21-Mat-A5 Phase Transformations and Thermal Treatment · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Paper format. National Exams, May 2013 — 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. 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. 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 premise of the question is worth stating first, because it frames all four answers. Strength tells you when a smooth, defect-free body starts to deform; toughness tells you what an already-defective body does when it is loaded. Since every real structure contains flaws — from casting porosity, from machining, from fatigue, from a dropped tool — the design-limiting property is usually the energy needed to make one of those flaws grow, not the stress needed to make a perfect specimen yield. Each of the four routes below is therefore a way of putting energy-absorbing processes between the crack tip and the material ahead of it.
In a 2xxx or 7xxx airframe alloy the toughness is limited almost entirely by the population of coarse second-phase particles, and the processing route is a campaign against them. Melt cleanliness comes first: iron and silicon form coarse, brittle constituent particles (Al$_7$Cu$_2$Fe, Mg$_2$Si) that crack at small strains and act as ready-made voids, so premium airframe grades restrict Fe and Si to a few tenths of a per cent and are degassed and filtered to remove oxide films and hydrogen porosity. This single change is what separates 2024 from the higher-toughness 2124 and 2524, and it typically buys 20–40 per cent in $K_{Ic}$ at the same yield strength.
Ageing practice comes second. A peak-aged (T6) temper gives the highest yield strength but the lowest toughness, because the shearable precipitates concentrate slip onto a few planes and the precipitate-free zone along the grain boundaries then fails intergranularly. Over-ageing to a T73 or T7451 temper coarsens the precipitates until they must be bypassed rather than sheared, which homogenises the slip, and simultaneously coarsens the grain-boundary phase; strength drops perhaps 10 per cent and toughness and stress-corrosion resistance both rise sharply.
Thermomechanical processing comes third: hot rolling with a controlled dispersoid population (Mn, Cr or Zr additions) leaves an unrecrystallised, pancake-shaped grain structure whose boundaries are strongly misoriented and which deflects a crack repeatedly out of plane. Finally, at the structural level the same objective is pursued by lamination — fibre-metal laminates such as GLARE, in which thin aluminium sheets are bonded with glass-fibre prepreg, arrest a fatigue crack in one layer by bridging it with intact fibres, and are used on the Airbus A380 upper fuselage for exactly this reason.
Monolithic ceramics have a fracture toughness of 2–4 MPa m${}^{1/2}$ because there is no dislocation plasticity to blunt a crack. Zirconia is the exception, and the reason is a stress-induced martensitic phase transformation. Pure ZrO$_2$ transforms from tetragonal to monoclinic on cooling through about 1170 °C, with a 3–5 per cent volume expansion and a shear strain of roughly 7 per cent — enough to shatter an unstabilised body. The processing trick is to add just enough stabiliser (typically 3 mol per cent Y$_2$O$_3$ for tetragonal zirconia polycrystal, or 8–10 mol per cent MgO for partially stabilised zirconia) to hold the tetragonal phase metastably at room temperature, so that it transforms only when the constraint is released.
The tensile field ahead of a crack tip is exactly such a release. Tetragonal particles within the process zone transform to monoclinic as the crack approaches; their expansion is resisted by the surrounding matrix, which therefore places the crack faces in compression and shields the tip. The apparent toughness rises to 8–15 MPa m${}^{1/2}$, three to five times the monolithic value, and the energy consumed by the transformation itself adds to the crack-growth resistance, giving a rising R-curve. The processing levers that follow are precise: stabiliser content must be controlled to a fraction of a mole per cent; the grain size must be held below a critical value (about 0.5 µm for 3Y-TZP) or the particles transform spontaneously on cooling; sintering temperature and time must be controlled to achieve that; and for Mg-PSZ a sub-eutectoid ageing treatment is used to precipitate lens-shaped tetragonal particles of the right size inside cubic grains. A parallel mechanism, microcrack toughening, is deliberately exploited in Mg-PSZ, where the transformation of larger particles leaves a field of stable microcracks that dissipate energy and deflect the main crack. The engineering caution worth stating is that transformation toughening fades above about 300–400 °C, where the tetragonal phase becomes thermodynamically stable, and that low-temperature degradation in humid service can transform the surface prematurely.
LDPE is already ductile at ambient temperature — its glass transition is near $-120$ °C, so it is far above $T_g$ in service — and the problem is not brittleness in a smooth bar but low modulus, creep, and brittle slow crack growth at notches and at low temperature. The processing route is therefore about molecular architecture and morphology.
The dominant variable is molecular weight and the density of tie molecules. A tie molecule is a chain that is incorporated into two different lamellar crystals and traverses the amorphous layer between them; it is the load path between crystallites, and it is the entity whose pull-out or scission controls slow crack growth. Raising the weight-average molecular weight, and broadening the distribution so that a long-chain tail is present, multiplies the tie-molecule density and raises the environmental-stress-crack resistance by orders of magnitude — this is precisely the difference between commodity LDPE and the PE100 pipe grades. Copolymerisation is the second lever: incorporating a few per cent of a longer $\alpha$-olefin comonomer (butene, hexene, octene) puts short branches on the backbone that are excluded from the crystal, thinning the lamellae, lowering crystallinity slightly and greatly increasing the amorphous tie-chain population — the basis of linear low-density polyethylene, which is markedly tougher than conventional LDPE at the same density.
Morphology control is the third: a fast quench and, better, a nucleating agent produce many small spherulites rather than a few large ones, and since brittle fracture in semicrystalline polymers initiates at spherulite boundaries, a fine spherulitic texture is significantly tougher. Fourth, orientation — drawing or profile extrusion with controlled draw-down — aligns chains along the beam axis and raises both modulus and toughness in that direction, at the cost of transverse properties. Finally, since the modulus of LDPE is only 0.2–0.4 GPa, a genuinely structural beam is normally a composite or a sandwich: a wood-plastic composite, a glass-reinforced grade, or a foamed core with solid skins, which raises the second moment of area rather than the intrinsic material properties.
A racing chassis must survive an impact test that dissipates a large amount of energy in a controlled way, and in a carbon-fibre-reinforced polymer the toughness comes almost entirely from mechanisms that operate at and around the fibre–matrix interface, not from either constituent. The processing route sets those mechanisms up.
Matrix toughening is the first step: a neat epoxy has $G_{Ic} \approx 100$ J m${}^{-2}$, but modifying it with dispersed rubber particles (CTBN) or, in modern aerospace and motorsport prepregs, with thermoplastic particles concentrated in the interlayer region raises $G_{Ic}$ by an order of magnitude by cavitation and shear-band formation ahead of the crack. Interlaminar reinforcement is the second: delamination is the dominant damage mode in a laminate, so the interleaf particles above, plus through-thickness stitching, z-pinning or a three-dimensional weave, put fibres across the plane where the crack wants to run. Interface control is the third and least obvious: the fibre sizing is chosen so that the interface is strong enough to transfer load but weak enough to debond ahead of the crack tip. Debonding, fibre bridging and subsequent fibre pull-out are the largest energy absorbers in the system — a perfectly bonded fibre gives a strong, brittle composite, and the deliberate weakness is what makes it tough (the Cook–Gordon mechanism). Hybridisation is the fourth: aramid or high-elongation carbon plies on the inner surface hold fragments together and prevent spalling, which is why the survival cell is a carbon–aramid hybrid rather than pure carbon. Finally, at the structural level, energy absorption is designed in through the honeycomb sandwich and the frangible nose crash structure, which dissipate energy by progressive crushing at a controlled, nearly constant force — the composite analogue of a plastic hinge.
