ADVANCED MECHANICS OF COMPOSITE MATERIALS Episode 1 ppt

[...]... (25–250) 15 00–4400 290 14 00 15 00 11 00 14 50 3300–4000 18 00–2200 18 0–200 69 12 0 240– 310 410 360 7.8 2.7 4.5 1. 8 1. 85 19 19 .3 10 .2 56.4 10 .7 33.3 80.5 21. 1 21. 5 2560 2550 2670 17 ,200 216 0 3500 Thermoset polymeric resins Epoxy Polyester Phenol-formaldehyde Organosilicone Polyimide Bismaleimide 60–90 30–70 40–70 25–50 55 11 0 80 2.4–4.2 2.8–3.8 7 11 6.8 10 3.2 4.2 1. 2 1. 3 1. 2 1. 35 1. 2 1. 3 1. 35 1. 4 1. 3 1. 43 1. 2...CONTENTS Preface to the Second Edition v Chapter 1 Introduction 1 1 .1 1.2 1. 2 .1 1.2.2 1. 2.3 1. 3 Structural Materials 1 Composite Materials 9 Fibers for Advanced Composites 10 Matrix Materials 16 Processing 22 References 30 Chapter 2 Fundamentals of Mechanics of Solids 31 2 .1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 2 .10 2 .11 2 .11 .1 2 .11 .2 2 .11 .3 2 .12 Stresses 31 Equilibrium Equations 33 Stress Transformation... Asbestos 15 –20 15 –30 10 –50 15 –40 75 10 –20 25 5 15 15 4 – – 0.2 16 0 550 580 540 17 0 250 18 0 10 0 400 17 50 270 560 17 00 23 36 22 28 5.9 5.5 9 6 13 12 .7 – – 16 0 1. 5 0.8 1. 5 1. 5 1. 32 1. 5 1. 25 1. 24 1. 35 – – – 2.5 16 Advanced mechanics of composite materials the tow, namely the K-number that gives the number of fibers in the tow (e.g., 3K tow contains 3000 fibers) and the tex-number which is the mass in grams of 10 00... In-Plane Shear 11 0 Longitudinal Compression 11 3 Transverse Compression 12 2 Hybrid Composites 12 3 Composites with High Fiber Fraction 12 7 Phenomenological Homogeneous Model of a Ply 12 9 References 13 1 Chapter 4 Mechanics of a Composite Layer 13 3 4 .1 4 .1. 1 4 .1. 2 4.2 4.2 .1 4.2.2 4.3 4.3 .1 4.3.2 4.4 4.4 .1 4.4.2 4.4.3 4.4.4 4.5 4.5 .1 4.5.2 4.5.3 4.6 4.7 4.8 4.9 Isotropic Layer 13 3 Linear Elastic Model 13 3 Nonlinear... specific strength, kσ × 10 3 (m) Maximum specific modulus, kE × 10 3 (m) 3000–3500 3500–5500 2600–3300 90 14 0 18 0 12 0 17 0 2.7–3.0 1. 4 1. 47 0.97 13 0 390 310 3300 12 ,800 17 ,500 7000 2700 2500–3700 2400– 410 0 2700 15 00 210 0–2500 14 00 Basalt (9 13 ) Aramid (12 15 ) Polyethylene (20–40) Carbon (5 11 ) High-strength High-modulus Boron (10 0–200) Alumina – Al2 O3 (20–500) Silicon Carbide – SiC (10 15 ) Titanium Carbide... 340–440 390–880 730–930 930 4.4 4.9 15 .7 2.9 4.9–8.8 4.4 20 1. 1 1. 4 2.3 1. 2 0.9 1. 52 70 60 19 0 70 10 0 60 400 14 30 13 0 730 480 13 00 72–95 74 2.4–2.6 2.2 200 270 3960 3360 Fibers for advanced composites (diameter, µm) Glass (3 19 ) 310 0–5000 Quarts (10 ) 6000 Maximum specific strength, kσ × 10 3 (m) Maximum specific modulus, kE × 10 3 (m) Chapter 1 Introduction 7 Table 1. 1 (Contd.) Material Ultimate tensile... 850 390–420 470–530 18 5 450 480 90 1. 75 1. 78 2.5–2.6 3.96 2.4–2.7 4.9 2.5 1. 9 400 15 0 15 0 10 0 11 0 30 10 0 70 17 ,10 0 47,700 16 ,800 13 ,300 7700 910 0 10 ,000 4700 g s e ds de s b a e Fig 1. 4 Introduction of secant and tangent moduli where t indicates the time moment, whereas σ and T are stress and temperature, corresponding to this moment In the general case, constitutive equation, Eq (1. 9), specifies strain... in Fig 1. 1 as dW = F d Then, work corresponding to point 1 of the curve in Fig 1. 2 is 1 W = Fd 0 s 1 0 e Fig 1. 2 Stress–strain curve for an elastic material 4 Advanced mechanics of composite materials where 1 is the elongation of the bar corresponding to point 1 of the curve The work W is equal to elastic energy of the bar which is proportional to the bar’s volume and can be presented as 1 E = L0... mechanics of composite materials 1 1 2 0.8 0.6 0.4 3 0.2 4 0 T,°C 0 40 80 12 0 16 0 200 (a) 1 1 2 0.8 0.6 0.4 3 0.2 4 0 T,°C 0 40 80 12 0 16 0 200 (b) Fig 1. 13 Dependence of normalized longitudinal moduli (1) , strength under longitudinal tension (2), bending (3), and compression (4) on temperature for unidirectional carbon composites with epoxy matrices having Tg = 13 0◦ C (a) and Tg = 80◦ C (b) (see Table 1. 1... 8.5 6.7 350 310 910 740 240 350 Thermoplastic polymers Polyethylene Polystyrene Teflon Nylon Polyester (PC) Polysulfone (PSU) Polyamide-imide (PAI) Polyetheretherketone (PEEK) Polyphenylene sulfide (PPS) 20–45 35–45 15 –35 80 60 70 90 19 0 90 10 0 80 6–8.5 30 3.5 2.8 2.5 2.7 2.8–4.4 3 .1 3.8 3.5 0.95 1. 05 2.3 1. 14 1. 32 1. 24 1. 42 1. 3 1. 36 4.7 4.3 1. 5 7.0 4.5 5.6 13 .4 7.7 5.9 890 2860 15 0 240 19 0 220 360 300 . 2550 Titanium (10 0–800) 14 00 15 00 12 0 4.5 33.3 2670 Beryllium (50–500) 11 00 14 50 240– 310 1. 8 1. 85 80.5 17 ,200 Tungsten (20–50) 3300–4000 410 19 19 .3 21. 1 216 0 Molybdenum (25–250) 18 00–2200 360 10 .2 21. 5. Structural Materials 1 1.2. Composite Materials 9 1. 2 .1. Fibers for Advanced Composites 10 1. 2.2. Matrix Materials 16 1. 2.3. Processing 22 1. 3. References 30 Chapter 2. Fundamentals of Mechanics of Solids. 2.4–4.2 1. 2 1. 3 7.5 350 Polyester 30–70 2.8–3.8 1. 2 1. 35 5.8 310 Phenol-formaldehyde 40–70 7 11 1. 2 1. 3 5.8 910 Organosilicone 25–50 6.8 10 1. 35 1. 4 3.7 740 Polyimide 55 11 0 3.2 1. 3 1. 43 8.5