21-Mat-B6 Ceramic Materials · December 2015
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. Its practical significance is that it tells the heat treater what SECTION SIZE and what quench severity are needed to through-harden a given part; hardenability is conventionally quantified by the Jominy end-quench test (hardness plotted against distance from the water-quenched end of a standard bar).
Mn and Cr are SUBSTITUTIONAL alloying elements dissolved in the austenite, and both retard the diffusional decomposition of austenite to ferrite/pearlite (and bainite) through two combined effects. First, being substitutional solutes their own diffusivity in austenite is far slower than carbon's interstitial diffusivity, so as the pearlite/ferrite interface advances it must drag or locally rearrange these slow-moving solute atoms (solute drag), throttling the interface velocity. Second, Cr in particular is a strong carbide former: instead of the eutectoid reaction only needing to redistribute carbon between the forming ferrite (low-C) and cementite (high-C) lamellae, an alloy carbide now also requires Cr to partition into it, adding a second, slower diffusional requirement on top of carbon partitioning. Both effects push the pearlite/bainite "nose" of the TTT (and hence CCT) curve to LONGER times, exactly the same nose-shifting outcome that increasing carbon content produces (Question III's own logic), but achieved here via substitutional-solute drag and alloy-carbide partitioning rather than via carbon's thermodynamic stabilization of austenite. A slower critical cooling rate is then enough to bypass the nose everywhere through the section, i.e. greater hardenability.
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, the same mechanism as the $k(C)^{1/2}$ term of Question III), so hardness rises with the amount of trapped carbon. Substitutional alloying elements such as Mn and Cr, by contrast, mainly control WHETHER martensite forms at all through a section (hardenability, part (ii)) rather than how hard the martensite is once it has formed — their own solid-solution contribution to hardness is comparatively small next to carbon's interstitial effect. 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).
