Sources and References

Primary texts — Callahan, D. R. Materials Science and Engineering: An Introduction, 10th ed. Wiley, 2018 (Callister & Rethwisch). Ashby, M. F. and Jones, D. R. H. Engineering Materials 1: An Introduction to Properties, Applications, and Design, 5th ed. Butterworth-Heinemann, 2019.

Supplementary texts — Dowling, N. E. Mechanical Behavior of Materials, 4th ed. Pearson, 2012. Mindess, S., Young, J. F., and Darwin, D. Concrete, 2nd ed. Prentice Hall, 2003. Mehta, P. K. and Monteiro, P. J. M. Concrete: Microstructure, Properties, and Materials, 4th ed. McGraw-Hill, 2014.

Online resources — MIT OpenCourseWare 3.032 Mechanical Behavior of Materials; MIT OCW 3.091 Introduction to Solid-State Chemistry; NIST phase diagram database (ASM International); ACI (American Concrete Institute) open educational materials; FHWA LTBP bridge corrosion reference data.

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Chapter 1: Atomic and Crystalline Structure

1.1 Bonding and the Origin of Mechanical Properties

The macroscopic mechanical response of an engineering material traces back to the nature of its interatomic bonds. Metallic bonds share delocalized electrons in a sea surrounding positive cores, producing ductility and conductivity. Covalent bonds are directional and strong, producing hardness but brittleness, as in diamond or silicon carbide. Ionic bonds bind dissimilar atoms by electrostatic attraction, producing high stiffness but brittleness, as in ceramics. Van der Waals and hydrogen bonds are weak but dominate in polymers, determining glass transition temperature.

A one-dimensional model places atoms at equilibrium spacing \(r_0\) in a potential well \(U(r)\) with minimum at \(r_0\). Expanding,

\[ U(r) \approx U_0 + \tfrac{1}{2}U''(r_0)(r-r_0)^2 + \cdots \]

the curvature \(U''(r_0)\) is proportional to the macroscopic stiffness. This is why covalent and ionic solids are stiff and polymers (van der Waals) are compliant.

1.2 Crystal Structures

Most metals adopt one of three close-packed structures:

• Face-centred cubic (FCC): aluminum, copper, austenitic steel. Atomic packing factor 0.74; twelve nearest neighbours; twelve active slip systems, giving high ductility.
• Body-centred cubic (BCC): iron at room temperature (ferrite), tungsten. Packing factor 0.68; slip systems depend strongly on temperature, producing a ductile-to-brittle transition.
• Hexagonal close-packed (HCP): magnesium, zinc, titanium. Packing factor 0.74; fewer slip systems than FCC, generally less ductile.

1.3 Defects

No real crystal is perfect. Point defects (vacancies, interstitials, substitutional atoms), line defects (dislocations), planar defects (grain boundaries, twins, stacking faults), and volume defects (voids, inclusions) all affect strength and ductility. Most strengthening mechanisms in metals are strategies to impede dislocation motion.

Chapter 2: Elastic and Plastic Deformation

2.1 Stress and Strain

Engineering stress \(\sigma = F/A_0\) and engineering strain \(\varepsilon = \Delta L/L_0\) are referenced to the original cross section and length. For small deformation the linear elastic regime obeys Hooke’s law,

\[ \sigma = E\varepsilon, \]

where \(E\) is the elastic (Young’s) modulus. For a general state of stress in an isotropic material,

\[ \varepsilon_x = \frac{1}{E}\left[\sigma_x - \nu(\sigma_y + \sigma_z)\right], \]

where \(\nu\) is Poisson’s ratio. Shear strain is related to shear stress by \(\tau = G\gamma\) with \(G = E/[2(1+\nu)]\).

2.2 The Monotonic Stress-Strain Curve

A uniaxial tension test of a ductile metal produces a curve with distinct regions: linear elastic (below yield \(\sigma_y\)), plastic strain hardening (between yield and ultimate tensile strength \(\sigma_u\)), necking, and fracture. Yielding is often defined by the 0.2% offset rule when there is no sharp yield point.

2.3 True Stress and Strain

At large deformation, referring to the original dimensions becomes misleading. True stress \(\sigma_t = F/A\) uses the instantaneous cross section and true strain \(\varepsilon_t = \ln(L/L_0)\). For plastic deformation of many metals, \(\sigma_t = K\varepsilon_t^n\), where \(n\) is the strain-hardening exponent. Values of \(n\) between 0.1 and 0.5 reflect the trade-off between strength and formability.

Chapter 3: Cyclic Loading and Fatigue

3.1 S-N Curves

Under cyclic loading a component can fail at stresses well below the monotonic ultimate strength. The S-N curve plots stress amplitude \(\sigma_a\) versus cycles to failure \(N_f\) on log axes. Steel curves often show an endurance limit near \(\sigma_e \approx 0.4\sigma_u\); aluminum alloys do not.

