Sources and References

Primary texts: Materials Science and Engineering: An Introduction by Callister and Rethwisch (Wiley); Physical Metallurgy Principles by Abbaschian, Abbaschian, and Reed-Hill; The Principles of Engineering Materials by Barrett, Nix, and Tetelman.

Supplementary texts: Engineering Materials 1 and 2 by Ashby and Jones; Materials Selection in Mechanical Design by Ashby; Mechanical Metallurgy by Dieter.

Online resources: MIT OpenCourseWare 3.40J Physical Metallurgy; ASM Handbook online; Cambridge DoITPoMS teaching and learning package; NIST material property databases.

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Chapter 1: Phase Equilibria and Diagrams

1.1 Thermodynamic Basis

At equilibrium the Gibbs free energy is minimised. For a single-phase solution of components A and B, \( G = x_A \mu_A + x_B \mu_B \), with chemical potentials \( \mu_i \). Two phases coexist when their chemical potentials are equal, setting the common-tangent construction on \( G(x) \) curves.

1.2 Binary Diagrams

Binary phase diagrams map temperature versus composition. Isomorphous systems form a continuous solid solution between liquidus and solidus. Eutectic systems exhibit the reaction \( L \to \alpha + \beta \) at a single temperature and composition. Peritectic, eutectoid, and peritectoid reactions enrich the menu.

1.3 Lever Rule

Within a two-phase field the fraction of phase \( \beta \) of composition \( C_\beta \) in an alloy of composition \( C_0 \) with \( \alpha \) of composition \( C_\alpha \) is

\[ W_\beta = \frac{C_0 - C_\alpha}{C_\beta - C_\alpha}. \]

This simple accounting guides microstructural design.

Chapter 2: Non-Equilibrium Transformations

2.1 Nucleation

Homogeneous nucleation of a new phase proceeds against the surface-energy penalty:

\[ \Delta G(r) = \tfrac{4}{3}\pi r^3 \Delta g_v + 4\pi r^2 \gamma, \]

with critical radius \( r^* = -2\gamma/\Delta g_v \) and critical barrier \( \Delta G^* \). Heterogeneous nucleation on existing surfaces reduces the barrier.

2.2 Growth

Growth proceeds by diffusion-controlled or interface-controlled mechanisms. The coupled nucleation-and-growth rate underlies the sigmoidal kinetics captured by the Avrami equation \( X = 1 - e^{-k t^n} \), with Avrami exponent \( n \) encoding dimensionality and nucleation mode.

2.3 TTT and CCT Diagrams

Isothermal time-temperature-transformation and continuous-cooling-transformation diagrams summarise the kinetics of diffusional and diffusionless transformations. In steels they reveal ferrite, pearlite, bainite, and martensite fields as functions of cooling path.

Chapter 3: Heat Treatment of Steels

3.1 Iron-Carbon System

The Fe-Fe\(_3\)C diagram identifies austenite, ferrite, and cementite phases. Eutectoid steel at 0.76 wt% C transforms to pearlite at 727°C. Hypo- and hyper-eutectoid steels develop proeutectoid constituents before pearlite formation.

3.2 Quenching and Tempering

Rapid cooling suppresses diffusional transformations, producing martensite, a body-centred tetragonal distortion of austenite that is hard but brittle. Tempering at intermediate temperatures precipitates carbides, restoring toughness while retaining strength. The Hollomon–Jaffe parameter \( P = T(C + \log t) \) correlates tempering conditions.

3.3 Hardenability

Hardenability measures the depth to which a given section achieves a target hardness. The Jominy end-quench test standardises measurement. Alloying elements (Mn, Cr, Mo, Ni) expand hardenability by shifting the TTT nose to longer times.

Chapter 4: Diffusion and Strengthening

4.1 Fick’s Laws

Steady-state diffusion obeys Fick’s first law \( J = -D\,\partial C/\partial x \). Transient diffusion obeys Fick’s second law

\[ \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}. \]

The diffusivity follows an Arrhenius dependence \( D = D_0 \exp(-Q/RT) \), with activation energy \( Q \).

4.2 Strengthening Mechanisms

Resistance to plastic flow increases through mechanisms that impede dislocation motion: solid-solution hardening \( \Delta \sigma \propto c^{1/2} \), precipitation hardening via coherent or incoherent obstacles, grain-size refinement per Hall-Petch \( \sigma_y = \sigma_0 + k_y/\sqrt{d} \), and strain hardening where \( \sigma = K \varepsilon_p^n \).

4.3 Age Hardening

Age hardening of aluminium or nickel alloys starts with solution treatment to create a supersaturated solid solution, quenching to retain it, then ageing at intermediate temperature. Coherent Guinier–Preston zones evolve through metastable phases to equilibrium precipitates, with hardness peaking before overageing.

Chapter 5: Alloying, Composites, and Processing

5.1 Alloy Families

Carbon and low-alloy steels provide versatile strength and toughness. Stainless steels resist corrosion through chromium-rich oxide films. Tool steels combine hardness with wear resistance. Aluminium, magnesium, and titanium alloys offer weight savings. Nickel-based superalloys sustain strength at elevated temperature.

5.2 Composites

Composites combine a matrix and a reinforcement to achieve property combinations unattainable individually. Long-fibre laminates follow the rule of mixtures for stiffness along fibre direction: \( E_c = V_f E_f + (1-V_f) E_m \). Transverse and shear moduli require Halpin–Tsai or numerical estimation.

5.3 Cold and Hot Working

Cold working below the recrystallisation temperature increases strength through dislocation accumulation at the cost of ductility. Hot working above recrystallisation temperature combines deformation with simultaneous softening, enabling large strains without fracture. Annealing restores ductility through recovery, recrystallisation, and grain growth.

Chapter 6: Failure Mechanisms and Prevention

6.1 Creep

At \( T/T_m > 0.4 \), time-dependent plastic flow under constant load becomes significant. The secondary creep rate follows

\[ \dot{\varepsilon}_{ss} = A \sigma^n \exp\!\left(-Q_c/RT\right), \]

with stress exponent \( n \) and activation energy \( Q_c \). Larson-Miller parameters correlate creep rupture life with temperature.

6.2 Fatigue

Cyclic loading below static yield produces eventual failure by crack initiation and growth. S-N curves summarise nominal-stress fatigue; strain-life approaches suit low-cycle fatigue; fracture-mechanics analysis uses Paris’s law

\[ \frac{da}{dN} = C (\Delta K)^m. \]

Surface finish, residual stress, mean stress, and notches govern fatigue performance.

6.3 Corrosion and Degradation

Corrosion is the electrochemical degradation of materials in an environment. Uniform, galvanic, pitting, crevice, intergranular, and stress-corrosion cracking are common morphologies. The Pourbaix diagram maps corrosion, passivation, and immunity regions as functions of potential and pH. Mitigation combines material selection, coatings, cathodic protection, and environment control.

6.4 Prevention of Service Failures

Engineers prevent service failures through rational material selection, inspection and nondestructive evaluation, design against identified failure modes, redundancy, and monitoring. Lessons from case histories, codified in standards and failure databases, inform each new design decision.