Analysis and design of composite structures Class notes 1
1. Introduction 2
Definition: composite means that different materials are combined to form a third material whose properties are superior to those of the individual constituents if considered alone. The individual constituents can often be identified by naked eye. Properties that may be improved: strength, stiffness, weight, fatigue life, thermal insulation, thermal conductivity, acoustical insulation, corrosion resistance, wear resistance, attractiveness 3
Different materials may be combined in a microscopic scale such as metal alloys but the resulting material is essentially macroscopically homogeneous. If well designed composites usually exhibit the best qualities of their constituents Not all properties are improved at the same time. Some are even contradictory: thermal insulation vs. thermal conductivity. The application will drive the most important properties. 4
1.1. Classification 5
Commonly accepted types of composite materials Fibrous composite materials Laminated composite materials Particulate composite materials Combinations of the above 6
Fibrous composite materials Long fibers are inherently much stiffer and stronger than the same material in bulk form. Geometry plays a decisive role: long fibers bulk material. In fibers the structure is more perfect and crystals are aligned along the fiber axis. There are fewer internal defects. Example: ordinary plate glass is much weaker than glass fibers. In fibers the crystals are aligned along the fiber axis. Moreover there are fewer internal defects in fibers than in bulk material. 7
Fibrous composite materials: properties of fibers High length/diameter ratio Near crystal size diameter Fiber or wire Density (kg/m 3 ) Tensile strength (GPa) S/ρ ( 10 5 ) Tensile stiffness (GPa) E/ρ ( 10 2 ) Aluminum 2630 0.62 24 73 2.8 Titanium 4610 1.9 41 115 2.5 Steel 7660 4.1 54 207 2.7 E-glass 2500 3.4 136 72 2.9 S-glass 2440 4.8 197 86 3.5 Carbon 1380 1.7 123 190 14 Beryllium 1820 1.7 93 300 16 Boron 2520 3.4 137 400 16 Graphite 1380 1.7 123 250 18 8
Fibrous composite materials Direct comparison is not fair since fibers must be surrounded by matrix Graphite and carbon fibers are commonly used today. Heat treatments at 1700 o C and higher. More temperature means higher modulus but lower strength. Whiskers have even more perfect structure than fibers 9
Fibrous composite materials: properties of whiskers Shorter than fibers but same near crystal size diameter Imperfections in crystalline structure Whisker Density (kg/m 3 ) Theoretical strength (GPa) Experimental strength (GPa) S E /ρ ( 10 5 ) Tensile stiffness (GPa) E/ρ ( 10 2 ) Copper 8740 12 3.0 34 124 1.4 Nickel 8790 21 3.9 4 215 2.5 Iron 7680 20 13 1701 200 2.6 B 4 C 2470 45 6.7 270 450 18 SiC 3120 83 11 350 840 27 Al 2 O 3 3880 41 19 490 410 11 C 1630 98 21 1300 980 60 10
Fibrous composite materials: properties of matrices Fibers and whiskers cannot be used without matrix Matrix gives support and protection for fibers Matrix transfers stresses Matrix may be polymers, metals, ceramics or carbon. The cost escalates. Polymeric matrices may be linear, branched or crosslinked (rubbers, thermoplastics and thermosets). Thermoplastics can be reheated. Thermosets cannot. 11
Fibrous composite materials: properties of matrices Matrices bond fibers and whiskers Lower density, stiffness and strength Fibers + matrix stiffness and strength density branched cross-linked linear Thermoplastics: Thermosets: nylon, polyethylene epoxies, phenolics 12
Fibrous composite materials: properties of matrices Metals matrices flow around in-plane fibers: aluminum, titanium, nickel-chromium alloys Ceramic matrices cast around in-plane fibers Carbon matrix vapor deposited on in-place fibers (challenging production) 13
Laminated composite materials Layers of two or more different materials bonded together Combined best aspects of constituent layers Examples: bimetals, clad metals, laminated glass, laminated fibrous composites etc. 14
Laminated composite materials: bimetals Two metal strips Bonded strips heat up heat up 15
Laminated composite materials: clad metals High-strength aluminum alloy covered with corrosion resistant aluminum alloy Copper clad aluminum wire is lightweight, connectable, stays cool and is less expensive Aluminum is lightweight and cheap. It could be used as replacement for copper. But aluminum overheats and is difficult to connect to terminals. Copper is expensive and heavy, but stays cool and connects easily. 16
