Phase Transformations and Heat Treatment

Introduction

Phase transformations are changes in the structure, composition, or state of a material that occur when temperature, pressure, composition, or time changes. In engineering materials, these transformations control grain size, phase constitution, hardness, strength, ductility, toughness, wear resistance, and dimensional stability. Heat treatment is the controlled heating and cooling of a material to produce a desired microstructure and property combination without changing the component’s overall shape.

The subject is central to mechanical engineering because two steels with the same chemical composition can have very different properties if they are cooled at different rates. Similarly, aluminum alloys can be strengthened by forming finely distributed precipitates, while surface treatments can produce a hard wear-resistant exterior over a tough interior.

Learning Objectives

After studying this chapter, you should be able to:

• explain nucleation, growth, solidification, and diffusion-controlled transformation;
• interpret binary phase diagrams and identify eutectic and eutectoid reactions;
• distinguish equilibrium from non-equilibrium transformations;
• use TTT and CCT diagrams to predict products of austenite transformation;
• describe annealing, normalizing, quenching, tempering, precipitation hardening, and surface hardening;
• select a suitable heat treatment for a mechanical component;
• evaluate practical limitations such as distortion, cracking, residual stress, and scale formation.

1. Thermodynamic and Kinetic Foundations

1.1 Phase and microstructure

A phase is a physically and chemically homogeneous region with a distinct structure and composition. In iron–carbon alloys, ferrite, austenite, cementite, and liquid are examples of phases. A microstructure is the spatial arrangement, size, shape, and distribution of phases and defects.

A phase transformation may involve:

1. a change in crystal structure, such as body-centered cubic ferrite changing to face-centered cubic austenite;
2. a change in composition, such as formation of cementite from carbon-rich regions;
3. a change in morphology, such as coarsening of precipitates;
4. a change in state, such as solidification from liquid to solid.

1.2 Driving force and free energy

At constant temperature and pressure, a transformation is thermodynamically favorable when it lowers Gibbs free energy. The Gibbs free energy is

where G is Gibbs free energy, H is enthalpy, T is absolute temperature in kelvin, and S is entropy. The equation applies to a system at specified temperature and pressure.

A transformation proceeds spontaneously toward the phase or combination of phases having the lowest possible free energy. However, a thermodynamic driving force does not guarantee rapid transformation. The material must also overcome an activation barrier, and atoms must move by diffusion or coordinated shear.

1.3 Nucleation

Nucleation is the formation of small regions of a new phase. Homogeneous nucleation occurs uniformly within the parent phase and requires substantial undercooling because a new interface must be created. Heterogeneous nucleation occurs at grain boundaries, inclusions, dislocations, and container walls. These sites reduce the energy required to form a stable nucleus and are much more common in engineering materials.

For a spherical nucleus, the qualitative competition is represented by

where r is nucleus radius, γ is interfacial energy per unit area, and ∆G_v is the volumetric free-energy change. For a transformation with a negative volume free-energy change, the first term is positive and the second is negative. Small nuclei tend to dissolve; nuclei larger than a critical radius can grow. The exact critical-radius expression depends on the transformation model and assumptions.

1.4 Growth and diffusion

After a stable nucleus forms, atoms move so that the new phase grows. Diffusion is the migration of atoms down a chemical-potential or concentration gradient. A simplified one-dimensional form of Fick’s first law is

where J is atomic flux, D is the diffusion coefficient, C is concentration, and x is distance. The negative sign indicates movement toward lower concentration. This form assumes steady one-dimensional diffusion and constant D.

The diffusion coefficient commonly follows an Arrhenius relationship:

where D₀ is a material constant, Q is activation energy for diffusion, R is the gas constant, and T is absolute temperature. Increasing temperature greatly increases diffusion, which explains why many transformations accelerate at higher temperatures.

A transformation may therefore be controlled by nucleation, diffusion, interface movement, or a combination of these processes. Martensitic transformation in steel is principally diffusionless, whereas pearlite formation is diffusion-controlled.

2. Solidification

2.1 Stages of solidification

Solidification consists of nucleation followed by growth. In a pure metal, solidification occurs at a single equilibrium temperature. In an alloy, solidification commonly occurs over a temperature range between the liquidus and solidus temperatures.

