Question 3 of 7: Question III: Why Tempering Softens Martensite, and Why the As-Quenched Carbon Effect Shrinks After Tempering

Question III: Why Tempering Softens Martensite, and Why the As-Quenched Carbon Effect Shrinks After Tempering (10 marks)

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.

3.1 — (i) Why tempering reduces martensite's hardness

As-quenched martensite is a highly METASTABLE, supersaturated body-centred-tetragonal (BCT) solid solution of carbon trapped in ferrite, produced by a diffusionless shear transformation that gives no time for carbon to escape to equilibrium sites. Its very high as-quenched hardness comes from three effects that are all, in different ways, a direct CONSEQUENCE of that non-equilibrium state: (1) strong interstitial solid-solution strengthening from carbon locked into the tetragonal lattice (the same lattice distortion quantified in Question I); (2) an extremely high density of dislocations/internal twin boundaries inherited from the shear transformation itself, which strongly obstruct further dislocation motion; and (3) large internal (residual) stresses left by the transformation. Tempering supplies thermal energy for diffusion, which relaxes all three simultaneously: carbon precipitates out of the supersaturated solid solution as fine transition carbides and, at higher temperature/longer time, coarser cementite, so the tetragonal distortion relaxes toward the BCC ferrite lattice ($c/a\rightarrow1$); the dislocation/twin substructure recovers (dislocations annihilate and rearrange into a lower-energy configuration); and residual stresses relax. Even though the precipitating carbides themselves provide some renewed (particle) strengthening, that contribution is smaller than the interstitial solid-solution plus high-dislocation-density strengthening it replaces, so the NET effect of tempering is a reduction in hardness — this softening trend continues and generally accelerates as tempering temperature/time increase, until the microstructure approaches coarse, well-recovered spheroidized cementite in ferrite.

3.2 — (iii) Why the two steels' hardness difference shrinks so much after tempering

In the AS-QUENCHED condition, hardness is dominated by the interstitial solid-solution and dislocation-density effects described in 3.1, and BOTH of those scale strongly and directly with the carbon content trapped in the martensite — more dissolved carbon means more lattice distortion (a larger $c/a$ ratio, exactly the trend built into Question I's lattice-parameter equations) and a higher shear-transformation dislocation density. This is why the 0.7%C steel is so much harder as-quenched than the 0.3%C steel (HV840 vs. HV510, a HV330 gap): the underlying strengthening mechanism is itself strongly carbon-sensitive. Tempering at $540^{\circ}\text{C}$ for 1 hour, however, is a comparatively HIGH-temperature, long-time temper, well into the regime where essentially all of the excess interstitial carbon in BOTH steels has already precipitated out as carbides and the dislocation substructure in both has substantially recovered — the mechanism that made hardness so carbon-sensitive in the as-quenched state has largely been eliminated in both samples alike. What remains to distinguish the two steels is only the (much weaker) influence of total carbide VOLUME FRACTION on the resulting carbide-dispersion/ferrite-matrix hardness, and that residual effect is a far shallower function of carbon content than interstitial solid-solution strengthening ever was. The result is the well-known convergence of tempered-hardness-vs-carbon curves at moderate-to-high tempering temperatures (in contrast to the steeply carbon-dependent as-quenched curve): the large HV330 as-quenched gap collapses to a comparatively small HV40 gap after the same $540^{\circ}\text{C}$/1 h temper, because tempering removes the very mechanism (interstitial carbon in solid solution) that made the as-quenched hardness so sensitive to carbon content in the first place.