3.2 Basquin’s Equation and Life Prediction

High-cycle fatigue data follow Basquin’s relation,

\[ \sigma_a = \sigma'_f(2N_f)^b, \]

with fatigue strength coefficient \(\sigma'_f\) and exponent \(b \approx -0.1\) for steels. Low-cycle fatigue is governed by the Coffin-Manson plastic-strain-life relation

\[ \Delta\varepsilon_p/2 = \varepsilon'_f(2N_f)^c, \]

with \(c \approx -0.6\). Total strain life is a sum of the two contributions.

3.3 Fracture Mechanics

A crack of length \(a\) at the tip of which the stress concentration is \(K_I = Y\sigma\sqrt{\pi a}\) grows under cyclic loading according to the Paris law

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

with \(m\) between 2 and 4 for most metals. Brittle fracture occurs when \(K_I\) exceeds the fracture toughness \(K_{Ic}\), a material property.

Chapter 4: Phase Diagrams and Phase Transformations

4.1 The Gibbs Phase Rule

For a system of \(C\) components and \(P\) phases at equilibrium, the Gibbs phase rule gives the degrees of freedom \(F = C - P + 2\). In a binary alloy at fixed pressure, \(F = 3 - P\). Binary phase diagrams plot temperature against composition.

4.2 Iron-Carbon Diagram

The iron-carbon diagram is the foundation of ferrous metallurgy. Austenite (FCC \(\gamma\) phase) dissolves up to 2.1% carbon at 1147 °C and transforms on cooling. The eutectoid at 0.76% carbon and 727 °C produces pearlite, a lamellar mixture of ferrite and cementite (Fe\(_3\)C). Hypoeutectoid steels (below 0.76% C) contain proeutectoid ferrite plus pearlite; hypereutectoid steels contain proeutectoid cementite plus pearlite.

The lever rule gives the mass fraction of each phase. At a two-phase region with composition \(C_0\) between phase compositions \(C_\alpha\) and \(C_\beta\),

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

4.3 Diffusion, Nucleation, and Growth

Diffusion obeys Fick’s laws. The steady-state flux is \(J = -D\,dc/dx\); the time-dependent equation is \(\partial c/\partial t = D\nabla^2 c\). The diffusion coefficient is Arrhenius,

\[ D = D_0\exp\left(-\frac{Q}{RT}\right). \]

Nucleation of a new phase requires overcoming a critical free energy barrier; homogeneous nucleation requires larger undercooling than heterogeneous nucleation at grain boundaries or inclusions. Growth kinetics follow the Johnson-Mehl-Avrami equation \(f = 1 - \exp(-kt^n)\).

4.4 Heat Treatment of Steels

Annealing softens and homogenizes by slow cooling from austenite. Normalizing produces a finer pearlite by faster air cooling. Quenching suppresses diffusion and produces martensite, a body-centred tetragonal phase supersaturated in carbon that is extremely hard and brittle. Tempering reheats martensite to precipitate fine carbides, trading hardness for toughness. The Jominy end-quench test characterizes hardenability.

Chapter 5: Iron, Steel, Aluminum, and Copper

5.1 Cast Irons

Gray cast iron contains graphite flakes in a ferrite or pearlite matrix, giving excellent damping and machinability but low tensile strength (roughly 150 to 400 MPa). Ductile (nodular) iron modifies the graphite into spheroids via magnesium addition, giving tensile strengths over 600 MPa with significant ductility.

5.2 Structural Steels

Low-carbon structural steels (ASTM A36, A992) rely on solid-solution strengthening and grain refinement. High-strength low-alloy (HSLA) steels add microalloying elements (Nb, V, Ti) that form fine precipitates. Weathering steels (A588) form a protective rust patina that inhibits further corrosion, useful for uncoated bridges.

5.3 Stainless Steels

Austenitic stainless (304, 316) contains 18% Cr and 8 to 10% Ni, remaining FCC at room temperature and thus ductile, non-magnetic, and non-heat-treatable by martensitic transformation. Ferritic (430) and martensitic (410) stainless steels cost less but offer less corrosion resistance. The passive chromium oxide layer requires at least 10.5% Cr to form.

5.4 Aluminum and Copper

Aluminum alloys are strengthened by solid solution (non-heat-treatable series 1000, 3000, 5000) or by precipitation hardening (series 2000 Al-Cu, 6000 Al-Mg-Si, 7000 Al-Zn-Mg-Cu). Heat treatment involves solutionizing, quenching, and aging at moderate temperature, producing fine coherent precipitates that impede dislocations. Copper alloys include brasses (Cu-Zn), bronzes (Cu-Sn), and cupronickels; their high conductivity makes them standard for electrical and plumbing applications.

