25-Nav-A6 Advanced Strength of Materials (25-Mec-A6) · May 2016
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
Reference texts: Kalpakjian & Schmid, Manufacturing Engineering and Technology, 8th ed.; Groover, Fundamentals of Modern Manufacturing, 7th ed.; Hibbeler, Mechanics of Materials, 10th ed.; Hibbeler, Engineering Mechanics: Statics, 14th ed.; Shigley's Mechanical Engineering Design, 11th ed.
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.
(i)(a) Why wide-freezing-range alloys make poor sand/gravity castings. A wide freezing (solidus–liquidus) range means the alloy spends a long time solidifying as a dispersed mixture of solid dendrites and liquid throughout a large fraction of the casting, rather than solidifying with a narrow, well-defined progressive front sweeping in from the mold wall. This dendritic "mushy zone" traps isolated pockets of liquid between the growing dendrite arms, which risers cannot feed because the interdendritic channels close off before solidification is complete — producing dispersed microporosity/shrinkage porosity and coarse dendritic segregation (coring) rather than a single, feedable shrinkage cavity.
(i)(b) Why the same alloys work well in die casting. Die casting injects molten metal under high pressure into a cold, high-conductivity steel die, giving very rapid, chill-dominated solidification. The short solidification time suppresses the coarse dendrite growth and macrosegregation that a wide freezing range would otherwise cause, while the sustained high injection/intensification pressure continues to feed the still-forming interdendritic network and suppress porosity that gravity feeding could not reach. Speed and pressure, not a narrow freezing range, are what make the process work.
(ii) Why leave the as-cast surface unmachined. The as-cast "skin" solidifies in direct contact with the cold mold wall and therefore cools far faster than the interior, producing a fine-grained, often harder and more wear- or corrosion-resistant surface layer than the coarser-grained core beneath it. Machining removes this beneficial chilled skin and can expose subsurface porosity or inclusions that were safely below the surface; where the as-cast surface already meets the dimensional and functional requirement (a near-net-shape casting), machining it away only adds cost while removing a layer that was doing useful work.
(iii)(a)–(b) Hot tearing. A hot tear typically appears as a jagged, intergranular crack at a geometric stress-raiser — a fillet, a thin-to-thick section change, or a re-entrant corner where a thin, quickly-solidifying section is anchored to a thicker, still-hot section. As solidification proceeds, the casting passes through a coherency point where the dendrite network becomes continuous but is still very weak, because thin films of liquid persist along the grain boundaries. If the mold, a core, or an adjoining thick section restrains the free thermal contraction of this coherent-but-still-mushy network, tensile strain is imposed on a structure that is both nearly zero-strength and non-feedable at that stage; the metal tears along the liquid-wetted grain boundaries while still partly molten, well before it has gained the strength of the fully solid state. A sketch would show a re-entrant fillet joining a thin rib to a thick boss, with a jagged crack running along the fillet root on the thin-section side, where restrained contraction concentrates strain.
(iii)(c) Alloys most prone to hot tearing. Alloys with a wide freezing range and high total solidification shrinkage — the same class flagged in part (i) as poor gravity-casting alloys — because they spend the longest time in the weak, liquid-film-wetted mushy state during which restrained contraction can tear the structure.
