9.6 Mechanical properties of composites

Types of composites

Composites combine two or more distinct materials to produce properties that neither component achieves alone. In polymer chemistry, the matrix is typically a polymer, while the reinforcement (fibers, particles, or layers) provides the mechanical boost. The three main composite architectures each offer different advantages.

Fiber-reinforced composites

These consist of strong fibers embedded in a softer polymer matrix. The fibers carry most of the load, while the matrix transfers stress between fibers and protects them from the environment.

• Common fiber materials: glass, carbon, and aramid (Kevlar)
• Matrix materials: thermosets (epoxy, polyester) or thermoplastics (PEEK, nylon)
• Fiber orientation has a major effect on mechanical properties, since fibers only reinforce strongly along their length
• Applications range from sporting goods to aerospace primary structures

Particulate composites

These use particles dispersed throughout a continuous matrix rather than elongated fibers. The particles can be metallic, ceramic, or polymeric.

• Enhance stiffness, wear resistance, and thermal conductivity
• Particle size, shape, and distribution all affect performance
• Example: aluminum reinforced with silicon carbide particles for automotive brake rotors
• Generally more isotropic (uniform in all directions) than fiber-reinforced composites, since particles don't have a preferred orientation

Laminar composites

These consist of layers (laminae) of different materials bonded together, where each layer can have distinct properties and orientations.

• Provide tailored mechanical properties in different directions by varying layer orientation
• Include sandwich structures with a lightweight core (foam or honeycomb) between strong face sheets
• Examples: plywood, fiber-metal laminates like GLARE (glass fiber/aluminum)
• Used in aircraft structures and ballistic protection

Stress-strain behavior

Stress-strain curves are the primary tool for understanding how a composite responds to applied force. They reveal elastic limits, yield behavior, and ultimate failure, all of which guide material selection.

Elastic vs. plastic deformation

Elastic deformation is reversible: remove the load and the material returns to its original shape. It follows Hooke's Law:

$\sigma = E\epsilon$

where $\sigma$ is stress, $E$ is the elastic (Young's) modulus, and $\epsilon$ is strain.

Plastic deformation is permanent. It begins after the yield point and involves mechanisms like polymer chain slippage in the matrix or microcracking. Fiber-reinforced composites tend to show more elastic behavior than the neat matrix because the stiff fibers restrict matrix deformation. Many composites, especially those with brittle thermoset matrices, fail with little plastic deformation at all.

Yield strength

Yield strength is the stress at which permanent deformation begins. On a stress-strain curve, it's the point where the response departs from linearity.

• For materials without a sharp yield point, the 0.2% offset method is used: draw a line parallel to the elastic region, offset by 0.2% strain, and find where it intersects the curve
• Higher fiber volume fractions generally increase yield strength
• Because composites are often anisotropic, yield strength depends on loading direction

Ultimate tensile strength

This is the maximum stress a material can withstand before failure, corresponding to the highest point on the engineering stress-strain curve.

• In fiber-reinforced composites, ultimate tensile strength is largely governed by fiber strength and the quality of the fiber-matrix interface
• Unidirectional composites show their highest ultimate tensile strength along the fiber direction
• Polymer matrix composites typically have higher specific strength (strength-to-weight ratio) than metals, which is why they're favored in aerospace

Mechanical properties

These properties describe how composites perform under different types of loading. Each can be tailored by adjusting composition, fiber architecture, and processing.

Tensile strength

Tensile strength measures resistance to breaking under a pulling force, calculated as maximum load divided by original cross-sectional area.

• In fiber-reinforced composites, tensile strength is primarily controlled by fiber properties
• Highest along the fiber direction; drops significantly at off-axis angles
• For unidirectional composites, the rule of mixtures gives a reasonable first estimate
• Composites routinely exceed unreinforced polymer tensile strengths by an order of magnitude

Compressive strength

Compressive strength measures resistance to loads that try to shorten or crush the material.

• In fiber-reinforced composites, compressive failure is often limited by fiber microbuckling, where fibers buckle locally within the matrix
• The matrix plays a bigger role here than in tension because it must laterally support the fibers
• High-modulus fibers and stiff matrices improve compressive performance
• Testing requires careful specimen preparation to avoid premature end-crushing artifacts

Flexural strength

Flexural strength measures resistance to bending, determined through three-point or four-point bending tests.

