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Design of Structural Elements Composite panel design • Laminate analysis gives the fundamental information on stiffness, elastic constants and uniaxial strengths. • For structural analysis, we need in-plane stiffness [A] and flexural rigidity [D]. A11 A12 A22 D11 D22 D12 D66 Remember that these values depend on laminate thickness. Composite panel design • For convenience, D1 = D11, D2 = D22, D3 = D12 - 2 D66 • For a homogeneous orthotropic plate, thickness h: D1 = Ex h3 / 12m D2 = Ey h3 / 12m D66 = Gxy h3 / 12 where m = 1 - nxy nyx = 1 - nxy2 Ey / Ex Composite panel design • For in-plane loads, the elastic constants are used in the normal way. • Under uniaxial compression, a plate is likely to buckle at some critical load Nx’. • Buckling loads depend on geometry, edge conditions and flexural properties. • Thin plates may fail by shear buckling before shear failure load. Buckling of Composite Panels • For small aspect ratios (0.5 < a/b < 2): 2 b2 a2 N x ' 2 D1 2 D2 2 2D3 b a b • For long, simply-supported plates with a/b > 2, buckling is independent of length: N x ' 4 2D1 K1 b2 where D 1/ 2 D K1 0.5 2 3 D1 D1 Transverse Loading of Composite Panels • Transverse point load P, or uniform pressure p, so that P = p a b: a b • Maximum transverse panel deflection is: w Pa2 D2 with max bending moments M x 1P and My 2P Transverse Loading of Composite Panels The design parameters , 1 and 2 depend on plate aspect ratio, flexural stiffness, edge conditions and load: Hollaway (ed), Handbook of Polymer Composites for Engineers Thin walled beam design • Standard isotropic design formulae for deflections may be used, but check whether a shear correction is required: w PL3 D 1 2 D LQ where D is the flexural rigidity and Q is the shear stiffness. Hollaway (ed), Handbook of Polymer Composites for Engineers Thin walled beam design • In torsion, wall buckling may be a critical condition. • In general, several failure modes are possible - a systematic design procedure is required. • Laminates may have different tensile and compressive strengths. Powell, Engineering with FibrePolymer Laminates Sandwich Construction • Thin composite skins bonded to thicker, lightweight core. • Large increase in second moment of area without weight penalty. • Core needs good shear stiffness and strength. • Skins carry tension and compression loads. Sandwich panels are a very efficient way of providing high bending stiffness at low weight. The stiff, strong facing skins carry the bending loads, while the core resists shear loads. The principle is the same as a traditional ‘I’ beam: Bending stiffness is increased by making beams or panel thicker - with sandwich construction this can be achieved with very little increase in weight: The stiff, strong facing skins carry the bending loads, while the core resists shear loads. Total deflection = bending + shear Bending depends on the skin properties; shear depends on the core Foam core comparison PVC (closed cell) - ‘linear’ – high ductility, low properties - ‘cross-linked’ – high strength and stiffness, but brittle - ~ 50% reduction of properties at 40-60oC - chemical breakdown (HCl vapour) at 200oC Foam core comparison PU - inferior to PVC at ambient temperatures - better property retention (max. 100oC) Phenolic - poor mechanical properties - good fire resistance - strength retention to 150oC Foam core comparison Syntactic foam - glass or polymer microspheres - used as sandwich core or buoyant filler - high compressive strength Balsa - efficient and low cost - absorbs water (swelling and rot) - not advisable for primary hull and deck structures; OK for internal bulkheads, etc? Both images from www.marinecomposites.com Airex R63 linear PVC 300 MPa 250 200 tensile modulus 150 shear modulus 100 shear strength 50 0 50 100 150 3 density (kg/m ) Why honeycomb? List compiled by company (Hexcel) which sells honeycomb! Material Property Honeycomb