21-Mat-B6 Ceramic Materials · May 2013
Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
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.
Hardenability is a measure of how DEEP a steel can be hardened (i.e. how far below the quenched surface a substantially martensitic structure can be produced) for a given quench severity — it describes the EASE with which martensite forms throughout a section, not the maximum hardness that martensite itself can reach. Two steels can have identical maximum (surface) hardness after quenching yet very different hardenability if one transforms to non-martensitic products (pearlite/bainite) just a few millimetres below the surface while the other stays martensitic through its full cross-section. Hardenability is conventionally quantified by the Jominy end-quench test (hardness plotted against distance from the water-quenched end of a standard bar).
Carbon in solid solution in austenite slows the diffusional pearlite (and bainite) reaction — more carbon means more redistribution of carbon between the forming ferrite (low-C) and cementite (high-C) lamellae is required for the eutectoid reaction to proceed, and carbon itself lowers the driving force available at any given undercooling by stabilising austenite thermodynamically. Both effects push the pearlite/bainite "nose" of the TTT (and hence CCT) curve to LONGER times. A slower critical cooling rate is then enough to bypass the nose everywhere in the section (not just at the surface) before it can start diffusional transformation, so a HIGHER-carbon steel can be hardened to greater depth for the same quench — i.e. it has greater hardenability. (Carbon also raises the maximum ACHIEVABLE hardness at any one point, per part (iii), but that is a distinct effect from hardenability itself.)
Martensite is a diffusionless, supersaturated interstitial solid solution of carbon trapped in a body-centred TETRAGONAL (BCT), not cubic, iron lattice — the carbon atoms that would normally have partitioned into cementite during a diffusional transformation are instead frozen in octahedral interstitial sites, and they distort the surrounding lattice anisotropically, stretching it along the tetragonal $c$-axis (the $c/a$ ratio rises roughly linearly with wt% C). This lattice distortion creates strong local strain fields that strongly impede dislocation motion (interstitial solid-solution strengthening), so hardness rises with the amount of trapped carbon. More carbon in the parent austenite means more carbon trapped in the resulting martensite and a larger $c/a$ distortion, hence higher hardness — up to the practical carbon limit for fully martensitic structures (beyond roughly 0.6–0.8 wt% C the benefit saturates and retained-austenite content starts to work against it).