During cooling, the liquid may become constitutionally undercooled near the solid–liquid interface. Solute rejected by the growing solid can enrich the remaining liquid, producing microsegregation. If cooling is rapid, the composition may vary from dendrite cores to interdendritic regions. Homogenization heat treatment can reduce this segregation by diffusion.

2.2 Dendritic growth and grain structure

Most cast alloys form dendrites: tree-like crystals with primary arms and secondary branches. The final grain structure depends on nucleation density, temperature gradient, cooling rate, alloy composition, and mold conditions. Fine grains generally improve strength and toughness, while coarse columnar grains may produce anisotropy.

Important solidification defects include shrinkage cavities, gas porosity, hot tearing, inclusions, segregation, and residual stress. Sound casting requires control of alloy cleanliness, feeding, mold design, pouring temperature, and solidification rate.

3. Binary Phase Diagrams

A phase diagram shows the equilibrium phases present as functions of temperature, composition, and sometimes pressure. For a binary alloy at constant pressure, the Gibbs phase rule is

where F is the number of degrees of freedom, C is the number of components, and P is the number of phases. The reduced form applies when pressure is fixed. For a binary, single-phase region, F = 2; for a two-phase region, F = 1; and at an invariant three-phase reaction, F = 0.

The liquidus is the boundary above which the alloy is completely liquid. The solidus is the boundary below which it is completely solid. A solvus separates a single solid solution from a two-solid-phase region.

3.1 Lever rule

In a two-phase region, the relative amounts of phases can be estimated by the lever rule. If an alloy of overall composition C₀ lies between phases α and β with compositions Cα and Cβ, then

where Wα and Wβ are mass fractions. All compositions must be expressed on the same basis, such as weight percent. The equations assume equilibrium and negligible differences in density for conversion to volume fractions.

3.2 Eutectic reaction

A eutectic reaction is an invariant liquid-to-two-solid transformation:

It occurs at a fixed eutectic temperature and composition under equilibrium conditions. The eutectic microstructure is usually fine and lamellar or rod-like because the two solid phases grow cooperatively from the liquid.

In the lead–tin system, the eutectic reaction produces α-rich and β-rich solid phases. In cast irons and aluminum–silicon alloys, eutectic structures strongly influence fluidity, machinability, strength, and fracture behavior.

3.3 Eutectoid reaction

A eutectoid reaction resembles a eutectic reaction but occurs entirely in the solid state:

In plain-carbon steel, the eutectoid transformation is approximately

where γ is austenite, α is ferrite, and Fe₃C is cementite. The resulting lamellar mixture is called pearlite. The eutectoid temperature is approximately 727 °C and the eutectoid composition is approximately 0.76 wt% carbon, although exact values depend on reference data and alloy condition.

Hypoeutectoid steels contain less carbon than the eutectoid composition. On slow cooling, proeutectoid ferrite forms before pearlite. Hypereutectoid steels contain more carbon and form proeutectoid cementite before pearlite.

4. Iron–Carbon Transformations

The metastable iron–iron carbide diagram is particularly important for steels. Ferrite has a body-centered cubic structure and low carbon solubility. Austenite has a face-centered cubic structure and substantially greater carbon solubility. Cementite is a hard, brittle iron carbide with composition Fe₃C.

When hypoeutectoid steel is slowly cooled from the austenite region, ferrite nucleates first, usually at prior-austenite grain boundaries. Carbon is rejected into the remaining austenite. At the eutectoid temperature, the remaining austenite transforms to pearlite. The final structure is proeutectoid ferrite plus pearlite.

When hypereutectoid steel is slowly cooled, cementite forms first, often as a network at austenite grain boundaries. The remaining austenite transforms to pearlite. Excessive grain-boundary cementite can reduce toughness, so heat treatment and composition must be controlled.

The equilibrium diagram predicts phases and compositions, but not the actual transformation time. For that purpose, kinetic diagrams are required.

5. Transformation Kinetics and TTT Diagrams

5.1 Time dependence

Transformation kinetics describe how rapidly a new phase forms. For many isothermal transformations, the fraction transformed can be approximated by the Johnson–Mehl–Avrami relationship:

where X is fraction transformed, t is time, k is a temperature-dependent rate constant, and n reflects nucleation and growth conditions. This empirical relationship is not universal; it assumes a reasonably consistent transformation mechanism and isothermal conditions.

