8.2 Phase Diagrams, Iron-Carbon System & Heat Treatment

8.2 Phase Diagrams, Iron-Carbon System & Heat Treatment

PRC MELE Core Focus: Phase diagrams and thermal processing are heavily tested in the MELE board exam. Mechanical engineers must be able to read equilibrium phase diagrams, perform lever rule calculations, identify invariant phase reactions, explain microstructural constituents ($Fe_3C$, $\alpha$, $\gamma$, pearlite, martensite), and select appropriate heat treatment parameters (annealing, normalizing, hardening, tempering, surface hardening).

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1. Phase Diagram Fundamentals & Gibbs Phase Rule

A phase diagram is a graphical representation of the phases present in an alloy system at equilibrium as a function of temperature, pressure, and chemical composition.

Gibbs Phase Rule

The number of operational degrees of freedom ($F$) for a system at equilibrium is given by Gibbs Phase Rule:

$$F = C - P + 2$$

where:

• $F$ = Degrees of freedom (number of internally controllable variables: temperature, pressure, composition).
• $C$ = Number of components (elements or chemically independent species, e.g., $Fe$ and $C$, so $C = 2$ for binary systems).
• $P$ = Number of phases coexisting at equilibrium.

For condensed-phase metallurgical systems operating at constant atmospheric pressure ($1\text{ atm}$), the pressure degree of freedom is fixed, yielding the Condensed Gibbs Phase Rule:

$$F = C - P + 1$$

In a binary system ($C = 2$):

• In a single-phase field ($P = 1$): $F = 2 - 1 + 1 = 2$ (both temperature and composition can vary independently).
• In a two-phase field ($P = 2$): $F = 2 - 2 + 1 = 1$ (univariant: specifying temperature fixes phase compositions).
• At an invariant point ($P = 3$): $F = 2 - 3 + 1 = 0$ (invariant: zero degrees of freedom; reaction occurs at a unique temperature and composition).

Lever Rule

In a two-phase field containing phases $\alpha$ and $\beta$, the tie-line construction and lever rule determine the weight fraction ($W$) of each phase for an alloy of overall composition $C_0$:

$$W\alpha = \frac{C_\beta - C_0}{C_\beta - C\alpha}$$ $$W_\beta = \frac{C_0 - C\alpha}{C_\beta - C\alpha} = 1 - W\alpha$$

where $C_\alpha$ and $C_\beta$ are the phase boundary compositions at the tie-line temperature.

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2. The Iron-Iron Carbide ($Fe-Fe_3C$) Equilibrium Diagram

The $Fe-Fe_3C$ system extends from pure iron ($0\% \text{ C}$) to the intermetallic compound Cementite ($Fe_3C$, $6.70\text{ wt}\% \text{ C}$).

Key Phases

1. $\alpha$-Ferrite (Ferrite): Solid solution of carbon in Body-Centered Cubic (BCC) iron. Stable up to $912^\circ\text{C}$. Maximum carbon solubility is extremely low: $0.022\text{ wt}\% \text{ C}$ at $727^\circ\text{C}$ (drops to $0.008\%$ at room temperature). Soft, ductile, magnetic.
2. $\gamma$-Austenite (Austenite): Solid solution of carbon in Face-Centered Cubic (FCC) iron. Stable between $727^\circ\text{C}$ and $1394^\circ\text{C}$. Maximum carbon solubility is $2.14\text{ wt}\% \text{ C}$ at $1148^\circ\text{C}$. Non-magnetic, highly formable.
3. Cementite ($Fe_3C$): Hard, brittle intermetallic compound containing $6.70\text{ wt}\% \text{ C}$. Crystal structure is complex orthorhombic. Hardness $\approx 68-70\text{ HRC}$.
4. $\delta$-Ferrite: High-temperature BCC solid solution stable between $1394^\circ\text{C}$ and $1538^\circ\text{C}$ (melting point of pure iron). Max carbon solubility $0.09\%$ at $1495^\circ\text{C}$.

