9.61) Using the lever rule and the phase diagram we can determine the overall composition of the alloy given the mass fraction of eutectoid ALPHA. There are TWO possibilities. In the first, we are dealing with a HYPER-EUTECTOID composition, so that the only ALPHA phase present formed BELOW the eutectoid temperature. Thus, all of the ALPHA phase comes from the eutectoid transformation, and appears in the microstructure as part of the pearlite. The lever rule equation (for a temperature just below the eutectoid temperature) is:
In the second possibility, we have a HYPO-EUTECTOID alloy, in which case there is both pro-eutectoid and eutectoid ALPHA phase present. For this case, the total amount of ALPHA phase will consist of a mass fraction due to the pro-eutectoid ALPHA and a mass fraction due to the eutectoid ALPHA. We get the mass fraction of the pro-eutectoid ALPHA from the lever rule at a temperature just above the eutectoid temperature, and the mass fraction of the eutectoid ALPHA at a temperature just below the eutectoid temperature:
At 1175 C: The green line shows the overall composition. The RED LINE shows the isotherm at approximately 1175 C. In equilibrium at this temperature are two phases:
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LIQUID of approximate composition 4.7wt%C (blue) and The microstructure might look like this: ZEROTH is the minimum information we get from the phase diagram using the lever rule: the approximate mass fractions of each phase. FIRST is using a little bit of physical insight into how the Fe3C phase will appear in the liquid (as grains nucleating from the liquid). |
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At 1145 C: The BLUE LINE shows the isotherm at approximately 1145 C. In equilibrium at this temperature are two phases:
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AUSTENITE of approximate composition 2.2wt%C (white),
and The microstructure might look like this: ZEROTH is the minimum information we get from the phase diagram using the lever rule: the approximate mass fractions of each phase. FIRST is using physical insight into how the liquid will freeze. It will undergo the EUTECTIC freezing, so we should see a EUTECTIC microstructure, with large scale lamellae of AUSTENITE and Fe3C, in addition to the pro-eutectic Fe3C that we had in the first picture. |
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At 700 C: The PURPLE LINE shows the isotherm at approximately 700 C. In equilibrium at this temperature are two phases:
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FERRITE of approximate composition 0.022wt%C (green),
and The microstructure might look like this: ZEROTH is the minimum information we get from the phase diagram using the lever rule: the approximate mass fractions of each phase. FIRST is understanding that the austenite will decompose by the EUTECTOID transformation into ALPHA + Fe3C, with a fine scale lamellar microstructure that we call PEARLITE. |
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The required answers for this problem are any of the microstructural drawings, and the following:
At 1175 C: LIQUID of approximate composition 4.7wt%C
and
Fe3C of composition 6.7wt%C.
At 1145 C: AUSTENITE of approximate composition 2.2wt%C,
and
Fe3C of composition 6.7wt%C.
At 700 C: FERRITE of approximate composition 0.022wt%C,
and
Fe3C of composition 6.7wt%C.
Solving for n and k give: n = 2.45, and k = 4.44e-4. Plug these into the Avrami equation y = 0.95 to find the time:
Time for 95% transformation = 36.5 sec.
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a) (RED) 100% martensite: Dropping rapidly to 250C produces the metastable martensite from about 80% of the austenite. Holding for 1000 seconds doesn't do anything more, as the temperature is too low for the diffusive phase transformation from the remaining austenite to ferrite and Fe3C. The final drop to room temperature completes the martensitic phase transformation from the remaining 20% austenite. b) (VIOLET) Pro-eutectoid ferrite + martensite: The 50 second hold at 700C transforms the austenite partially into pro-eutectoid ferrite (in the A + F region), but is not long enough to transform the remaining austenite into pearlite. The drop to room temperature completes the martensitic phase transformation of the remaining austenite. c) (BLUE) 100% Bainite (ferrite + Fe3C): The drop to 400C misses the nose of the austenite to pearlite transformation, but is not low enough to form martensite. Holding for 500s completely transforms the austenite into ferrite and Fe3C in the form of the ultra fine lamellae of Bainite. d) (GREEN) 100% Spheroidite: Holding at 700C for 100,000 s completes the equilibrium phase transformation from austenite to ferrite and Fe3C. Initially some of the pro-eutectoid-ferrite forms, then very coarse pearlite. The high temperatures probably allow the Fe3C to agglomerate into spherical precipitates, yielding spheroidite.
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e) (RED) Ferrite, pearlite, Bainite, and martensite: Holding at 650C produces some pro-eutectoid ferrite, plus about 75% of the remaining austenite transforming into pearlite. On dropping the temperature to 400C, and holding for 10s, about half of the reaming austenite transforms to Bainite. The final quench to room temperature takes the last small amount of austenite into martensite. f) (VIOLET) Bainite + martensite: At 450C , about 75% of the austenite transforms into Bainite. The final quench takes the last 25% of the austenite into martensite. g) (BLUE) Pro-eutectoid ferrite, pearlite, and martensite: At 625C we get a partial transformation of the austenite into pro-eutectoid ferrite, followed by medium pearlite. The final quench takes the remaining austenite into martensite. h) (GREEN) Pro-eutectoid ferrite + pearlite: At 625C we fully transform the austenite into pro-eutectoid ferrite and pearlite. The second heat treatment at 400C doesn't do anything further because we have already achieved the equilibrium phases.
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Coarse pearlite has fewer Fe3C/ferrite interfaces than fine pearlite. Fewer pinning centers for dislocations means a lower yield strength.
Spheroidite has a microstructure in which the pearlitic lamellae have coalesced into spherical precipitates, once again reducing the amount of surface area between the Fe3C and the ferrite.