• Bending creates a combination of tensile, compressive, and shear stresses through the specimen thickness
• Fiber orientation and laminate stacking sequence strongly influence flexural performance
• Critical in applications like aircraft wings and wind turbine blades, where bending loads dominate
• Can be optimized by placing the strongest plies at the outer surfaces, where bending stresses are highest

Impact strength

Impact strength measures the ability to absorb energy during sudden loading, tested using Charpy, Izod, or drop-weight methods.

• Governed by matrix toughness and fiber-matrix interface strength
• Aramid (Kevlar) fibers and toughened epoxy or thermoplastic matrices improve impact performance
• There's often a trade-off: very stiff, high-strength composites can be brittle under impact
• Critical for automotive crash structures and aerospace components exposed to bird strike or tool drop

Factors affecting properties

Fiber orientation

Fiber orientation is the single biggest factor controlling directional properties in fiber-reinforced composites.

• Unidirectional (0°): maximum strength and stiffness along the fiber direction, but very weak transversely
• Quasi-isotropic laminates (e.g., 0°/±45°/90°): balanced properties in all in-plane directions, at the cost of lower peak strength in any one direction
• Off-axis loading can dramatically reduce strength; even a few degrees of misalignment matters
• Automated fiber placement (AFP) allows precise control of orientation during manufacturing

Fiber length

Fiber length determines how efficiently load transfers from the matrix into the fiber.

• Continuous fibers provide the best mechanical properties because stress builds up fully along the fiber length
• Short (chopped) fibers are easier to process (injection molding, for example) but give lower strength and stiffness
• The critical fiber length is the minimum length needed for effective load transfer. Fibers shorter than this pull out before reaching their full strength.
• Critical length depends on fiber diameter, fiber strength, and the interfacial shear strength between fiber and matrix

Fiber-matrix interface

The interface is where load transfers from matrix to fiber, making it central to composite performance.

• A strong interface promotes efficient stress transfer and high strength, but can cause brittle, catastrophic failure
• A weak interface allows fiber pullout, which absorbs energy and improves toughness, but reduces strength
• Surface treatments (silane coupling agents for glass fibers, oxidation treatments for carbon fibers) and sizing agents are used to tune interface strength
• Good interface design balances strength and toughness for the intended application

Matrix properties

The matrix controls composite behavior in transverse loading, shear, and compression, and it also determines environmental resistance.

• Thermoset matrices (epoxy, vinyl ester): high stiffness, good temperature resistance, but brittle and not recyclable
• Thermoplastic matrices (PEEK, nylon): tougher, weldable, recyclable, but often harder to process with continuous fibers
• Matrix modulus directly affects composite stiffness in compression and transverse tension
• Viscoelastic behavior of the polymer matrix introduces time-dependent effects like creep under sustained loads

Composite failure modes

Composites don't fail the way metals do. Instead of a single crack propagating, multiple failure mechanisms can occur simultaneously or sequentially. Understanding these modes helps in designing damage-tolerant structures.

Matrix cracking

Matrix cracking is typically the first form of damage in a composite.

• Occurs when stress in the matrix exceeds its tensile strength
• More common in brittle thermoset systems like standard epoxy
• Reduces composite stiffness and can allow moisture ingress
• Can trigger other failure modes (delamination, fiber breakage)
• Mitigated by using toughened epoxies or ductile thermoplastic matrices

Fiber pullout

Fiber pullout happens when fibers debond from the matrix and slide out during fracture.

• Indicates a relatively weak fiber-matrix interface
• Actually beneficial for toughness because the sliding friction absorbs energy
• More common with short fibers or poorly bonded interfaces
• The extent of pullout depends on fiber length relative to the critical fiber length, fiber strength, and interface shear strength
• Can be controlled through surface treatments and sizing agents

Delamination

Delamination is the separation of adjacent layers in a laminated composite.

• Caused by interlaminar stresses, especially at free edges, around holes, or under impact
• Significantly reduces compressive strength because unsupported sublaminates buckle easily
• Prone to occur where there are large mismatches in ply orientation between adjacent layers
• Mitigated through ply drop-off design, interleaving with tough adhesive layers, or through-thickness reinforcement (z-pinning, stitching)
• Detected using ultrasonic C-scan inspection or acoustic emission monitoring

Fiber breakage

Fiber breakage occurs when stress in the fibers exceeds their tensile strength.

