4.2 Corrosion, Polymers, Ceramics, and Composites

4.2 Corrosion, Polymers, Ceramics, and Composites

Corrosion Mechanisms and Fundamentals

Corrosion is the electrochemical degradation of a metal due to reaction with its environment. In chemical plants, corrosion can cause piping leaks, vessel thinning, and structural failures. For corrosion to occur, four essential components must be present to form a functioning electrochemical cell:

1. Anode: The site where oxidation occurs. The metal loses electrons and dissolves as ions: $M \rightarrow M^{n+} + ne^-$
2. Cathode: The site where reduction occurs. Electrons are consumed by species in the electrolyte: $2H^+ + 2e^- \rightarrow H_2 \quad \text{(in acidic environments)}$ $O_2 + 2H_2O + 4e^- \rightarrow 4OH^- \quad \text{(in neutral or basic environments)}$
3. Electrical Path: A metallic connection that allows electrons to flow from anode to cathode.
4. Electrolyte: An aqueous solution containing ions that conducts ionic current between the anode and cathode.

Specific Corrosion Mechanisms

• Galvanic Corrosion: Occurs when two metals with different electrochemical potentials are electrically coupled in an electrolyte. The more active metal (higher in the galvanic series) becomes the anode and corrodes, while the more noble metal becomes the cathode and is protected. The rate of galvanic corrosion is proportional to the potential difference and is highly accelerated by a high cathode-to-anode surface area ratio. A large cathode draws a large total reduction current, which must be balanced by the oxidation current at the small anode, leading to high current density and rapid localized penetration.
• Pitting Corrosion: A highly localized form of corrosion that produces deep cavities or 'pits.' It occurs when a metal's passive oxide film is damaged or broken down, typically by halide ions like chloride ($Cl^-$). Once initiated, pitting is autocatalytic (self-sustaining). Metal dissolution inside the pit creates an excess of positive charge, causing chloride ions to migrate into the pit to maintain charge neutrality. Hydrolysis of the metal chloride follows: $M^{n+} + nH_2O \rightarrow M(OH)_n + nH^+$ This increases the acidity ($H^+$ concentration) inside the pit, which accelerates the dissolution rate, while the outer surface remains cathodic and protected by oxygen reduction.
• Crevice Corrosion: Localized corrosion occurring in shielded environments (e.g., under gaskets, bolts, or deposits) where oxygen diffusion is restricted. Oxygen depletion inside the crevice makes it anodic relative to the oxygen-rich bulk surfaces (cathodic), driving localized metal dissolution.
• Stress Corrosion Cracking (SCC): The spontaneous cracking of a ductile alloy subjected to a constant tensile stress in a specific corrosive environment. For example, austenitic stainless steels are highly susceptible to SCC when exposed to tensile stress in hot aqueous chloride solutions.
• Intergranular Corrosion: Selective attack along grain boundaries. In stainless steels, sensitization occurs when heating between $500^\circ\text{C}$ and $800^\circ\text{C}$ causes carbon to diffuse to grain boundaries and react with chromium, forming chromium carbide ($Cr_{23}C_6$). This depletes the adjacent region of chromium below the 12% threshold required for passivation, leaving the grain boundaries vulnerable to rapid corrosion.

Corrosion Control Strategies

1. Cathodic Protection: Keep the metal cathodic relative to its environment.
   • Sacrificial Anode: Connect the structure to a more active metal (e.g., zinc or magnesium anodes on steel tanks).
   • Impressed Current (ICCP): Use an external DC power source to force electrons into the metal.
2. Inhibitors: Chemical additives that slow down corrosion reactions. Anodic inhibitors (e.g., chromates, nitrites) help form a passive film on the anode. Cathodic inhibitors (e.g., carbonates) restrict the reduction reaction.
3. Coatings: Barrier coatings (e.g., epoxies, polyurethanes, or zinc galvanizing) isolate the metal from the electrolyte.
4. Material Selection: Use corrosion-resistant alloys, such as molybdenum-containing stainless steels (Grade 316) to resist pitting.

Polymers

Polymers are macromolecules composed of repeating structural units (monomers) linked by covalent bonds.

• Thermoplastics vs. Thermosets:
  • Thermoplastics: Consist of linear or branched chains held together by weak secondary bonds (van der Waals or hydrogen bonds). They soften and melt upon heating and solidify upon cooling, making them recyclable (e.g., PE, PVC, PP, PTFE).
  • Thermosets: Consist of cross-linked three-dimensional network structures. Once cured, they cannot be melted or reshaped because heating decomposes the covalent cross-links (e.g., epoxy, polyurethane, phenolic resins).
• Thermal Transitions:
  • Glass Transition Temperature ($T_g$): The temperature below which amorphous polymer regions are rigid, glassy, and brittle, and above which they are rubbery and flexible.
  • Melting Temperature ($T_m$): The temperature at which crystalline regions of semi-crystalline polymers melt.
• Degradation: Polymers do not corrode electrochemically but degrade via solvent swelling, environmental stress cracking (ESC), hydrolysis, or UV oxidation.

Ceramics

Ceramics are inorganic, non-metallic materials characterized by ionic and covalent bonding.

