4 SANDWICH STRUCTURES Sandwich structures occupy a large proportion of composite materials design. They appear in almost all applications.Historically they were the first light and high-performance structures.'In the majority of cases,one has to design them for a specific purpose.Sandwich structures usually appear in industry as semi- finished products.In this chapter we will discuss the principal properties of sandwich structures. 4.1 WHAT IS A SANDWICH STRUCTURE? A sandwich structure results from the assembly by bonding-or welding-of two thin facings or skins on a lighter core that is used to keep the two skins separated (see Figure 4.1). Their properties are astonishing.They have Very light weight.As a comparison,the mass per unit area of the dome of the Saint Peter's Basilica in Rome (45 meter diameter)is 2,600 kg/m whereas the mass per surface area of the same dome made of steel/ polyurethane foam sandwich (Hanover)is only 33 kg/m2 Very high flexural rigidity.Separation of the surface skins increases flexural rigidity. Excellent thermal insulation characteristics. However,be careful: Sandwich materials are not dampening (no acoustic insulation). Fire resistance is not good for certain core types. The risk of buckling is greater than for classical structures The facing materials are diverse,and the core materials are as light as possible One can denote couples of compatible materials to form the sandwich (see Figure 4.2). Be careful:Polyester resins attack polystyrene foams. TSee Section 7.1. 2003 by CRC Press LLC
4 SANDWICH STRUCTURES Sandwich structures occupy a large proportion of composite materials design. They appear in almost all applications. Historically they were the first light and high-performance structures.1 In the majority of cases, one has to design them for a specific purpose. Sandwich structures usually appear in industry as semi- finished products. In this chapter we will discuss the principal properties of sandwich structures. 4.1 WHAT IS A SANDWICH STRUCTURE? A sandwich structure results from the assembly by bonding—or welding—of two thin facings or skins on a lighter core that is used to keep the two skins separated (see Figure 4.1). Their properties are astonishing. They have Very light weight. As a comparison, the mass per unit area of the dome of the Saint Peter’s Basilica in Rome (45 meter diameter) is 2,600 kg/m2 , whereas the mass per surface area of the same dome made of steel/ polyurethane foam sandwich (Hanover) is only 33 kg/m2 . Very high flexural rigidity. Separation of the surface skins increases flexural rigidity. Excellent thermal insulation characteristics. However, be careful: Sandwich materials are not dampening (no acoustic insulation). Fire resistance is not good for certain core types. The risk of buckling is greater than for classical structures. The facing materials are diverse, and the core materials are as light as possible. One can denote couples of compatible materials to form the sandwich (see Figure 4.2). Be careful: Polyester resins attack polystyrene foams. 1 See Section 7.1. TX846_Frame_C04 Page 53 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
core(materials with weak mechanical properties) ec skins(materials with strong mechanical properties) Figure4.1 Sandwich Structure(10≤EE,≤10o) Facings Core metal laminate wood expanded materials thermoplastics asbestos/cement metal ribbed plate in metal laminate or laminate wood plate laminated impregnated carbon wood plate (honeycombs) aluminum stretched aluminum laminate (honeycomb) Figure 4.2 Constituents of Sandwich Materials The assembly of the facings to the core is carried out using bonding adhesives. In some exceptional cases,the facings are welded to the core.The quality of the bond is fundamental for the performance and life duration of the piece.In practice we have 0.025mm≤adhesive thickness≤0.2mm 4.2 SIMPLIFIED FLEXURE 4.2.1 Stresses Figure 4.3 shows in a simple manner the main stresses that arise due to the application of bending on a sandwich beam.'The beam is clamped at its left end, and a force T is applied at its right end.Isolating and magnifying one elementary segment of the beam,on a cross section,one can observe the shear stress resultant T'and the moment resultant M.The shear stress resultant Tcauses shear stresses t and the moment resultant causes normal stresses o. For more details on these stresses,see Chapters 15 and 17,and also Applications 18.3.5 and 18.3.8. 2003 by CRC Press LLC
The assembly of the facings to the core is carried out using bonding adhesives. In some exceptional cases, the facings are welded to the core. The quality of the bond is fundamental for the performance and life duration of the piece. In practice we have 4.2 SIMPLIFIED FLEXURE 4.2.1 Stresses Figure 4.3 shows in a simple manner the main stresses that arise due to the application of bending on a sandwich beam.2 The beam is clamped at its left end, and a force T is applied at its right end. Isolating and magnifying one elementary segment of the beam, on a cross section, one can observe the shear stress resultant T and the moment resultant M. The shear stress resultant T causes shear stresses t and the moment resultant causes normal stresses s. Figure 4.1 Sandwich Structure (10 £ Ec/Ep £ 100) Figure 4.2 Constituents of Sandwich Materials 0.025 mm £ adhesive thickness £ 0.2 mm 2 For more details on these stresses, see Chapters 15 and 17, and also Applications 18.3.5 and 18.3.8. TX846_Frame_C04 Page 54 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