5.2 TTT diagrams

A time–temperature–transformation diagram shows the start and finish of transformation when austenite is rapidly cooled to a constant temperature and held there. The horizontal axis is usually logarithmic time; the vertical axis is temperature.

For eutectoid steel, the diagram commonly contains:

• a high-temperature pearlite region;
• a lower-temperature bainite region;
• a martensite-start temperature, Ms;
• a martensite-finish temperature, Mf.

The curves are often C-shaped because transformation is slow near the equilibrium temperature, faster at intermediate undercooling, and slow again at lower temperatures where diffusion is sluggish. The nose of the curve represents the shortest time to transformation. To form martensite by quenching, the cooling path must avoid the pearlite and bainite start curves until it reaches Ms.

5.3 CCT diagrams

Continuous-cooling-transformation diagrams describe transformations during uninterrupted cooling. They are more directly applicable to industrial heat treatment than TTT diagrams. CCT curves are generally shifted relative to TTT curves because the material is continuously changing temperature rather than holding isothermally.

A cooling curve intersecting the ferrite, pearlite, or bainite regions predicts those products. A sufficiently rapid curve that reaches Ms before diffusional transformation produces martensite. Actual results depend on steel composition, austenite grain size, section thickness, prior processing, and cooling medium.

6. Products of Austenite Transformation

6.1 Pearlite

Pearlite is a lamellar mixture of ferrite and cementite. Fine pearlite forms at lower transformation temperatures and has smaller interlamellar spacing, giving higher strength and hardness. Coarse pearlite forms at higher temperatures and is softer and more ductile.

6.2 Bainite

Bainite forms between the pearlite and martensite temperature ranges. Upper bainite consists of ferrite laths or plates with carbides between them; lower bainite contains finer carbides within ferrite plates. Bainite often provides a useful combination of strength and toughness.

6.3 Martensite

Martensite forms when austenite is cooled rapidly enough to suppress diffusion. Carbon becomes trapped in a supersaturated body-centered tetragonal structure. The transformation is approximately diffusionless and involves coordinated shear.

Martensite hardness increases with carbon content, but untempered martensite is brittle and contains high residual stress. The amount formed depends on cooling below Ms and Mf; retained austenite may remain when Mf is below room temperature.

The ideal critical diameter concept compares hardenability rather than surface hardness. Hardenability is the ability of a steel section to form martensite to a specified depth. It increases with alloying additions such as chromium, molybdenum, manganese, and nickel, although carbon strongly affects maximum hardness.

7. Heat-Treatment Processes

7.1 Annealing

Annealing generally involves heating to a suitable temperature, holding long enough for transformation or diffusion, and slow cooling, often in a furnace. Its purposes include reducing hardness, increasing ductility, relieving residual stress, improving machinability, and producing a stable microstructure.

Common forms include:

• Full annealing: heating steel into the austenite region followed by slow furnace cooling; produces relatively coarse pearlite and ferrite or cementite.
• Process annealing: subcritical heating used to restore ductility in cold-worked low-carbon steel.
• Spheroidizing: prolonged heating near the eutectoid temperature to produce rounded cementite particles in ferrite; useful for machining high-carbon steel.
• Stress-relief annealing: heating below the transformation range to reduce residual stress without major phase change.

Overheating can cause excessive grain growth, while insufficient holding time can leave a nonuniform structure.

7.2 Normalizing

Normalizing involves heating steel above the critical transformation range and cooling in still air. Air cooling is faster than furnace cooling, so normalized steel usually has finer pearlite and higher strength than fully annealed steel. Normalizing refines coarse cast or forged structures, reduces chemical and structural nonuniformity, and provides a useful conditioning treatment before hardening.

7.3 Quenching

Quenching is rapid cooling from the austenitizing temperature. Water, brine, oil, polymer solutions, gas, and molten salts are used depending on hardenability and distortion requirements.

Quenching intensity is not the same as hardenability. A severe quenchant extracts heat rapidly but increases thermal gradients, distortion, and cracking risk. A high-hardenability alloy may achieve through-hardening in oil or gas, whereas a low-hardenability steel may require water or brine.

