ME 107 – Thermodynamics and Phase Transformations

ME 107 – Thermodynamics and Phase Transformations

October/November 1996

(a) Refer to answers for Qn 1 (a) and (c) in Oct/Nov 1997 paper.

(b) G = H – TS

(1): Free energy of a molten liquid: G^L= H^L – TS^L

(2): Free energy of a solid: G^S = H^S – TS^S

(2) – (1):

G^S - G^L= H^S – H^L – T (S^S- S^L)

(3): D G = D H - TD S

At equilibrium, D G = 0

D H = T_mDS (where T_m is the melting point of the solid)

(4): D S_m = D H/ T_m = L/ T_m (where L is the latent heat of fusion)

Subst (4) with (3):

D G = D H – TD S

= L – TL/ T_m

= L(1 – T/ T_m)

= L(T_m – T/ T_m)

= L D T/ T_m (where D T is the undercooling)

The above expression is the driving force for solidification. The greater the driving force for solidification, the smaller the size of the dendrites obtained.

(a) Refer to answers for Qn 2 (a) in Oct/Nov 1997 paper.

Refer to answers for Qn 2 (b) in Oct/Nov 1997 paper.

(a) Refer to Calister pg. 245, example problem 9.1.

(b) (i) Refer to Calister pg. 257, Figure 9.10, the microstructure at point (g).

(ii) Refer to Calister pg. 260, Figure 9.14, the microstructure at point (m).

(iii) Refer to Calister pg. 258, Figure 9.11, the microstructure at point (i).

(i) ^cooling

L à a + b

_heating

(ii) ^cooling

d à g + e

_heating

(iii) ^cooling

d + Là e

_heating

(iv) ^cooling

a + b à g

_heating

(v) ^cooling

L₁ à a + L₂

_heating

(a) Hardness and strength decrease from fine pearlite to coarse pearlite to spheroidite.

Fine pearlite	Coarse pearlite	Spheroidite
Fine alternating layers (lamellae) of ferrite and cementite.	Thicker alternating layers (lamellae) of ferrite and cementite.	Spherelike cementite particles embedded in a continuous ferrite matrix.

(Give diagrams of the 3 microstructures)

There is a great degree of adherence between the ferrite and cementite phases across the phase boundary. The strong and rigid cementite phase severely restricts deformation of the softer ferrite phase in the regions adjacent to the boundary, i.e. cementite reinforces the ferrite phase. Fine pearlite is harder and stronger than coarse pearlite because there is greater degree of reinforcement since there is a greater phase boundary area per unit volume of material for fine pearlite than for coarse pearlite. Moreover, phase boundaries act as barriers to dislocation motion. In fine pearlite, since there is more phase boundaries, there are more obstacles which dislocations must pass through during plastic deformation.

Spheroidite is even less strong and hard than coarse pearlite because of the discontinuity of the cementite plates. Hence dislocations need not pass through the hard cementite phase but can pass through the softer ferrite phase where the restricyion to dislocation motion is lesser. Hence, overall, the plastic deformation is not as constrained as in pearlite.

(b) Fine pearlite of composition between 0.45 – 0.56 wt%C.

(a) Proeutectoid ferrite is formed at temperatures above the eutectoid temperature, whereas eutectoid ferrite is formed at the eutectoid temperature. Proeutectoid ferrite is normally present as a continuous matrix phase surrounding the isolated pearlite colonies, whereas eutectoid ferrite forms alternating layers with cementite in the pearlitic colonies.

(b) (i) Wt% of proeutectoid ferrite = (0.80 - 0.40)/(0.80-.02) = 0.513 = 51.3%

(ii) Wt% of total ferrite = (6.67-0.40)/(6.67-0.02) = 0.943 = 94.3%

Wt% of eutectiod ferrite = 94.3% - 51.3% = 43.0%

(iii) Wt% of eutectoid cementite = (0.40 – 0.02)/(6.67-0.02) = 0.057 = 5.7%

6. (a)

Martensitic Transformation	Pearlitic Transformation
Diffusionless – steel is quenched sufficiently to prevent C diffusion to form cementite and ferrite. All the C is retained in solid solution. Large numbers of atoms experience cooperative movement, such that there is only a slight displacement of each atom relative to their neighbours.	Redistribution of C occurs in the steel by diffusion. Formed from the nucleation of cementite from the austenite grain boundaries. C diffuse to the cementite layers (C rich), leaving behind the ferrite rich area depleted of C.
Athermal transformation – reaction is not thermally activated. Transformation is instantaneous (martensitic grains nucleate and grow very rapidly at the velocity of sound). Extent of reaction depends on temperature.	Reaction takes time and is thermally activated.