• Usually the final, catastrophic failure mode in tension
• Results in sudden loss of load-bearing capacity
• In a unidirectional composite under tension, individual fibers break progressively at their weakest points, redistributing load to neighbors until the remaining fibers can't carry the load
• Often accompanied by matrix cracking and debonding in the surrounding region

Testing methods

Standardized testing ensures that composite properties can be compared consistently across materials and laboratories.

Tensile testing

Measures material response to uniaxial pulling loads.

• Uses a universal testing machine with specialized grips
• Fiber-reinforced composite specimens typically require bonded tabs at the grip ends to prevent premature failure from grip pressure
• Provides elastic modulus, yield strength, ultimate tensile strength, and strain to failure
• Standard: ASTM D3039 for polymer matrix composites

Compression testing

Evaluates behavior under compressive loads, which is trickier than tensile testing because the specimen can buckle globally.

• Methods include end-loading, shear-loading, and combined loading approaches
• The Combined Loading Compression (CLC) fixture (ASTM D6641) is widely used
• Provides compressive strength and modulus
• Particularly important for structures subject to buckling, like aircraft fuselage panels

Flexural testing

Assesses bending behavior using three-point or four-point configurations.

• Three-point bending is simpler but induces higher shear stress at the midpoint
• Four-point bending creates a region of pure bending (constant moment) between the inner load points, which is better for measuring true flexural properties
• Standard: ASTM D7264 for polymer matrix composites
• Relevant for beam-like structures such as wind turbine blades

Impact testing

Evaluates response to sudden, high-rate loading.

• Charpy and Izod tests use a pendulum striking a notched specimen; they give a single energy absorption value
• Drop-weight impact tests use a falling mass on a plate specimen, allowing measurement of force-time history and damage area
• Drop-weight tests are more representative of real service impacts (tool drops, debris strikes)
• Critical for automotive and aerospace components where impact damage tolerance is required

Composite design considerations

Rule of mixtures

The rule of mixtures provides quick estimates of composite properties from the properties of the individual constituents. It assumes perfect bonding and no voids.

Longitudinal (isostrain) model predicts stiffness along the fiber direction:

$E_c = E_f V_f + E_m V_m$

Transverse (isostress) model predicts stiffness perpendicular to fibers:

$\frac{1}{E_c} = \frac{V_f}{E_f} + \frac{V_m}{E_m}$

where $E_c$, $E_f$, and $E_m$ are the moduli of the composite, fiber, and matrix, and $V_f$ and $V_m$ are their volume fractions.

The isostrain model works well for longitudinal modulus. The isostress model gives a lower bound for transverse modulus but tends to underestimate it. For strength and off-axis properties, more sophisticated models are needed.

Fiber volume fraction

Fiber volume fraction ($V_f$) is the proportion of the composite volume occupied by fibers. It's one of the most important parameters controlling mechanical properties.

• Structural composites typically target 50-70% $V_f$
• Increasing $V_f$ raises strength and stiffness but reduces toughness and makes processing harder
• There's a practical upper limit: you need enough resin to wet all fibers and fill the spaces between them, minimizing voids
• Controlled through manufacturing process selection (autoclave curing, resin transfer molding, filament winding)

Critical fiber length

The critical fiber length ($l_c$) is the minimum length a fiber must have to be loaded to its full strength through shear stress transfer at the interface:

$l_c = \frac{\sigma_f d}{2\tau_i}$

where $\sigma_f$ is fiber tensile strength, $d$ is fiber diameter, and $\tau_i$ is interfacial shear strength.

• Fibers shorter than $l_c$ pull out before breaking, meaning their full strength is never utilized
• Fibers much longer than $l_c$ (and especially continuous fibers) achieve nearly full reinforcement efficiency
• This parameter guides the choice between short-fiber and continuous-fiber composite designs

Environmental effects

Composites in service face temperature swings, moisture, and chemical exposure. These environmental factors can degrade properties over time and must be accounted for in design.