Quenching produces three stages in many liquid media: vapor blanket formation, nucleate boiling, and convective cooling. Agitation, quenchant temperature, part orientation, and surface condition affect heat extraction.

7.4 Tempering

Tempering reheats quenched steel to a temperature below the eutectoid temperature, holds it, and cools it. It reduces brittleness and residual stress while improving toughness and dimensional stability. Carbon redistributes and carbides precipitate from supersaturated martensite.

Low-temperature tempering retains high hardness for tools and wear components. Medium-temperature tempering provides a balance of strength and resilience. High-temperature tempering produces tempered martensite with substantially improved toughness and is common in structural machine parts.

Some alloy steels exhibit temper embrittlement after exposure to certain temperature ranges. Slow cooling through susceptible ranges and control of impurity and alloy content can reduce this problem.

8. Precipitation Hardening

Precipitation hardening, or age hardening, strengthens alloys through a fine dispersion of particles that obstruct dislocation motion. The standard sequence is:

1. Solution treatment: heat into a single-phase region so solute dissolves.
2. Quenching: rapidly cool to retain a supersaturated solid solution.
3. Aging: hold at room temperature or an elevated temperature so fine precipitates form.

The precipitates must be sufficiently small, numerous, and well distributed. Strength initially rises with aging time, reaches a peak, and then decreases during overaging as particles coarsen and become less effective barriers.

The Orowan strengthening concept indicates that closely spaced particles increase the stress required for dislocations to pass. A simplified relationship is

where ∆σ is the increase in flow stress, G is shear modulus, b is Burgers vector, and L is effective obstacle spacing. This proportionality is qualitative and applies when dislocations bypass non-shearable particles; other mechanisms apply when particles are sheared.

Examples include Al–Cu, Al–Mg–Si, nickel-based superalloys, and precipitation-hardened stainless steels. Excessive aging reduces strength but may improve dimensional stability and stress-corrosion performance.

9. Surface Hardening

Surface hardening produces a hard exterior and tougher, more damage-tolerant core.

9.1 Carburizing

Carburizing adds carbon to the surface of a low-carbon steel at elevated temperature. After carburizing, the component is usually quenched and tempered. The case has high carbon content and can form hard martensite, while the low-carbon core remains relatively tough.

9.2 Nitriding

Nitriding introduces nitrogen, commonly using ammonia or plasma processes, at temperatures below the austenite transformation range. Nitrides form with alloying elements such as aluminum, chromium, and molybdenum. Nitriding provides high surface hardness, good wear resistance, and relatively low distortion, but the case is usually thinner than a carburized case.

9.3 Carbonitriding and cyaniding

Carbonitriding adds both carbon and nitrogen, generally to shallow cases on small components. Cyaniding historically used molten cyanide salts but is now restricted because of severe toxicity and environmental hazards. Modern practice favors safer gas, salt-free, plasma, or vacuum processes.

9.4 Induction and flame hardening

Induction hardening uses electromagnetic heating to austenitize only the surface, followed by quenching. Flame hardening uses a controlled fuel-gas flame. These processes require a steel with adequate carbon content and a suitable initial microstructure. They are rapid and economical for gears, shafts, rails, and bearing seats, but heating uniformity and quench control are critical.

10. Worked Example: Phase Fractions in a Hypoeutectoid Steel

Consider a 0.40 wt% carbon steel just above the eutectoid temperature in the ferrite–austenite region. Use approximate equilibrium compositions Cα = 0.022 wt% C and Cγ = 0.76 wt% C.

The ferrite mass fraction is

Thus, the austenite mass fraction is

Approximately 48.8% ferrite and 51.2% austenite are present immediately above the eutectoid temperature under equilibrium conditions. On further slow cooling, the austenite transforms to pearlite. Therefore, just below the eutectoid temperature, the approximate final constituents are 48.8% proeutectoid ferrite and 51.2% pearlite. This calculation predicts equilibrium phase fractions, not hardness, grain size, or transformation time.

11. Applied Case: Heat Treatment of a Medium-Carbon Steel Gear

Background

An illustrative manufacturer produces a medium-carbon alloy-steel gear for a power-transmission system. The gear requires a wear-resistant tooth surface, a tough core, dimensional accuracy, and resistance to tooth-root fatigue.