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3. Invariant Reactions in the $Fe-Fe_3C$ System

Three distinct invariant reactions occur on the $Fe-Fe_3C$ phase diagram:

Classification of Steels and Cast Irons

• Hypoeutectoid Steels: $< 0.77\text{ wt}\% \text{ C}$ (microstructure consists of proeutectoid ferrite + pearlite).
• Eutectoid Steel: Exactly $0.77\text{ wt}\% \text{ C}$ (microstructure is $100\%$ pearlite).
• Hypereutectoid Steels: $0.77\% \text{ to } 2.14\text{ wt}\% \text{ C}$ (microstructure consists of proeutectoid cementite + pearlite).
• Cast Irons: $> 2.14\text{ wt}\% \text{ C}$ up to $6.70\text{ wt}\% \text{ C}$ (typically $2.5 - 4.0\text{ wt}\% \text{ C}$).

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4. Heat Treatment Processes

Heat treatment is the controlled heating and cooling of metals in the solid state to alter mechanical properties, refine microstructures, or relieve internal stresses.

Bulk Heat Treatments

1. Full Annealing:
   • Procedure: Heating hypoeutectoid steel $30-50^\circ\text{C}$ above $A_3$ line (or hypereutectoid steel above $A_1$), holding, followed by very slow furnace cooling ($10-30^\circ\text{C/hr}$).
   • Microstructure: Coarse pearlite + proeutectoid ferrite/cementite.
   • Purpose: Minimum hardness, maximum ductility, stress relief, optimum machinability.
2. Normalizing:
   • Procedure: Heating $30-50^\circ\text{C}$ above $A_3$ (hypoeutectoid) or $A_{cm}$ (hypereutectoid), holding, followed by cooling in still air.
   • Microstructure: Fine pearlite with refined grain size.
   • Purpose: Higher yield strength, UTS, and hardness than full annealing; eliminates columnar grains and forging segregation.
3. Process Annealing & Stress-Relief Annealing:
   • Process Annealing: Subcritical heating ($550-650^\circ\text{C}$, below $A_1$) to soften cold-worked low-carbon steel sheet/wire via recrystallization.
   • Stress-Relief Annealing: Subcritical heating ($500-650^\circ\text{C}$) to relieve residual stresses from machining, welding, or casting without phase transformation.
4. Quenching (Hardening):
   • Procedure: Austenitizing above $A_3$, followed by rapid cooling in water, brine, or oil faster than the critical cooling rate.
   • Mechanism: Suppresses carbon diffusion; FCC austenite transforms via diffusionless shear reaction into Martensite (Body-Centered Tetragonal, BCT, supersaturated solid solution of carbon in iron).
   • Properties: Extremely high hardness ($60-65\text{ HRC}$), low toughness, high internal stress, extreme brittleness.
5. Tempering:
   • Procedure: Reheating quenched martensitic steel to subcritical temperatures ($150-650^\circ\text{C}$) for $1-2\text{ hours}$, followed by air cooling.
   • Microstructure: Tempered Martensite (extremely fine dispersion of $Fe_3C$ particles in a ferrite matrix).
   • Effect: Reduces brittleness, relieves internal stresses, and restores toughness and impact strength while slightly reducing hardness.
     • Low Tempering ($150-250^\circ\text{C}$): Relieves stress ($58-62\text{ HRC}$, cutting tools).
     • Medium Tempering ($350-500^\circ\text{C}$): High elastic limit, spring steel ($40-50\text{ HRC}$).
     • High Tempering ($500-650^\circ\text{C}$): High toughness and fatigue strength ($25-35\text{ HRC}$, shafts, gears).

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5. Surface & Case Hardening Methods

When components require a hard, wear-resistant outer surface (case) backed by a ductile, tough interior (core) to absorb impact loads (e.g., gears, shafts, camshafts):

1. Carburizing (Pack, Gas, Liquid): Carbon diffusion into low-carbon steel ($0.15-0.25\% \text{ C}$) surface at $900-950^\circ\text{C}$ in a carbonaceous environment (CO gas or liquid cyanide bath). Case depth up to $1.5-2.0\text{ mm}$, followed by quenching and tempering.
2. Nitriding: Nitrogen diffusion into special alloy steel containing $\text{Al}, \text{Cr}, \text{Mo}$ at subcritical temperatures ($500-550^\circ\text{C}$) using ammonia gas ($\text{NH}_3$). Forms extremely hard alloy nitrides ($\approx 68-72\text{ HRC}$). No quenching required, producing minimal distortion.
3. Cyaniding & Carbonitriding: Simultaneous diffusion of carbon and nitrogen at $800-870^\circ\text{C}$ in a molten cyanide salt bath or gas atmosphere.
4. Induction Hardening & Flame Hardening: Localized surface heating of medium-carbon steels ($0.40-0.50\% \text{ C}$) via high-frequency electromagnetic induction coils or oxy-acetylene flames above $A_3$, immediately followed by direct water spray quenching. Chemical composition of core and surface remains unchanged.