Laminated composite materials: laminated glass Protect one layer of material by another Glass is brittle and transparent Polyvinyl butyral is a tough and flexible plastic Safety glass is a layer of polyvinyl butyral sandwiched between layers of glass 17
1.2. Mechanical behavior of composite materials 18
Common engineering materials are homogeneous and isotropic A homogeneous body has uniform properties throughout, i.e., they are independent of position An isotropic body has material properties that are the same in every direction, i.e., the properties are independent of orientation Example: a body with temperature dependent properties subject to temperature gradient is not homogeneous but is still isotropic. 19
Common engineering materials are homogeneous and isotropic A heterogeneous body has nonuniform properties throughout, i.e., they are dependent on position An anisotropic body has material properties that are different in all directions, i.e., the properties depend on orientation 20
Composite materials are inherently heterogeneous and can be analyzed under two points of view: Micromechanics: the iteration between constituents is examined on a microscopic scale to determine their effects on the properties of the composite material Macromechanics: the material is presumed homogeneous and the effects of constituents materials are detected only on an average sense as macroscopic properties of the composite material. 21
Comparison of mechanical behavior isotropic anisotropic 22
Isotropic materials: Normal stress causes no shear deformation Shear stress causes no extension (or contraction) Only two properties are needed to quantify deformation: Young modulus and Poisson ratio 23
Anisotropic materials: Normal stress causes shear deformations Shear stress causes extension (or contraction) There is coupling between both modes Conventional tensile specimen cannot be used L B A B C W R G T 24
1.3. Terminology 25
Lamina, ply or layer Flat (or curved) arrangement of unidirectional fibers or woven fibers in a matrix. Fibers carry loads (strong and stiff) and matrix support and protects fibers and transmit loads 26
Lamina, ply or layer Matrix distributes load in broken fibers or whiskers τ σ σ 27
Lamina, ply or layer (stress strain behavior) Fibers generally linear elastic behavior Metals approx. elastic perfectly plastic Aluminum, polymers elastic plastic Matrix viscoelastic (resinous) σ σ σ σ ε& 1 ε& 2 ε& 3 ε ε ε Linear elastic Elastic perfectly plastic Elastic-plastic ε Viscoelastic 28
Laminates Laminate is a bonded stack of laminae with various orientations. Usually bonded together by the same matrix material. Purpose: to tailor the directional dependence of strength and stiffness to match loadings 29
1.4. Potential advantages 30
Qualitative facts Advanced reinforced fiber composites ultrahigh strength and stiffness such as boron or graphite Glass fibers have lower quality compared to carbon Composites can have the same strength and stiffness as steel and yet are 70% lighter As much as 3 stronger than aluminum and weight only 60% Composites can be tailored to meet design requirements and support a variety of load cases 31
Strength and stiffness advantages Strength/density and stiffness/density ratios are commonly mentioned although they disregard costs What good will this material do per unit weight? fiber strength lamina 0 o laminate matrix 90 o stiffness quasi-isotropic 32
Specific strength and stiffness S/ρ (specific strength) 300 250 200 150 100 S-glass Kevlar 49 Graphite Boron Beryllium High modulus graphite Bulk metal quasi-isotropic unidirectional lamina fiber 50 Ti Beryllium Al 0 0 5 10 15 20 25 30 E/ρ (specific stiffness) 33
Cost advantages Various aspects must be considered Raw material cost Design cost Fabrication cost Assembly cost Operation cost Maintenance cost Salvage cost initial cost life-cycle cost 34
Cost advantages Operating costs are lower for composites compared to metals Trade-off: pay more initially and less latter Carbon and graphite are hard to recycle Epoxy is thermoset: it cannot be melt and reused Labor cost is related to part count. Composite structures have generally fewer parts, reduced fastener counts and bonding operations 35
Material utilization factor Definition: r = (raw material weight) / (final structure weight) r = 15 to 25 for metals (machining + milling) r = 1.2 to 1.3 for composites Metal remove material from large blocks Composites lay-up of plies R. M. Jones. Mechanics of Composite Materials 36
Weight advantage Value of weight savings in structures Small civil aircraft Helicopter Aircraft engines Fighters Commercial aircraft Satellites Space shuttle $55/kg $110/kb $440/kg $440/kg $880/kg $22000/kg $33000/kg 37