Sources and References

• Callister and Rethwisch, Materials Science and Engineering: An Introduction, 10th ed., Wiley.
• Daniel and Ishai, Engineering Mechanics of Composite Materials, 2nd ed., Oxford University Press.
• Jones, Mechanics of Composite Materials, 2nd ed., Taylor & Francis.
• Strong, Fundamentals of Composites Manufacturing, SME.
• Odian, Principles of Polymerization, 4th ed., Wiley.
• Barsoum, Fundamentals of Ceramics, 2nd ed., CRC Press.

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Chapter 1: Polymers: Structure and Properties

Non-metallic materials—polymers, ceramics, and their composites—fill engineering roles that metals cannot. Polymers offer low density, chemical inertness, and toughness at modest temperatures. Ceramics sustain high temperatures, resist wear, and are stiff but brittle. Combining them with reinforcing fibres produces composites whose specific stiffness and strength surpass those of any monolithic engineering material.

1.1 Molecular Architecture

A polymer molecule is a chain of repeating monomer units, formed by step-growth (polycondensation) or chain-growth (addition) polymerization. The number-average molecular weight \( M_n \) is

\[ M_n = \frac{\sum_i N_i M_i}{\sum_i N_i}, \]

while the weight-average \( M_w \) weights by mass. The polydispersity index \( M_w/M_n \) characterizes the breadth of the distribution. Chains may be linear, branched, or cross-linked; they may be isotactic, syndiotactic, or atactic depending on the stereochemistry at chiral centres.

1.2 States of a Polymer

Amorphous polymers pass through a glass transition at \( T_g \), above which chains gain segmental mobility and the modulus drops dramatically. Semicrystalline polymers additionally have a crystalline fraction that melts at \( T_m > T_g \). Thermoplastics can be melted and reformed; thermosets are cross-linked networks that decompose rather than flow.

1.3 Mechanical Behaviour

Polymers are viscoelastic: their response is a superposition of elastic and viscous components. A linear viscoelastic material obeys the Boltzmann superposition integral,

\[ \sigma(t) = \int_{-\infty}^{t} E(t-\tau) \frac{d\varepsilon}{d\tau} d\tau. \]

Creep compliance \( J(t) \) and relaxation modulus \( E(t) \) are the material’s characteristic functions; time–temperature superposition using WLF shift factors extends short-time data across service time scales.

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Chapter 2: Ceramics and Glasses

2.1 Bonding and Structure

Ceramics are compounds of metals with non-metals—oxides, carbides, nitrides, borides—held together by a mixture of ionic and covalent bonds. Bond strengths are high and largely directional, which makes ceramics stiff, hard, and heat-resistant but also brittle: they lack the slip systems needed for significant plastic deformation at ordinary temperatures.

2.2 Brittle Strength and Weibull Statistics

Failure originates at the largest critical flaw. Griffith’s criterion gives

\[ \sigma_f = \left(\frac{2 E \gamma_s}{\pi a}\right)^{1/2}, \]

where \( a \) is half the flaw length and \( \gamma_s \) the surface energy. Because flaw populations are variable, ceramic strength is best described statistically. The Weibull cumulative failure probability is

\[ P_f = 1 - \exp\!\left[-\left(\frac{\sigma}{\sigma_0}\right)^m\right], \]

with shape parameter \( m \) reflecting scatter. Design with ceramics uses Weibull parameters together with effective-volume scaling to translate small-sample data to full-size components.

2.3 Glasses

Silicate glasses cool from the melt without crystallizing, forming a network of SiO₄ tetrahedra. Network modifiers (Na, Ca) disrupt the network and lower viscosity. Viscosity follows Vogel–Fulcher–Tammann,

\[ \eta = \eta_0 \exp\!\left(\frac{B}{T - T_0}\right), \]

allowing processing windows (working, softening, annealing, strain points) to be defined. Tempering and chemical strengthening introduce compressive surface stresses that must be exceeded before tensile fracture can occur.

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Chapter 3: Composite Materials: Constituents and Micromechanics

3.1 Fibres, Matrices, and Interfaces

High-performance composites pair stiff, strong fibres (glass, carbon, aramid, ceramic) with a more compliant matrix (polymer, metal, ceramic). The matrix transfers load into the fibres, protects them from abrasion and environment, and holds them in geometric arrangement. The fibre–matrix interface is the locus of load transfer and the first line of defence against environmental attack; interfacial shear strength controls whether a crack is arrested by fibre pull-out or propagates without deflection.