Chapter 6: Concrete and Cementitious Materials

6.1 Hydration

Portland cement is mainly tricalcium silicate (C\(_3\)S), dicalcium silicate (C\(_2\)S), tricalcium aluminate (C\(_3\)A), and tetracalcium aluminoferrite (C\(_4\)AF). On mixing with water, C\(_3\)S and C\(_2\)S hydrate to produce calcium silicate hydrate (C-S-H) gel, which provides most of the strength, plus calcium hydroxide. The degree of hydration grows in time, approaching but never reaching unity.

6.2 Strength and the Water-Cement Ratio

Abrams’ law states that concrete compressive strength decreases monotonically with the water-cement ratio \(w/c\). A typical expression is

\[ f_c = \frac{A}{B^{w/c}}, \]

with empirical constants. A \(w/c\) of 0.4 produces roughly 50 MPa concrete; \(w/c\) of 0.7 gives roughly 20 MPa. Lower \(w/c\) means less capillary porosity, denser C-S-H, and improved durability, but also worse workability, addressed with superplasticizers.

6.3 Reinforced and Prestressed Concrete

Concrete tensile strength is about 10% of compressive. Steel reinforcement carries tension in beams and slabs; the thermal expansion coefficients of steel and concrete match to within 10% so differential thermal stress is modest. Prestressed concrete pre-loads the concrete in compression using tensioned strands, allowing longer spans and thinner sections.

Chapter 7: Wood, Masonry, Polymers, and Composites

7.1 Wood

Wood is an anisotropic cellular composite of cellulose fibres in a lignin matrix. Strength parallel to the grain is roughly 10 to 20 times strength perpendicular to the grain. Moisture content below the fibre saturation point (about 30%) strongly affects strength; design values assume about 12% equilibrium moisture content. Engineered wood products such as glulam, laminated veneer lumber, and cross-laminated timber overcome the defects of solid lumber by gluing small pieces into large, more uniform sections.

7.2 Masonry

Masonry is a composite of units (brick, concrete masonry unit, stone) and mortar. Its compressive strength derives from the unit; the mortar carries bed shear. Masonry is strong in compression and weak in tension; unreinforced masonry is vulnerable to lateral loads, which is why modern masonry construction uses reinforced cells or post-tensioned columns.

7.3 Polymers

Polymers are long-chain molecules whose mechanical properties depend on chain length, degree of crystallinity, and glass transition temperature \(T_g\). Thermoplastics (polyethylene, polycarbonate) soften on heating and can be remelted; thermosets (epoxy, phenolic) are cross-linked and cannot. Below \(T_g\) polymers are glassy and stiff; above \(T_g\) they become rubbery. Creep and stress relaxation are strong for polymers at service temperature.

7.4 Fibre-Reinforced Polymers

FRP combines high-stiffness, high-strength fibres (glass, carbon, aramid) in a polymer matrix (epoxy, vinyl ester). The rule of mixtures predicts longitudinal modulus \(E_1 = V_fE_f + V_mE_m\). Transverse and shear moduli are matrix-dominated. FRP pultruded bars are used as non-corroding reinforcement for concrete in aggressive environments.

Chapter 8: Degradation

8.1 Fracture

Brittle fracture initiates at a flaw. The Griffith criterion for a crack of length \(2a\) in an infinite plate under tension \(\sigma\) gives critical stress

\[ \sigma_c = \sqrt{\frac{2E\gamma_s}{\pi a}}, \]

where \(\gamma_s\) is the surface energy. In ductile materials plastic zone size at the crack tip raises this threshold substantially.

8.2 Corrosion

Aqueous corrosion of steel is an electrochemical process combining anodic dissolution (Fe → Fe\(^{2+}\) + 2e\(^-\)) and cathodic reduction of dissolved oxygen. Rates depend on temperature, chloride concentration, pH, and availability of oxygen. Reinforced concrete is protected by the alkaline pore solution (pH near 13), which passivates the steel. Carbonation lowers pH to below 9 and chloride ingress disrupts the passive layer; both initiate corrosion. The expansion of rust (2 to 6 times the original steel volume) cracks the cover concrete and accelerates deterioration.

8.3 Decay and Moisture

Wood decays by fungi requiring oxygen, moisture above about 20%, and temperatures between 5 and 40 °C. Removing any of these prevents decay. Freeze-thaw damages concrete saturated with water; air entrainment provides pressure relief voids.

8.4 Radiation Damage

High-energy neutron radiation produces point defects that embrittle ferritic steels at power-plant doses. Concrete above 65 °C for long periods loses water from C-S-H and suffers strength loss. Polymers are especially sensitive to ultraviolet radiation, which breaks backbone bonds; UV stabilizers (carbon black, hindered amine light stabilizers) extend service life of outdoor polymers.