Composite material Study Guide

📖 Core Concepts Composite material – a product of two or more distinct constituents (matrix + reinforcement) that retain their individual identities. Matrix (binder) – surrounds and protects the reinforcement, transfers loads between fibers/particles. Reinforcement – provides the primary stiffness and strength (fibers, particles, or skins). Anisotropy – mechanical properties (modulus, strength, conductivity) vary with direction; most composites are orthotropic (three orthogonal symmetry planes). Rule of Mixtures (parallel direction) $$Pc = Vf Pf + (1-Vf)Pm$$ predicts elastic or strength properties when load is aligned with fibers. Inverse Rule of Mixtures (perpendicular direction) $$\frac{1}{Pc}= \frac{Vf}{Pf}+ \frac{1-Vf}{Pm}$$ Tsai‑Hill Failure Criterion – combines longitudinal, transverse, and shear stresses to predict failure in orthotropic laminates. Fiber orientation effects – 0° maximizes axial strength, ±45° optimizes shear/torsion, 90° gives transverse strength; intermediate angles shift failure from tensile to shear‑dominated. --- 📌 Must Remember Volume fraction \(Vf\): fraction of total composite volume occupied by fibers (0 ≤ \(Vf\) ≤ 1). Longitudinal modulus \(Ec = VfEf+(1-Vf)Em\). Transverse modulus via inverse rule of mixtures. Continuous‑fiber tensile strength $$TSc = Vf TSf + (1-Vf) TSm$$ Short‑fiber shear‑lag: \(\displaystyle \frac{d\sigmaf}{dx}= \frac{2\tau}{d}\). Particle‑reinforced modulus \(Ec = Em(1+\eta Vp)\). Strength vs. angle (approximate): \(\theta\approx0^\circ\): \(\sigma \approx \sigma{\parallel}/\cos^{2}\theta\) \(\theta\approx45^\circ\): \(\sigma \approx \tau{my}/(\sin\theta\cos\theta)\) \(\theta\approx90^\circ\): \(\sigma \approx \sigma{\perp}/\sin^{2}\theta\) Key fiber types – carbon (highest specific strength & stiffness), glass (moderate, low cost), aramid/Kevlar (high impact resistance, lower modulus). --- 🔄 Key Processes Design a composite part Choose matrix (environmental resistance, processing temperature). Choose reinforcement (type, volume fraction, orientation). Lay‑up fibers on/in the mold according to required orientation schedule. Fabrication workflow Wetting/mixing of reinforcement with matrix. Placement into open or closed mold. Apply binding reaction (heat cure, chemical polymerization, pressure). Post‑cure inspection (NDE). Applying the Rule of Mixtures Identify loading direction → use parallel formula for 0°, inverse for 90°. Insert known \(Vf\), \(Pf\), \(Pm\) to compute \(Pc\). Tsai‑Hill evaluation Compute stress invariants: \((\sigma{11}/X)^2 + (\sigma{22}/Y)^2 - (\sigma{11}\sigma{22})/(X^2) + (\tau{12}/S)^2 \le 1\). Compare to 1; if >1, predicted failure. --- 🔍 Key Comparisons Matrix material Metal vs. Ceramic: metal matrix → good ductility, high thermal conductivity; ceramic matrix → high temperature resistance, brittle. Reinforcement form Continuous fibers vs. Short fibers vs. Particulates: continuous → max strength & stiffness; short → moderate load transfer, shear‑lag limited; particles → increase stiffness/toughness, low strength gain. Failure prediction Simple strength‑orientation model vs. Tsai‑Hill: simple model ignores interaction of stresses; Tsai‑Hill captures coupled longitudinal, transverse, shear effects. Fabrication method Autoclave (high pressure, high quality) vs. Vacuum bag (lower cost, good for large parts) vs. Filament winding (ideal for axisymmetric shapes). --- ⚠️ Common Misunderstandings “All composites are isotropic.” They are typically anisotropic; only random‑fiber mats approach isotropy, at the cost of peak strength. Using the parallel rule of mixtures for transverse loading. Must switch to the inverse rule. Assuming Tsai‑Hill always over‑predicts strength. It can over‑predict only when fibers are short or poorly bonded; for well‑bonded continuous fibers it is accurate. Believing higher fiber volume fraction always improves performance. Excessive \(Vf\) can cause brittleness, processing defects, and poor wetting. --- 🧠 Mental Models / Intuition “Load‑sharing bridge” – imagine fibers as strong steel cables and matrix as the deck; the matrix distributes load to each cable via shear, like the deck spreads vehicle weight to all cables. Directional wood analogy – wood’s grain shows why composites are stronger along fibers and weaker across them; rotate the grain (fiber angle) and the failure mode changes. Rule of mixtures as a weighted average – think of mixing two colors: the final hue (property) is a blend weighted by how much of each color (volume fraction) you add. --- 🚩 Exceptions & Edge Cases Inverse rule of mixtures breaks down when fiber‑matrix interfacial shear is low or fibers are highly misaligned. Short‑fiber composites: shear‑lag theory shows stress builds only over a finite length; the simple continuous‑fiber strength formula over‑estimates. Random fiber orientation: reinforcement factor \(K\) is less than the theoretical maximum of aligned fibers; isotropy is achieved at the expense of peak modulus. Tsai‑Hill over‑prediction occurs for composites with low interfacial strength or significant fiber waviness. --- 📍 When to Use Which Rule of Mixtures (parallel) → predict modulus/strength when load ‑ direction ≈ fiber direction (θ < 15°). Inverse Rule (perpendicular) → predict transverse properties (θ ≈ 90°). Tsai‑Hill → design or check any laminate with arbitrary ply angles; especially when combined stresses are present. Autoclave molding → high‑performance aerospace parts needing low void content. Vacuum bag/Resin transfer molding → large, relatively low‑cost structures (boat hulls, wind‑turbine blades). Filament winding → circular or tubular components (pressure vessels, rocket motor casings). --- 👀 Patterns to Recognize Strength vs. angle curve: follows \(\cos^{2}\theta\) → \(\sin\theta\cos\theta\) → \(\sin^{2}\theta\) progression; a “U‑shaped” plot with minimum near 45°. Delamination indicators: sudden drop in load, acoustic emission spikes, ultrasonic “bright spots”. High \(Vf\) + poor wetting → voids → lower measured modulus than predicted. Consistent 0°, 45°, 90° test results → validates orthotropic stiffness matrix; deviations hint at processing defects. --- 🗂️ Exam Traps Choosing the wrong mixture rule – applying the parallel formula for a 90° test leads to an unrealistically high modulus. Ignoring matrix shear strength in intermediate‑angle strength calculations; the \(\tau{my}\) term is often omitted in distractors. Assuming carbon‑fiber density equals steel – carbon is 1.6 g/cm³ vs. steel 7.8 g/cm³; specific strength questions often test this. Confusing Tsai‑Hill with simple strength‑orientation – exam may present the latter’s formula as a “failure criterion”; remember Tsai‑Hill includes interaction terms. Misdirected fiber orientation – a diagram showing fibers at 30° but asking for 0° strength; watch the angle notation. ---