3.2 Rule of Mixtures

For a unidirectional lamina loaded parallel to the fibres, iso-strain holds and

\[ E_1 = V_f E_f + (1 - V_f) E_m. \]

Transverse to the fibres, iso-stress gives the lower bound,

\[ \frac{1}{E_2} = \frac{V_f}{E_f} + \frac{1 - V_f}{E_m}. \]

More accurate transverse predictions come from the Halpin–Tsai equations with empirical reinforcement factors. Longitudinal strength is governed by fibre strength and statistical bundle mechanics; transverse and shear strengths are matrix- and interface-limited.

3.3 Laminated Plate Theory

Composite structures are built by stacking laminae at different orientations. Classical laminated plate theory (CLPT) relates in-plane forces \( \{N\} \) and moments \( \{M\} \) to mid-plane strains \( \{\varepsilon^0\} \) and curvatures \( \{\kappa\} \) through the ABD matrix,

\[ \begin{Bmatrix} N \\ M \end{Bmatrix} = \begin{bmatrix} A & B \\ B & D \end{bmatrix} \begin{Bmatrix} \varepsilon^0 \\ \kappa \end{Bmatrix}. \]

A balanced, symmetric layup decouples bending from extension and suppresses unwanted curvatures during cure. Failure of the laminate is predicted by ply-by-ply application of criteria such as maximum stress, Tsai–Hill, or Tsai–Wu, with progressive failure tracked as plies degrade.

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Chapter 4: Processing of Non-Metallics and Composites

4.1 Polymer Processing

Injection moulding forces molten thermoplastic into a mould under high pressure, filling, packing, and cooling in a cycle of a few seconds. Extrusion produces continuous profiles, films, and pipe. Blow moulding forms hollow parts from a parison. Thermoforming drapes a heated sheet over a mould. Each process imposes specific shear histories that affect molecular orientation, residual stress, and therefore properties. Rheological characterization—shear viscosity as a function of rate and temperature—underlies mould and die design.

4.2 Ceramic Processing

Ceramic components are shaped from powders by pressing, slip casting, or injection moulding of filled binders, then sintered at a high fraction of the melting temperature. Densification proceeds through grain-boundary diffusion and grain growth; coupled models predict density and grain size as functions of particle size, green density, and sintering schedule. Glass processing uses viscosity-controlled forming at temperatures within the working range, followed by controlled annealing.

4.3 Composite Processing

Polymer-matrix composites are laid up by hand or by automated tape placement and cured under heat and pressure. Autoclave cure cycles are designed to allow resin flow, achieve full cure, and minimize residual stress. Resin transfer moulding injects resin into a dry fibre preform in a closed mould. Filament winding produces pressure vessels and pipes with fibre angles optimized to internal pressure. Pultrusion pulls continuous rovings through a resin bath and heated die, producing constant-section profiles.

Metal- and ceramic-matrix composites require more demanding processing—liquid-metal infiltration, chemical-vapour infiltration, hot isostatic pressing—because of high processing temperatures and interfacial reactivity.

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Chapter 5: Design and Applications

5.1 Comparing Materials

Material indices from Ashby charts guide the preliminary choice. For a beam of fixed stiffness and minimum mass, the index is \( E^{1/2}/\rho \), and composites dominate. For a pressure vessel of fixed radius, minimum mass requires \( \sigma_y/\rho \) to be maximized, again favouring composites for hoop-wound tanks. Life-cycle considerations—manufacturing energy, recyclability, cost per kilogram of strength—often reorder the ranking in favour of metals or engineering thermoplastics.

5.2 Case: Composite Pressure Vessel

A Type IV hydrogen storage tank is a polymer liner overwrapped by carbon/epoxy filament winding. Hoop windings resist circumferential stress \( \sigma_\theta = p r / t \); helical windings resist axial stress \( \sigma_z = p r / (2 t) \). The angle of helical layers is chosen from netting analysis as \( \theta = \arctan(\sqrt{2}) \approx 54.7° \). Burst tests validate the netting-plus-CLPT prediction, and cyclic pressure tests qualify the design for service.

5.3 Case: Engineering Plastic for a Gear

A nylon-6,6 gear with short-glass-fibre reinforcement operates at 80 °C. Tooth root stress is estimated from Lewis’s equation and compared to allowable stress derated for temperature, moisture (nylons absorb water and lose stiffness), and fatigue. Wear is controlled by PTFE filler; heat rise is limited by choosing a sufficient face width.