Question 7 of 7: Material selection for a reusable water bottle

Question 7: Material selection for a reusable water bottle (15 marks)

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.

Part A — Three candidate materials and their challenges (3 marks)

AISI 304 (18-8) austenitic stainless steel. Challenges: it is heavy — density 7.9 Mg/m³, about six times that of the polymer candidate — so a single-wall bottle is noticeably heavier than a plastic one and a vacuum-insulated one heavier again; it is the most expensive of the three per bottle; deep drawing to a bottle form needs several draw stages with interstage annealing because of its high work-hardening rate; any weld or seam is a hygiene and corrosion risk and must be smooth and passivated; and in single-wall form it conducts heat, so a hot drink makes the outside too hot to hold and a cold one sweats.

Tritan copolyester (a bisphenol-A-free copolyester). Challenges: modest stiffness at 2.1 GPa means thick walls, and creep under sustained load must be considered; the service temperature is limited to roughly 90 to 95 °C, which restricts boiling-water fills and some sanitising cycles; it scratches, and scratched polymer retains odour and harbours biofilm; environmental stress cracking is a real risk with certain detergents and with citrus or ethanol-containing contents; and it is a copolyester rather than a commodity resin, so kerbside recycling streams generally do not accept it and it is a contaminant in the polyethylene terephthalate stream.

3003-H14 aluminium with an internal polymer lining. Challenges: bare aluminium is attacked by acidic contents and imparts a metallic taste, so the liner is not optional and its integrity governs the safety of the whole product; a dent that cracks the liner condemns the bottle, and aluminium dents easily at the wall thicknesses that make it attractive; the liner cure adds a thermal process step and a volatile-organic-compound control problem; and the liner makes the bottle a mixed-material article that is much harder to recycle than the metal alone.

Part B — How the material choice drives the design (3 marks)

The material fixes the wall thickness, and the wall thickness then propagates through the whole product. A stiffness-limited wall in stainless steel can be about 0.5 mm; in Tritan it has to be nearer 1.6 to 2.0 mm to reach comparable panel stiffness, which changes the internal-to-external volume ratio, the mouth diameter and the grip. Threads are moulded integrally in the polymer but must be rolled or formed into a separate collar and welded on the steel bottle, so the closure design and the sealing strategy are different problems in the two materials. Vacuum insulation is available only in the metal versions, so if hot retention is a requirement then a double-wall steel construction is effectively mandated and the mass penalty follows. Drop performance differs in kind rather than degree: the steel bottle dents and survives, the polymer bottle flexes and recovers but can craze at a stress concentration, and the lined aluminium bottle can fail invisibly by cracking its liner. Colour and finish are moulded-in for the polymer but require powder coat or anodising on the metals, which adds a process and a scratch-resistance requirement.

Part C — How the material choice drives the manufacturing process (3 marks)

Stainless steel: blank, then multi-stage deep draw or impact extrusion, interstage anneal, trim, neck-form or spin the shoulder, weld and dress the collar, electropolish and passivate, then leak-test. Tooling is moderate in cost, cycle times are seconds per stage across a transfer press, and the process is forgiving of volume because draw tooling is repairable. Tritan: injection-mould a preform, then injection stretch blow mould to final shape, with in-mould threads and no secondary joining; tooling is expensive and a multi-cavity mould is a major capital item, but the cycle is on the order of ten to fifteen seconds for several cavities at once, so unit cost collapses at volume and the process only makes sense above a break-even quantity. Lined aluminium: impact-extrude the slug, iron and neck the body, spray or roller-coat the internal liner, cure it in an oven, then decorate and inspect — and the liner cure is the rate-limiting and quality-limiting step, with pinhole detection required on every unit. The general rule is that the polymer route has the highest fixed cost and the lowest variable cost, so the choice of material is also a choice of the volume at which the business works.

Part D — A material selection framework, applied (6 marks)

The framework is Ashby's, in four steps: translate the design requirement into function, objective, constraints and free variables; screen on the constraints, which are pass or fail; rank the survivors by a material index derived from the objective; and document, by seeking supporting information on the shortlisted candidates before committing.