Problem

Through-hardening the entire gear would produce high hardness but could make the component brittle and increase quench distortion. A soft surface would cause adhesive and abrasive wear.

Analysis

The functional requirements differ by location. Tooth flanks require high hardness, while the core and tooth root require toughness. The steel’s hardenability must be sufficient for the tooth section, and the treatment must limit distortion.

Approach

The gear is first normalized or otherwise conditioned to refine the initial structure. It is then carburized so that carbon enters the tooth surface. After diffusion to the specified case depth, the gear is quenched using a controlled medium and tempered at a low-to-moderate temperature. Fixturing, staged quenching, press quenching, or gas quenching may be used to reduce distortion. Quality control includes hardness traverses, case-depth measurement, dimensional inspection, metallography, and inspection for grinding cracks.

Outcome

The final component has a high-carbon martensitic case, a lower-carbon tempered-martensitic or bainitic core depending on alloy and cooling rate, and improved wear and fatigue performance. The treatment is successful only if the case depth, retained austenite, residual stress, distortion, and core toughness meet design specifications.

Learning points

Heat treatment is a systems-design problem rather than a single furnace operation. Material selection, geometry, atmosphere, heating rate, quenching, tempering, inspection, and service loading must be considered together.

12. Limitations, Safety, and Best Practice

Heat treatment has unavoidable trade-offs. Faster cooling may increase hardness but also increases distortion and cracking. Higher austenitizing temperatures may improve dissolution of carbides but promote grain growth. Longer aging may stabilize dimensions but reduce peak strength. Surface treatments may improve wear resistance while introducing brittle compounds or tensile residual stress.

Good practice includes accurate furnace calibration, controlled atmosphere, clean loading, documented time–temperature records, appropriate thermocouple placement, validated quenchants, and traceable inspection. Operators must manage burns, hot surfaces, fumes, pressurized gases, flammable quenchants, cyanide hazards, and hydrogen-related risks. Environmental regulations increasingly favor vacuum carburizing, plasma nitriding, induction heating, and low-toxicity quenchants.

Computer-controlled furnaces, finite-element thermal models, digital process records, and machine-learning tools can improve repeatability. However, AI predictions must be validated against composition, geometry, actual cooling curves, metallography, and mechanical testing. No model replaces process qualification and engineering judgment.

Chapter Summary

Phase transformations determine the microstructure and properties of engineering materials. Solidification begins with nucleation and continues through crystal growth, often producing dendritic structures and segregation. Binary phase diagrams describe equilibrium phase fields and invariant reactions such as the eutectic liquid-to-two-solids reaction and the eutectoid solid-to-two-solids reaction.

In steels, austenite can transform to ferrite, pearlite, bainite, or martensite depending on temperature and cooling rate. TTT diagrams describe isothermal transformation, whereas CCT diagrams are more suitable for practical continuous cooling. Heat treatments exploit these transformations: annealing softens and relieves stress, normalizing refines structure, quenching forms martensite, tempering restores toughness, precipitation hardening forms strengthening particles, and surface hardening combines a hard exterior with a tough core.

Successful treatment requires balancing hardness, strength, toughness, wear resistance, dimensional accuracy, cost, safety, and environmental impact. The correct treatment is selected from material composition, geometry, service conditions, transformation kinetics, and quality requirements.

Key Terms

Phase: A chemically and physically homogeneous region of material.

Microstructure: The arrangement and morphology of phases, grains, and defects.

Nucleation: Formation of a stable region of a new phase.

Growth: Enlargement of a newly nucleated phase.

Diffusion: Atomic transport caused by concentration or chemical-potential gradients.

Liquidus: Boundary above which an alloy is completely liquid.

Solidus: Boundary below which an alloy is completely solid.

Solvus: Boundary separating a single solid solution from a multiphase solid region.

Eutectic reaction: Liquid transforming into two solid phases.

Eutectoid reaction: One solid phase transforming into two solid phases.

Pearlite: Lamellar ferrite–cementite constituent.

Bainite: Fine ferrite–carbide transformation product formed below the pearlite range.

Martensite: Hard, supersaturated, diffusionless transformation product.