Advantages Foam includes – polyvinyl chloride (PVC) – polymethacrylimide – polyurethane – polystyrene – phenolic – polyethersulfone (PES) Relatively low crush strength and stiffness Increasing stress with increasing strain Friable Limited strength Fatigue Cannot be formed around curvatures Excellent crush strength and stiffness Constant crush strength Structural integrity Exceptionally high strengths available High fatigue resistance OX-Core and Flex-Core cell configurations for curvatures Wood-based includes – plywood – balsa – particleboard Very heavy density Subject to moisture degradation Flammable Excellent strength-to-weight ratio Excellent moisture resistance Self-extinguishing, low smoke versions available Sandwich constructions made with other core materials (balsa, foam, etc) have a large surface are available for bonding the skins. In honeycomb core, we rely on a small fillet of adhesive at the edge of the cell walls: The fillet is crucial to the performance of the sandwich, yet it is very dependent on manufacturing factors (resin viscosity, temperature, vacuum, etc). Honeycomb is available in polymer, carbon, aramid and GRP. The two commonest types in aerospace applications are based on aluminium and Nomex (aramid fibre-paper impregnated with phenolic resin). Cells are usually hexagonal: but ‘overexpanded’ core is also used to give extra formability: Core properties depend on density and cell size. They also depend on direction - the core is much stronger and stiffer in the ‘ribbon’ or ‘L’ direction: 5056 aluminium honeycomb 600 shear modulus 500 400 L' direction 300 'W' direction 200 100 0 30 40 50 60 density (kg/m 3) 70 80 Aluminium generally has superior properties to Nomex honeycomb, e.g: 'L' direction plate shear modulus 600 500 MPa 400 Nomex 300 Al 200 100 0 20 40 60 density (kg/m 3) 80 Aluminum Honeycomb • relatively low cost • best for energy absorption • greatest strength/weight • thinnest cell walls • smooth cell walls • conductive heat transfer • electrical shielding • machinability Aramid Fiber (Nomex) Honeycomb • flammability/fire retardance • large selection of cell sizes, densities, and strengths • formability and parts-making experience • insulative • low dielectric properties Sandwich Construction • Many different possible failure modes exist, each of which has an approximate design formula. Design Formulae for Sandwich Construction t c core: tensile modulus Ec shear modulus Gc skin: tensile modulus Es d=c+t h Sandwich Construction - flexural rigidity • Neglecting the core stiffness: Es bh 3 c 3 D 12 • Including the core: 3 2 Es bt Es btd Ec bc D 6 2 12 • If core stiffness is low: Es btd 2 D 2 3 Sandwich Construction - flexural rigidity • Shear stiffness is likely to be significant: w PL3 D 1 2 D LQ where shear stiffness Q = b c Gc • If D/L2Q < 0.01, shear effects are small. • If D/L2Q > 0.1, shear effects are dominant. Sandwich Construction - flexural rigidity • Plate stiffnesses can be calculated by CLA, but shear effects must be considered. • Formula for plate deflection is of the form: w Pa2 D2 1 2 D a Q 2 where the transverse shear stiffness is now Q = c Gc. a is the longest side of a rectangular panel. Shear correction factor (pressure loaded panel) 4 3.5 3 2.5 2 1.5 1 0 1000 2000 span (mm) 3000 Bending stresses in sandwich beams • It is often assumed that the core carries no bending stress, but are under a constant shear stress. For an applied bending moment M: MEs h • Skin stress s • Core shear stress: 2D 4 S Estd Ec c 2 y c D 2 2 4 where S is the shear force y is distance from neutral axis S • If core stiffness can be neglected: c bd Further reading: L Hollaway (ed.), Handbook of Polymer Composites for Engineers, Woodhead (1994). Hexcel Honeycomb Sandwich Design Technology: http://www.hexcel.com/NR/rdonlyres/80127A98-7DF2-4D06A7B3-7EFF685966D2/0/7586_HexWeb_Sand_Design.pdf Eric Green Associates, Marine Composites chapter 3 (1999): http://www.marinecomposites.com