Step 1, translate. Function: a thin-walled pressure-free container that must resist denting and be stiff enough not to buckle when gripped. Objective: minimise mass for a given panel stiffness. Constraints: food contact safe and taste-neutral; dishwasher capable; tolerant of drops from about 1.5 m; no leaching; recyclable at end of life. Free variable: wall thickness.

Step 2, screen. Borosilicate glass passes on hygiene and taste and fails outright on drop resistance, so it is eliminated before ranking; unlined aluminium fails on taste and corrosion; polycarbonate is excluded on the bisphenol-A constraint. Three candidates survive.

Given. Modulus, density and yield strength for the three surviving candidates, and a bottle wall treated as a panel of fixed area whose thickness is free.

Find. The material index that ranks the candidates, and whether the ranking is sensitive to how the wall is idealised.

1. Derive the index for the correct loading mode. For a panel of fixed area and free thickness $t$, bending stiffness goes as $Et^{3}$ and mass as $\rho t$; eliminating $t$ gives $m \propto \rho/E^{1/3}$, so the index to maximise is $M_{1}=E^{1/3}/\rho$. For a beam of free section the same elimination gives $M_{2}=E^{1/2}/\rho$ instead — a different exponent for a different idealisation.
2. Evaluate the panel index. With $E$ in GPa and $\rho$ in Mg/m³: steel $193^{1/3}/7.90 = 5.779/7.90 = 0.732$; Tritan $2.10^{1/3}/1.18 = 1.281/1.18 = 1.085$; aluminium $69^{1/3}/2.73 = 4.102/2.73 = 1.502$, so $$\boxed{M_{1}:\ \text{aluminium }1.502 \succ \text{Tritan }1.085 \succ \text{steel }0.732}$$
3. Check the sensitivity to the idealisation. Using the beam index on the same data gives steel $193^{1/2}/7.90=1.759$, Tritan $2.10^{1/2}/1.18=1.228$ and aluminium $69^{1/2}/2.73=3.043$: the wrong exponent flatters the metals enough to move steel above Tritan. A bottle wall is a panel, so $M_{1}$ is the right index and the beam result is a trap.
4. Add the dent-resistance index. Denting is a yield event in a panel, for which the corresponding index is $\sigma_{y}^{1/2}/\rho$: steel $250^{1/2}/7.90=2.001$, Tritan $50^{1/2}/1.18=5.992$, aluminium $145^{1/2}/2.73=4.411$. On mass-normalised dent resistance the polymer leads, which is why the light bottle in a backpack is usually plastic.

Step 4, document — and let the whole brief decide. The indices rank one objective, minimum mass, and the brief has five. Supporting information now enters: food contact acceptability under Health Canada's food packaging materials guidance and NSF/ANSI 51; dishwasher and repeated-sanitising performance; scratch and odour retention over a two-year life; and end-of-life route, where 304 stainless has an established high-value recycling stream, aluminium has one that the liner compromises, and the copolyester has effectively none in Canadian kerbside collection. Those enter a weighted matrix on the same discipline used in Question 1 — weights fixed first, ratings 1 to 5 afterwards.

Computing the first column, $0.15(2)+0.25(5)+0.20(5)+0.20(3)+0.20(5)=4.15$, and the others the same way, $$\boxed{\text{304 stainless } 4.15 \succ \text{lined aluminium } 3.70 \succ \text{Tritan } 3.35}$$

Selection: AISI 304 stainless steel, in a double-wall vacuum construction, for a bottle intended for daily use over many years. The material index says it is the worst choice on mass, and that is a genuine finding rather than something to hide — the bottle will be the heaviest of the three. It wins because four of the five weighted criteria are about lasting, staying clean and being recyclable, and mass carries only 0.15. Had the brief been a bottle to be carried up a mountain, mass would take 0.40 or more and the ranking would invert, which is exactly the sensitivity check the framework demands. Stating the functional unit — one bottle serving one user for five years — before selecting is what makes the answer defensible.