Hardenability: Ability of steel to form martensite to a specified depth.

TTT diagram: Isothermal time–temperature–transformation diagram.

CCT diagram: Continuous-cooling-transformation diagram.

Tempering: Subcritical reheating of quenched steel to improve toughness.

Precipitation hardening: Strengthening by finely dispersed second-phase particles.

Carburizing: Addition of carbon to a steel surface.

Nitriding: Addition of nitrogen to form a hard nitride-bearing surface.

Review Questions

Short Answer Questions

1. What is the difference between a phase and a microstructure?
2. Why does heterogeneous nucleation occur more readily than homogeneous nucleation?
3. Define eutectic and eutectoid reactions.
4. Why is martensite harder than pearlite?
5. State the three principal steps of precipitation hardening.

Long Answer Questions

1. Explain nucleation and growth using the concepts of interfacial energy and free-energy change.
2. Describe the iron–carbon transformations in hypoeutectoid and hypereutectoid steels during slow cooling.
3. Compare TTT and CCT diagrams and explain their use in heat-treatment design.
4. Discuss the purposes, procedures, and typical outcomes of annealing, normalizing, quenching, and tempering.
5. Explain how carburizing, nitriding, induction hardening, and flame hardening produce a hard surface.

Analytical / Application Questions

1. A 0.40 wt% carbon steel is cooled slowly from the austenite region. Using the lever rule and the approximate compositions provided in this chapter, determine the proeutectoid ferrite and pearlite fractions.
2. A gear requires a hard wear-resistant surface but a tough core. Compare through-hardening with carburizing followed by quenching and tempering, and recommend one treatment with justification.
3. A quenched steel part has high hardness but cracks and unacceptable distortion. Analyze at least four possible causes and propose process modifications.

Multiple Choice Questions with Answers

Question 1

Which reaction is characteristic of a eutectoid transformation?

A. L → α + β

B. γ → α + Fe₃C

C. α → L + β

D. β → γ + L

Correct Answer: B. γ → α + Fe₃C

Question 2

What does the lever rule calculate in a two-phase equilibrium region?

A. Cooling rate

B. Diffusion coefficient

C. Relative phase amounts

D. Critical quench severity

Correct Answer: C. Relative phase amounts

Question 3

Which transformation product is principally diffusionless?

A. Coarse pearlite

B. Bainite

C. Proeutectoid ferrite

D. Martensite

Correct Answer: D. Martensite

Question 4

What is the principal purpose of tempering quenched steel?

A. Increase brittleness

B. Reduce residual stress and improve toughness

C. Melt cementite completely

D. Convert all ferrite to liquid

Correct Answer: B. Reduce residual stress and improve toughness

Question 5

Which diagram is most directly suited to predicting transformations during continuous industrial cooling?

A. CCT diagram

B. Binary equilibrium diagram only

C. Stress–strain diagram

D. TTT diagram only

Correct Answer: A. CCT diagram

Question 6

In precipitation hardening, overaging generally causes strength to decrease because precipitates

A. dissolve instantly during quenching

B. become coarser and less effective as obstacles

C. transform into liquid

D. eliminate all dislocations

Correct Answer: B. become coarser and less effective as obstacles

Question 7

For the 0.40 wt% carbon steel example, what is the approximate proeutectoid ferrite fraction?

A. 0.022

B. 0.400

C. 0.488

D. 0.760

Correct Answer: C. 0.488

Question 8

Which treatment is designed to produce a hard exterior and relatively tough interior?

A. Surface hardening

B. Full annealing only

C. Stress relief only

D. Homogenization only

Correct Answer: A. Surface hardening

Question 9

Increasing temperature generally increases the diffusion coefficient because

A. atomic mobility rises exponentially with temperature

B. grain boundaries disappear immediately

C. the gas constant becomes zero

D. all transformations become diffusionless

Correct Answer: A. atomic mobility rises exponentially with temperature

Question 10

Which statement correctly distinguishes hardenability from hardness?

A. Hardenability is resistance to indentation only

B. Hardness is the ability to form martensite at depth

C. Hardenability concerns depth of hardening; hardness concerns resistance to deformation

D. They are always identical properties

Correct Answer: C. Hardenability concerns depth of hardening; hardness concerns resistance to deformation