{m}}$, ASTM E399) is the geometry-independent material property that governs unstable fracture of a cracked structure, and is exactly the quantity computed in Question 5.
