04-BS-11 · May 2017
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exam 04-BS-11, Properties of Materials — May 2017. 3 hours, closed-book examination (approved Casio or Sharp calculator only). Any five of the seven questions constitute a complete paper (only the first five in the answer book are marked); all questions are of equal value. All seven questions are solved below for completeness.
Reference texts: Callister & Rethwisch, Materials Science and Engineering: An Introduction, 9th ed. (dislocations and slip / Schmid’s law, mechanical behaviour, ionic crystal geometry and the radius-ratio rule, X-ray diffraction, diffusion and Fick’s laws, polymer molecular weight, ASTM grain size, strengthening and annealing, steel heat treatment and hardenability, casting defects, ceramics, glasses and composites).
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.
Porosity. Pores lower ceramic strength in two ways: they reduce the load-bearing cross-section, and, more importantly, they act as stress concentrators and pre-existing flaws from which brittle cracks initiate. Strength falls roughly exponentially with volume fraction porosity $P$, often written $\sigma\approx\sigma_0\exp(-nP)$, so even a few percent porosity markedly weakens the material. Grain size. Because a ceramic fails from its largest flaw and the critical flaw size scales with the grain size, a finer grain gives higher strength — a Hall–Petch-like $\sigma\propto d^{-1/2}$ trend — as well as impeding what little plastic accommodation occurs. Dense, fine-grained ceramics are therefore the strongest.
Vitreous silica is a continuous three-dimensional network of SiO$_4$ tetrahedra joined at every corner by bridging oxygens. Network modifiers are oxides of the type Na$_2$O, K$_2$O, CaO and MgO added to the melt. Their metal cations do not enter the network; instead each modifier oxygen breaks a Si–O–Si bridge, creating two non-bridging oxygens and disrupting the network’s connectivity. The modifier cations sit in the interstices to balance charge. The practical effect is to lower the viscosity, softening point and working temperature of the glass, so it can be melted and shaped far more cheaply than pure silica (which needs $\sim$1700°C). The trade-off is reduced chemical durability, which is why soda–lime glass also contains CaO to restore some resistance.
Key design factors include: the fibre properties (high strength and stiffness, low density — glass, carbon, aramid); the matrix (which transfers load, protects the fibres and sets the service temperature); the fibre volume fraction (more fibre gives more reinforcement up to a packing/processing limit); the fibre orientation and length relative to the loads (continuous aligned fibres for unidirectional loading, woven or random chopped fibres for multi-axial loading, with lengths above the critical length for effective load transfer); the fibre–matrix interfacial bond (strong enough to transfer stress but able to arrest cracks); and the service environment (temperature, moisture, corrosion) together with density/cost targets. Good design tailors these so the fibres carry the load along their axis while the matrix binds and protects them.
