21-Mat-B6 Ceramic Materials · December 2016
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 NOT the same property as hardness. Hardness describes how hard a piece of martensite is once formed; hardenability describes HOW DEEP a steel can be hardened to martensite through a given cross-section on quenching, i.e. how far the cooling rate can fall below the surface value before the transformation product changes from martensite to softer pearlite or bainite. A high-hardenability steel achieves a largely martensitic (fully hard) structure even at the slower cooling rate that prevails at the core of a thick section; a low-hardenability steel hardens fully only in a thin surface layer where the cooling rate is highest, with a soft pearlitic/bainitic core. This distinction is significant because it determines what section thicknesses, quench severities, and quenching media (water, oil, air) can be used to achieve uniform, through-section properties in a real component (shafts, gears, dies): specifying a steel by hardness alone says nothing about whether the interior of a large part will also harden. Hardenability is quantified experimentally by the Jominy end-quench test (hardness vs. distance-from-quenched-end) or expressed as the ideal critical diameter, $D_I$.
Almost every substitutional alloying element (cobalt is the notable exception) increases hardenability because it RETARDS the diffusional (pearlite/bainite) transformation, pushing the "nose" of the TTT/CCT curve to LONGER times — to the right. A slower critical cooling rate is then sufficient to miss the nose entirely and transform to martensite instead, so a much thicker section (with its inherently slower core cooling rate) can still be through-hardened. The retardation happens for several linked reasons: (1) elements like Mn, Ni, and Cr dissolve substitutionally in austenite, and for pearlite to form, these elements must partition between the growing ferrite and cementite lamellae — substitutional diffusion is far slower than carbon's interstitial diffusion, so it becomes the rate-limiting step and slows nucleation and growth; (2) these elements also alter the thermodynamics of the eutectoid reaction (shifting $A_1$ and the eutectoid composition), which can lower the driving force available at a given undercooling; (3) some alloying elements segregate to and pin prior-austenite grain boundaries, reducing the density of easy pearlite-nucleation sites. The net practical effect is a TTT/CCT nose shifted well to the right, a much lower critical cooling rate, and hence higher hardenability.
Martensite forms by a diffusionless (shear) transformation, so every carbon atom that was dissolved in the parent austenite is trapped, as-is, in the resulting body-centred TETRAGONAL (BCT) martensite lattice — carbon has no opportunity to partition out. The degree of tetragonal distortion (the $c/a$ ratio) scales directly with how much interstitial carbon is trapped: more carbon forces a larger lattice strain, which in turn produces stronger interstitial solid-solution hardening and a denser fine substructure of dislocations/twins (the substructure itself also becomes finer and more twin-dominated as carbon content rises). Both effects raise strength/hardness sharply with carbon content, essentially independent of which substitutional alloying elements are present. Substitutional elements such as Mn, Ni and Cr, by contrast, contribute comparatively little direct lattice strengthening of martensite once it has formed — their dominant role, as established in Part (ii), is ENABLING martensite to form at all through the section (hardenability), not raising the intrinsic hardness of the martensite that does form. Carbon therefore sets the ceiling on achievable martensite hardness, while alloying elements mainly determine how deep that hardness ceiling can be reached.