• Structure and Properties: They can be crystalline or amorphous (glasses). They possess high melting points, high hardness, excellent wear resistance, and low thermal/electrical conductivity. However, they are highly brittle and fail under tensile stress with little to no plastic deformation.
• Fracture Mechanics: The mechanical strength of ceramics is limited by internal and surface flaws. The stress intensity factor ($K$) describes the stress field near a crack tip. Catastrophic failure occurs when $K$ reaches the critical fracture toughness ($K_{Ic}$): $K_{Ic} = Y \sigma \sqrt{\pi a}$ where $\sigma$ is the nominal applied stress, $a$ is the crack length (or half-length for an internal crack), and $Y$ is a dimensionless geometry factor (typically $\approx 1.0$). According to Griffith's Theory, the fracture stress $\sigma_f$ is related to the surface energy $_\gamma_s$ and Young's modulus $E$: $\sigma_f = \sqrt{\frac{2 E \gamma_s}{\pi a}}$

Composites

Composites are multiphase materials engineered to combine the desirable properties of their constituents (usually a strong reinforcement phase embedded in a ductile matrix phase).

• Fiber-Reinforced Composites: Properties depend on fiber alignment.
• Rule of Mixtures: Estimates the effective properties of the composite. Let $V_f$ and $V_m$ be the volume fractions of the fiber and matrix, respectively ($V_f + V_m = 1$).
  • Longitudinal Direction (Isostrain): When loading is parallel to continuous fibers, both fibers and matrix experience the same strain ($\epsilon_c = \epsilon_f = \epsilon_m$). The longitudinal elastic modulus ($E{cl}$) is: $E_{cl} = E_f V_f + E_m V_m$ The longitudinal strength ($\sigma{cl}$) is: $\sigma_{cl} = \sigma_f V_f + \sigma_m V_m$
  • Transverse Direction (Isostress): When loading is perpendicular to the fibers, both phases experience the same stress ($_\sigma_c = _\sigma_f = \sigma_m$). The transverse elastic modulus ($E{ct}$) is: $\frac{1}{E_{ct}} = \frac{V_f}{E_f} + \frac{V_m}{E_m} \implies E_{ct} = \frac{E_f E_m}{V_f E_m + V_m E_f}$ The transverse modulus is dominated by the weaker matrix phase, making it significantly lower than the longitudinal modulus.

Worked Examples

Worked Example 1: Critical Flaw Size in a Ceramic Pipe

A silicon nitride ($Si_3N_4$) ceramic tube is used in a high-temperature reactor. It has a fracture toughness $K_{Ic} = 5.0 \text{ MPa}\cdot\text{m}^{1/2}$ and Young's modulus $E = 310 \text{ GPa}$. During operation, the tube wall is subjected to a tensile stress of $250 \text{ MPa}$. Assuming a geometry factor $Y = 1.0$, calculate the maximum allowable length of an internal crack that will not cause catastrophic failure. Solution:

1. State the relationship between fracture toughness, stress, and crack size: $K_{Ic} = Y \sigma_f \sqrt{\pi a}$
2. Rearrange the equation to solve for the critical crack half-length $a$: $\sqrt{\pi a} = \frac{K_{Ic}}{Y \sigma_f} \implies \pi a = \left(\frac{K_{Ic}}{Y \sigma_f}\right)^2 \implies a = \frac{1}{\pi} \left(\frac{K_{Ic}}{Y \sigma_f}\right)^2$
3. Substitute the given values: $a = \frac{1}{\pi} \left(\frac{5.0 \times 10^6 \text{ Pa}\cdot\text{m}^{1/2}}{1.0 \times 250 \times 10^6 \text{ Pa}}\right)^2$ $a = \frac{1}{\pi} \left(0.02 \text{ m}^{1/2}\right)^2 = \frac{0.0004 \text{ m}}{\pi} \approx 1.273 \times 10^{-4} \text{ m} = 0.127 \text{ mm}$
4. Since $a$ represents the crack half-length for an internal crack, the total allowable length of the internal crack is $2a$: $\text{Total Length} = 2a = 2(0.127 \text{ mm}) = 0.254 \text{ mm} = 254 \ \ \mu\text{m}$

Worked Example 2: Rule of Mixtures for a Fiber-Reinforced Polymer

A unidirectional carbon fiber-reinforced polymer composite contains $65 \text{ vol}\%$ carbon fibers ($E_f = 230 \text{ GPa}$) in an epoxy matrix ($E_m = 4.0 \text{ GPa}$). Calculate the longitudinal modulus ($E_{cl}$) and the transverse modulus ($E_{ct}$) of the composite. Solution:

1. Identify the volume fractions: $V_f = 0.65, \quad V_m = 1 - 0.65 = 0.35$
2. Calculate the longitudinal modulus using the isostrain Rule of Mixtures: $E_{cl} = E_f V_f + E_m V_m$ $E_{cl} = (230 \text{ GPa})(0.65) + (4.0 \text{ GPa})(0.35) = 149.5 \text{ GPa} + 1.40 \text{ GPa} = 150.9 \text{ GPa}$
3. Calculate the transverse modulus using the isostress Rule of Mixtures: $E_{ct} = \frac{E_f E_m}{V_f E_m + V_m E_f}$ $E_{ct} = \frac{(230 \text{ GPa})(4.0 \text{ GPa})}{(0.65)(4.0 \text{ GPa}) + (0.35)(230 \text{ GPa})} = \frac{920}{2.60 + 80.5} = \frac{920}{83.1} = 11.07 \text{ GPa}$ The transverse modulus is significantly lower than the longitudinal modulus because it is dominated by the softer matrix phase, illustrating the anisotropic nature of unidirectional composites.