Temperature sensitivity

• The glass transition temperature ($T_g$) of the polymer matrix is the key threshold: above $T_g$, the matrix softens dramatically, reducing composite stiffness and strength
• Mismatch in coefficient of thermal expansion (CTE) between fibers and matrix generates internal (residual) stresses during cooling from processing temperature
• High-temperature applications use thermally stable matrices like polyimides and carbon fibers
• Cryogenic applications (e.g., liquid hydrogen tanks) require matrices that remain tough at very low temperatures

Moisture absorption

• Most polymer matrices absorb moisture from the environment through diffusion
• Absorbed water plasticizes the matrix, lowering $T_g$ and reducing stiffness and strength
• Moisture can also weaken the fiber-matrix interface, particularly in glass fiber composites
• Rate of absorption depends on matrix chemistry, temperature, and relative humidity
• Mitigated through moisture-resistant resins (vinyl ester, certain epoxies) or protective coatings and sealants
• Especially important for marine composites and structures in tropical climates

Chemical resistance

• Resistance to chemicals and solvents depends primarily on the matrix material
• Thermoset matrices (especially vinyl ester and epoxy novolacs) generally offer better chemical resistance than most thermoplastics
• The fiber-matrix interface can be a pathway for chemical attack through wicking along debonded regions
• Relevant for composites in chemical processing equipment, fuel tanks, and piping
• Improved through chemical-resistant resin selection or application of protective barrier coatings (gel coats, liners)

Applications in polymer chemistry

Automotive composites

• Primary driver: weight reduction for improved fuel efficiency and lower emissions
• Carbon fiber reinforced polymers (CFRP) appear in high-performance vehicles (e.g., carbon fiber monocoques in Formula 1)
• Glass fiber composites are more common in mass-market vehicles for body panels and semi-structural parts
• Natural fiber composites (flax, hemp) are increasingly used for interior trim panels
• Key challenges: achieving low cycle times for high-volume production and developing recycling pathways for end-of-life vehicles

Aerospace composites

• The Boeing 787 Dreamliner uses approximately 50% composites by weight, including CFRP in the fuselage and wings
• The Airbus A350 XWB similarly relies heavily on advanced composites
• CFRP is used in primary structures; glass fiber composites handle secondary structures and interiors
• High-temperature composites (carbon/polyimide, ceramic matrix composites) serve in engine nacelles and exhaust components
• Aerospace composites face strict certification requirements (damage tolerance, fatigue life) and high manufacturing costs

Construction composites

• Valued for high strength-to-weight ratio and corrosion resistance
• Glass fiber reinforced polymer (GFRP) rebars replace steel in concrete where corrosion is a concern (bridges, marine structures, parking garages)
• Carbon fiber sheets and wraps are bonded to existing concrete or masonry for structural strengthening and seismic retrofit
• Wood-plastic composites (WPC) are popular for decking and outdoor furniture due to rot resistance
• Challenges include ensuring fire resistance (polymer matrices are combustible) and demonstrating long-term durability for structures with 50+ year design lives

Modeling and prediction

Computational models reduce the need for extensive physical testing by predicting composite behavior virtually. Three levels of modeling are commonly used, each at a different length scale.

Micromechanical models

These predict composite properties from the properties of the individual fibers and matrix, plus the microstructure.

• Analytical approaches include the Halpin-Tsai equations, which account for fiber aspect ratio and are more accurate than the simple rule of mixtures for transverse and shear properties
• Numerical approaches use a representative volume element (RVE), a small repeating unit of the microstructure modeled with finite elements
• Account for fiber volume fraction, aspect ratio, orientation distribution, and interface properties
• Limitations: difficulty modeling complex fiber architectures (woven, braided) and nonlinear behavior like damage

Laminate theory

Classical Lamination Theory (CLT) predicts the stiffness and strength of multi-ply laminates from the properties and orientations of individual plies.

• Uses the ABD matrix to relate in-plane forces and moments to mid-plane strains and curvatures
• Accounts for ply orientations, stacking sequence, and individual ply properties
• Enables optimization of layup design for specific loading conditions (e.g., choosing a stacking sequence that minimizes coupling between bending and twisting)
• Limitations: assumes thin plates, neglects through-thickness (interlaminar) stresses, and doesn't directly predict delamination

Finite element analysis

FEA is a numerical method that divides a structure into small elements and solves the governing equations at each node.

• Handles complex geometries, boundary conditions, and anisotropic material properties
• Used for stress analysis, buckling prediction, and failure analysis of composite structures
• Progressive damage models can simulate the sequence of matrix cracking, delamination, and fiber breakage
• Challenges include computational cost for large structures and the need for validated failure criteria specific to composites