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6. TTT Diagrams & Hardenability

Time-Temperature-Transformation (TTT / Isothermal) Diagrams

TTT curves plot temperature vs. logarithmic time for isothermal phase transformations of austenite. Key features:

• Nose of the TTT Curve: Minimum time required for Pearlite transformation to begin (around $550^\circ\text{C}$).
• Pearlite Region ($727 - 550^\circ\text{C}$): High temperatures yield coarse pearlite; lower temperatures near the nose yield fine pearlite.
• Bainite Region ($550 - 250^\circ\text{C}$): Formed by isothermal transformation between the nose and $M_s$ temperature. Microstructure consists of non-lamellar needle-like ferrite and fine $Fe_3C$ precipitates (Upper Bainite at $400-550^\circ\text{C}$, Lower Bainite at $250-400^\circ\text{C}$).
• Martensite Start ($M_s$) & Finish ($M_f$) Lines: Athermal transformation lines. $M_s \approx 220^\circ\text{C}$ for $0.80\% \text{ C}$ steel.

Hardenability & The Jominy End-Quench Test

• Hardenability: The depth to which a steel alloy can be hardened by martensitic transformation upon quenching (distinct from maximum hardness, which depends purely on carbon content).
• Jominy End-Quench Test (ASTM A255): A standard $25.4\text{ mm}$ diameter $\times 101.6\text{ mm}$ long specimen is austenitized, placed in a fixture, and quenched at one end by a controlled water jet. Hardness is measured along the length at $1/16\text{ inch}$ intervals. Alloy steels (e.g., 4340) maintain high hardness deep along the bar due to high hardenability, whereas plain carbon steels (1045) show a rapid drop in hardness away from the quenched end.

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7. Worked Engineering Calculation

Problem: A $0.45\text{ wt}\% \text{ C}$ plain carbon steel is slowly cooled from $900^\circ\text{C}$ to just below the eutectoid temperature ($727^\circ\text{C} - \Delta T$). Calculate:

1. The weight fraction of proeutectoid ferrite ($W_{\alpha'}$) formed prior to the eutectoid transformation.
2. The weight fraction of total ferrite ($W_{\alpha, \text{total}}$) at room temperature.
3. The weight fraction of pearlite ($W_P$) present at room temperature.

Given data: Carbon solubility in ferrite $C_\alpha = 0.022\text{ wt}\% \text{ C}$; Eutectoid composition $C_e = 0.77\text{ wt}\% \text{ C}$; Cementite composition $C Fe_3C = 6.70\text{ wt}\% \text{ C}$.

Solution:

1. Proeutectoid Ferrite ($W_{\alpha'}$): Calculated using tie-line between $C_\alpha = 0.022\%$ and $C_e = 0.77\%$:

   $$W_{\alpha'} = \frac{C_e - C_0}{C_e - C\alpha} = \frac{0.77 - 0.45}{0.77 - 0.022} = \frac{0.32}{0.748} = 0.4278 \implies 42.78\%$$

2. Total Ferrite ($W_{\alpha, \text{total}}$): Calculated using full tie-line between $C_\alpha = 0.022\%$ and $C Fe_3C = 6.70\%$:

   $$W_{\alpha, \text{total}} = \frac{C Fe_3C - C_0}{C Fe_3C - C\alpha} = \frac{6.70 - 0.45}{6.70 - 0.022} = \frac{6.25}{6.678} = 0.9359 \implies 93.59\%$$

3. Pearlite ($W_P$): The pearlite fraction equals the remaining austenite fraction just above $727^\circ\text{C}$:

   $$W_P = 1 - W_{\alpha'} = 1 - 0.4278 = 0.5722 \implies 57.22\%$$

   (Check via tie-line formula: $W_P = \frac{C_0 - C_\alpha}{C_e - C_\alpha} = \frac{0.45 - 0.022}{0.77 - 0.022} = \frac{0.428}{0.748} = 0.5722$. Exact match!)

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8. MELE Exam Tips