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Lecture 35 - Composites C OMPOSITES • Combine two (or more) materials to enhance (i) stiffness (ii) strength (iii) toughness • Form of reinforcements: laminates (layers), long fibers, short fibers / whiskers, particles • Role of interfaces between constituents is very important For stiffness: Interface must be strong - for strain transfer • Metal-matrix composites: Ceramics (fibers or particles) in metals • Polymer-matrix composites: Stiff polymer fibers to epoxy matrix Glass, ceramic, C or B fibers to epoxy matrix For strength: Interface must be strong - for stress transfer • Metal-matrix composites to increase strength above yield strength • Polymer-matrix composites to increase strength For toughness: Weak (& tough) interface for crack deflection and energy dissipation • Brittle fibers in ceramics or polymers (energy absorbed by interface debond) • Ductile metal in ceramics (energy absorbed by plasticity) - e.g., WC/Co tools • Other more sophisticated mechanisms to absorb energy at crack tip Density of composites Consider unit volume of composite Volume of fiber = f; Volume of matrix = 1-f 3 Mass of fiber = fρf Mass of matrix = 1( f ρ) m (in 1 m of composite) ∴ Mass of 1 m composite: fρf+ (− f ρ) m ∴ Density of composite: ρ c fρ +f1−(f ρ ) m “Rule of mixtures” Stiffness of composites • Random orientation of reinforcing phase may result in isotropic properties • In general, composites are anistropic (see Lecture 04) εij S ijklij • A special class are fiber-reinforced composites (fibers along X, Y and Z directions) € ME382 - 18/iv/14 1 Lecture 35 - Composites • These are known as orthotropic materials - 9 elastic constants • A further special case are fiber laminates in plane stress with fibers in X, Y directions ⎛1 νYX ⎞ ⎜ − 0 ⎟ ⎛ ⎞ ⎜ x E Y ⎟⎛ ⎞ ε XX ⎜ ⎟σ XX ⎜ε ⎟= − νXY 1 0 ⎜σ ⎟ ⎜YY ⎟ ⎜ E E ⎟⎜YY ⎟ ⎝ XY⎠ ⎜ X Y ⎟⎝XY ⎠ ⎜ 1 ⎟ ⎜ 0 ⎟ ⎝ G XY ⎠ Where, since Sij S ji νXY /E Xν YX /E Y € • Consider an area A oc composite with a force F applced || to fibers (plates) € € • Modulus of fibers: E f • Modulus of matrix: Em • Volume fraction of fibers: f • Area of fibers = fA c Area of matrix = (1-f)A c • Strain in composite: c = ε m = ε f strain instrain instrain in composite matrix fibers • Force in composite, F ,cgiven by: Fc = F m + F f force in force inforce in composite matrix fibers ∴ A σ = σ (1− f ) + σ fA c c  m c  f c compositensmatrixin stress in fibers • Modulus of composite: E c σ /c c σ m(1− f ) σ ff ∴ E c + but, εc= ε m ε f εc εc σ m( f ) σ ff ∴ E c + but, σ mε =mE ; σm/ε = Ef f f ε m ε f ∴ E c E 1m(f + E)f f (“Rule of mixtures”, “Upper-bound modulus”) • Now consider a length l oc composite with a force F applced ⊥ to fibers (plates) ME382 - 18/iv/14 2 Lecture 35 - Composites • Modulus of fibers: Ef • Modulus of matrix: Em • Volume fraction of fibers:f • Total length of fib
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