ME 235: Materials Science and Engineering
Estimated study time: 9 minutes
Table of contents
Sources and References
Primary texts: Materials Science and Engineering: An Introduction by Callister and Rethwisch; The Science and Engineering of Materials by Askeland, Fulay, and Wright; Physical Metallurgy Principles by Abbaschian and Reed-Hill.
Supplementary texts: Engineering Materials 1 and 2 by Ashby and Jones; Introduction to Polymers by Young and Lovell; Introduction to Ceramics by Kingery, Bowen, and Uhlmann.
Online resources: MIT OpenCourseWare 3.091 Introduction to Solid-State Chemistry; Cambridge DoITPoMS; ASM Handbook online; Granta Design EduPack material indices.
Chapter 1: Atomic Bonding and Structure
1.1 Primary and Secondary Bonds
Materials owe their properties to bonding between atoms. Ionic bonding transfers electrons between electropositive and electronegative atoms. Covalent bonding shares electron pairs. Metallic bonding delocalises valence electrons in a sea around cation cores. Secondary bonds (van der Waals, hydrogen) produce weaker but ubiquitous interactions.
1.2 Crystal Structures
Metals adopt body-centred cubic, face-centred cubic, or hexagonal close-packed arrangements, characterised by lattice parameter, atomic packing factor, and coordination number. The packing factor of FCC and HCP is \( \pi/(3\sqrt{2}) \approx 0.74 \); BCC is 0.68.
1.3 Miller Indices and Diffraction
Planes and directions in crystals are labelled by Miller indices. X-ray diffraction measures plane spacings through Bragg’s law
\[ n\lambda = 2 d_{hkl} \sin\theta, \]permitting identification of phases and measurement of residual stresses.
Chapter 2: Imperfections and Microstructure
2.1 Point Defects
Vacancies and interstitials exist in equilibrium concentrations \( n/N = \exp(-Q/kT) \). Substitutional and interstitial solutes modify mechanical, thermal, and electrical properties. Frenkel and Schottky defect pairs in ionic crystals preserve charge neutrality.
2.2 Line Defects
Edge and screw dislocations are line defects whose motion carries plastic deformation. The Burgers vector \( \mathbf{b} \) characterises the magnitude and direction of slip. Dislocation energy scales with \( G b^2 \) per unit length, with shear modulus \( G \).
2.3 Planar and Volume Defects
Grain boundaries, stacking faults, twin boundaries, and phase boundaries are planar defects. Voids, inclusions, and second-phase particles constitute volume defects. Microstructure—the ensemble of phases, grains, and defects—determines macroscopic behaviour.
Chapter 3: Mechanical Behaviour of Metals
3.1 Elastic Deformation
Elastic response is characterised by Young’s modulus \( E \), shear modulus \( G \), and Poisson’s ratio \( \nu \) with \( G = E/[2(1+\nu)] \). For isotropic linear elasticity, Hooke’s law in matrix form links stress and strain tensors through stiffness or compliance.
3.2 Plastic Deformation
Once yield stress is exceeded, plastic flow proceeds by dislocation glide on close-packed planes. True stress-strain follows
\[ \sigma_T = K \varepsilon_{T,p}^n \]in the uniform plastic regime. Necking begins when \( d\sigma_T/d\varepsilon_T = \sigma_T \) (Considere’s criterion).
3.3 Strengthening
Strengthening mechanisms include grain refinement per Hall-Petch, solid-solution hardening, strain hardening, precipitation hardening, and dispersion strengthening. Their contributions approximately superpose.
Chapter 4: Polymers
4.1 Chain Chemistry and Architecture
Polymers consist of long-chain molecules produced by addition or condensation polymerisation. Degree of polymerisation \( n \), tacticity, branching, and cross-linking control behaviour. Thermoplastics soften on heating; thermosets cure into infusible networks; elastomers deform reversibly to large strains.
4.2 Viscoelastic Deformation
Polymers exhibit time-dependent strain under stress. The Maxwell and Kelvin–Voigt models combine springs and dashpots. The generalised relaxation modulus
\[ E(t) = E_\infty + \sum_i E_i \exp(-t/\tau_i) \]fits experimental data. Time–temperature superposition through the WLF equation shifts curves along the \( \log t \) axis for different temperatures.
4.3 Glass Transition
Below the glass transition temperature \( T_g \) an amorphous polymer is rigid; above, it flexes. Free-volume and kinetic theories explain \( T_g \). Crystalline polymers have both a \( T_g \) for amorphous domains and a melting temperature \( T_m \) for crystallites.
Chapter 5: Ceramics and Glasses
5.1 Bonding and Structure
Ceramics are inorganic, non-metallic compounds with mixed ionic-covalent bonds. Crystalline ceramics include oxides (Al\(_2\)O\(_3\), ZrO\(_2\)), carbides (SiC, WC), and nitrides (Si\(_3\)N\(_4\), AlN). Amorphous ceramics include silicate and borosilicate glasses.
5.2 Mechanical Behaviour
Ceramics are stiff and strong in compression but brittle in tension. Fracture strength obeys Weibull statistics
\[ P_f = 1 - \exp\!\left[-\left(\frac{\sigma}{\sigma_0}\right)^m\right], \]with Weibull modulus \( m \) characterising scatter. Toughening mechanisms include transformation toughening in zirconia, crack deflection in composites, and compressive surface stresses in tempered glass.
5.3 Viscous Deformation
Above the glass transition, silicate glasses flow viscously. The viscosity follows a temperature dependence well approximated by Vogel–Fulcher–Tammann
\[ \eta(T) = \eta_0 \exp\!\left(\frac{B}{T - T_0}\right). \]This behaviour underlies glass forming and fibre drawing.
Chapter 6: Phase Equilibria and Heat Treatment
6.1 Phase Diagrams
Binary diagrams map phase stability against temperature and composition. Eutectic and eutectoid reactions produce two-phase microstructures. The lever rule quantifies phase fractions. Gibbs phase rule gives degrees of freedom.
6.2 Non-Equilibrium Transformations
Deviation from slow cooling produces microstructures far from equilibrium. In steels, rapid cooling produces martensite; intermediate cooling produces bainite; slow cooling produces pearlite. Each carries distinct mechanical properties. TTT and CCT diagrams guide heat-treatment recipes.
6.3 Diffusion and Strengthening
Fick’s laws govern atomic transport. Case hardening, carburising, and nitriding use diffusion to produce hard surfaces over tough cores. Age-hardening heat treatments exploit the precipitation sequence in Al-Cu and related systems.
Chapter 7: Fracture
7.1 Ductile and Brittle Fracture
Ductile fracture proceeds by microvoid coalescence after significant plastic deformation, showing fibrous surfaces. Brittle fracture proceeds by cleavage or intergranular separation with little plasticity. Impact tests such as Charpy identify ductile-to-brittle transition temperatures.
7.2 Linear Elastic Fracture Mechanics
A crack in a linear elastic body produces a stress singularity characterised by the stress intensity factor \( K_I = Y\,\sigma \sqrt{\pi a} \). Fracture occurs when \( K_I \) reaches the material’s fracture toughness \( K_{IC} \). Design ensures that \( K_I \) remains below \( K_{IC} \) for all foreseeable flaws.
7.3 Fatigue and Environment
Cyclic stresses produce eventual fracture through crack initiation and subcritical growth. The Paris law links crack-growth rate to \( \Delta K \). Aggressive environments accelerate failure through hydrogen embrittlement, stress-corrosion cracking, and corrosion fatigue. Integrated material, design, and inspection strategies prevent service failures.