de compression. M(moment) elongation Simplified stresses Figure 4.3 Bending Representation -0 M T 0= 1×ecep t Γ1×ec 0 Figure 4.4 Stresses in Sandwich Structure To evaluate t and o,one makes the following simplifications: The normal stresses are assumed to occur in the facings only,and they are uniform across the thickness of the facings. The shear stresses are assumed to occur in the core only,and they are uniform in the core.' One then obtains immediately the expressions for t and o for a beam of unit width and thin facings shown in Figure 4.4. 4.2.2 Displacements In the following example,the displacement A is determined for a sandwich beam subjected to bending as a consequence of Deformation due to normal stresses o and Deformation created by shear stresses t (see Figure 4.5). 3 See Section 17.7.2 and the Applications 18.2.1 and 18.3.5 for a better approach. 2003 by CRC Press LLC
To evaluate t and s, one makes the following simplifications: The normal stresses are assumed to occur in the facings only, and they are uniform across the thickness of the facings. The shear stresses are assumed to occur in the core only, and they are uniform in the core. 3 One then obtains immediately the expressions for t and s for a beam of unit width and thin facings shown in Figure 4.4. 4.2.2 Displacements In the following example, the displacement D is determined for a sandwich beam subjected to bending as a consequence of Deformation due to normal stresses s and Deformation created by shear stresses t (see Figure 4.5). Figure 4.3 Bending Representation Figure 4.4 Stresses in Sandwich Structure 3 See Section 17.7.2 and the Applications 18.2.1 and 18.3.5 for a better approach. TX846_Frame_C04 Page 55 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
””””▣▣ ””2““ in practice: support support 合≤ 1 Figure 4.5 Bending Deflection To evaluate A,one can,among other methods,use the Castigliano theorem W 高+r elastic energy contribution contribution from bending from shear △ oW energy deflection dF load where the following notations'are used for a beam of unit width: M=Moment resultant T=Shear stress resultant Ep=Modulus of elasticity of the material of the facings Ge Shear modulus of the core material (E）*Eex1×e:+e22 2 l(GS)=1/Gc(ec+2e)×1. Example:A cantilever sandwich structure treated as a sandwich beam (see Figure 4.6). Elastic energy is shown by +高r w=5 +高) See Equation 15.16 that allows one to treat this sandwich beam like a homogeneous beam. One can also use the classical strength of materials approach. 5 See Application 18.2.1 or Chapter 15. 2003 by CRC Press LLC
To evaluate D, one can, among other methods,4 use the Castigliano theorem where the following notations5 are used for a beam of unit width: M = Moment resultant T = Shear stress resultant Ep = Modulus of elasticity of the material of the facings Gc = Shear modulus of the core material Example: A cantilever sandwich structure treated as a sandwich beam (see Figure 4.6). Elastic energy is shown by Figure 4.5 Bending Deflection 4 See Equation 15.16 that allows one to treat this sandwich beam like a homogeneous beam. One can also use the classical strength of materials approach. 5 See Application 18.2.1 or Chapter 15. W 1 2 -- M2 · Ò EI ---------- dx Ú 1 2 -- k · Ò GS ------------T 2 dx Ú = + elastic energy contribution contribution from bending from shear D deflection ∂W ∂F = ------- energy load · Ò EI #Epep 1 ec + ep ( )2 2 ¥ ----------------------; k/· Ò GS 1/Gc ec + 2ep ¥ = ( ) ¥ 1. W 1 2 -- F2 ( ) – x 2 · Ò EI ------------------------ 0 Ú dx 1 2 -- k · Ò GS ------------F2 dx 0 Ú = + W F2 2 ---- 3 3 · Ò EI -------------- k · Ò GS + ------------ Ë ¯ Ê ˆ = TX846_Frame_C04 Page 56 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
aluminum AG5 ep=2.15 mm Ep=65200 MPa Gp=24890 MPa =1m. (width:0.1 m) polystyrene ec=80.2 mm T=F foam Ec=21.5 MPa Gc=7.7 MPa M=F- Figure 4.6 Cantilever Beam where (ED=475×103:G=650×102 The end displacement A can be written as ∂W Then for an applied load of 1 Newton △=0.7×10-2mm/N+1.54×102mm/N Flexure Shear Remark:Part of the displacement A due to shear appears to be higher than that due to bending,whereas in the case of classical homogeneous beams,the shear displacement is very small and usually neglected.Thus,this is a specific property of sandwich structures that strongly influences the estimation of the bending displacements. 4.3 A FEW SPECIAL ASPECTS 4.3.1 Comparison of Mass Based on Equivalent Flexural Rigidity (EI) Figure 4.7 allows the comparison of different sandwich structures having the same flexural rigidity (En).Following the discussion in the previous section,this accounts for only a part of the total flexural deformation. 2003 by CRC Press LLC
where The end displacement D can be written as Then for an applied load of 1 Newton Remark: Part of the displacement D due to shear appears to be higher than that due to bending, whereas in the case of classical homogeneous beams, the shear displacement is very small and usually neglected. Thus, this is a specific property of sandwich structures that strongly influences the estimation of the bending displacements. 4.3 A FEW SPECIAL ASPECTS 4.3.1 Comparison of Mass Based on Equivalent Flexural Rigidity (EI) Figure 4.7 allows the comparison of different sandwich structures having the same flexural rigidity ·EIÒ. Following the discussion in the previous section, this accounts for only a part of the total flexural deformation. Figure 4.6 Cantilever Beam · Ò EI 475 102 ¥ ; · Ò GS k ------------ 650 102 = = ¥ D ∂W ∂F = ------- D 0.7 10–2 mm/N 1.54 10–2 = ¥ + ¥ mm/N Flexure Shear TX846_Frame_C04 Page 57 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC