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
steel sheet aluminum sheet wooden plate mass =16 10 5 3 plies of satin fabric 3 plies of satin fabric 2 plies of satin fabric 套 I sandwich: sandwich: sandwich: sandwich: nida-aluminum nida Nomex- nida-Kevlar nida-carbon skins glass skins skins skins mass =1. 1.12 0.86 0.69 cost:1 cost:1 c0st1.57 c0st:2.42 Figure 4.7 Comparison of Plates Having Similar Flexural Rigidity El Figure 4.8 Buckling of Sandwich Structure 4.3.2 Buckling of Sandwich Structures The compression resistance of all or part of a sandwich structure is limited by the so-called critical values of the applied load,above which the deformations become large and uncontrollable.This phenomenon is called buckling of the structure (see Figure 4.8).Depending on the type of loading,one can distinguish different types of buckling which can be global or local. 4.3.2.1 Global Buckling Depending on the supports,the critical buckling load F is given by K π(EI) 2+π织k (GS) ■ K=1 K=4 K=2.04 K=0.25 See Application 18.3.4. 2003 by CRC Press LLC
4.3.2 Buckling of Sandwich Structures The compression resistance of all or part of a sandwich structure is limited by the so-called critical values of the applied load, above which the deformations become large and uncontrollable. This phenomenon is called buckling of the structure (see Figure 4.8). Depending on the type of loading, one can distinguish different types of buckling which can be global or local. 4.3.2.1 Global Buckling Depending on the supports, the critical buckling load Fc is given 6 by Figure 4.7 Comparison of Plates Having Similar Flexural Rigidity EI Figure 4.8 Buckling of Sandwich Structure 6 See Application 18.3.4. Fcr K p2 · Ò EI 2 p2 · Ò EI · Ò GS + -------------kK = -------------------------------------- TX846_Frame_C04 Page 58 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
Figure 4.9 Local Buckling of Facings delamination 12 Fcr#1.64ep×1×Ep× crushing Figure 4.10 Damage by Local Buckling 4.3.2.2 Local Buckling of the Facings The facings are subject to buckling due to the low stiffness of the core.Depending on the type of loading,one can find the modes of deformation as shown in Figure 4.9. The critical compression stress is given in the equation below where ve is the Poisson coefficient of the core. o,=a×(EpX丽 with =3123-)1+)} The critical load to cause local damage by local buckling of a facing and the types of damage are shown in Figure 4.10. 4.3.3 Other Types of Damage Local crushing:This is the crushing of the core material at the location of the load application (see figure below). local crushing 2003 by CRC Press LLC
4.3.2.2 Local Buckling of the Facings The facings are subject to buckling due to the low stiffness of the core. Depending on the type of loading, one can find the modes of deformation as shown in Figure 4.9. The critical compression stress is given in the equation below where nc is the Poisson coefficient of the core. The critical load to cause local damage by local buckling of a facing and the types of damage are shown in Figure 4.10. 4.3.3 Other Types of Damage Local crushing: This is the crushing of the core material at the location of the load application (see figure below). Figure 4.9 Local Buckling of Facings Figure 4.10 Damage by Local Buckling scr a Ep Ec 2 ( ) ¥ 1/3 = ¥ with a 3 12 3 – vc ( )2 1 + vc ( )2 { }–1/3 = TX846_Frame_C04 Page 59 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
Compression rupture:In this case (see figure below),note that the weak com- pression resistance of Kevlar fibers'leads to a compression strength about two times less than for sandwich panels made using glass fibers. Fo rupture Fo rupture 2 glass Kevlar 4.4 FABRICATION AND DESIGN PROBLEMS 4.4.1 Honeycomb:An Example of Core Material These well-known materials are made of hexagonal cells that are regularly spaced. Such geometry can be obtained using a technique that is relatively simple.Many thin sheets are partially bonded.Starting from stacked bonded sheets,they are expanded as shown in Figure 4.11. The honeycomb material can be metal (light alloy,steel)or nonmetal (carton impregnated with phenolic resin,polyamide sheets,or impregnated glass fabrics) Metallic honeycombs are less expensive and more resistant.Nonmetallic hon- eycombs are not sensitive to corrosion and are good thermal insulators.The following table shows the mechanical and geometric characteristics of a few current honeycombs,using the notations of Figure 4.11. Table 4.1 Properties of Some Honeycomb Bonded Sheets of Light Alloy Light Alloy Polyamide:Nomex" AG3 2024 Dia.(D):inscribed 6;8;12 4 6 circle (mm) Thickness e (mm) 0.05 0.04 Specific mass(kg/m) 64 80 46 Shear strength 1.7 3.2 1.5 T rup (MPa) Shear modulus: 58 520 280 G (MPa)# 1.5 Gmat(e/D) Shear strength trup 0.85 2 0.9 (MPa) Shear modulus:G= 24 250 140 (MPa) Compression strength: 2.8 4.4 2 C=rup (MPa) Nomex is a product of Du Pont de Nemours. See Section 3.3.3. 2003 by CRC Press LLC
Compression rupture: In this case (see figure below), note that the weak compression resistance of Kevlar fibers7 leads to a compression strength about two times less than for sandwich panels made using glass fibers. 4.4 FABRICATION AND DESIGN PROBLEMS 4.4.1 Honeycomb: An Example of Core Material These well-known materials are made of hexagonal cells that are regularly spaced. Such geometry can be obtained using a technique that is relatively simple. Many thin sheets are partially bonded. Starting from stacked bonded sheets, they are expanded as shown in Figure 4.11. The honeycomb material can be metal (light alloy, steel) or nonmetal (carton impregnated with phenolic resin, polyamide sheets, or impregnated glass fabrics). Metallic honeycombs are less expensive and more resistant. Nonmetallic honeycombs are not sensitive to corrosion and are good thermal insulators. The following table shows the mechanical and geometric characteristics of a few current honeycombs, using the notations of Figure 4.11. 7 See Section 3.3.3. Table 4.1 Properties of Some Honeycomb Bonded Sheets of Polyamide: Nomexa Light Alloy AG3 Light Alloy 2024 Dia. (D): inscribed circle (mm) 6; 8; 12 4 6 Thickness e (mm) 0.05 0.04 Specific mass (kg/m3 ) 64 80 46 Shear strength txz rup (MPa) 1.7 3.2 1.5 Shear modulus: Gxz (MPa) # 1.5 Gmat(e/D) 58 520 280 Shear strength tyz rup (MPa) 0.85 2 0.9 Shear modulus: Gyz (MPa) 24 250 140 Compression strength: sz rup (MPa) 2.8 4.4 2 a Nomex® is a product of Du Pont de Nemours. TX846_Frame_C04 Page 60 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
expansion diameter of inside circle Figure 4.11 Honeycomb low angle #14 milling cutter for honeycombs Figure 4.12 Processing of Honeycomb a'>a b'<b Figure 4.13 Deformation of Honeycomb 4.4.2 Processing Aspects The processing of the honeycomb is done with a diamond disk(peripheral speed in the order of 30 m/s).The honeycomb is kept on the table of the machine by an aluminum sheet to which it is bonded.Below the aluminum sheet,a depression anchors it to the table (see Figure 4.12). One can also deform the honeycomb.It is important to constrain it carefully, because the deformation behavior is complex.For example,a piece of honeycomb under cylindrical bending shows two curvatures as illustrated in Figure 4.13. This phenomenon is due to the Poisson effect,particularly sensitive here (see Section 12.1.4). 2003 by CRC Press LLC
4.4.2 Processing Aspects The processing of the honeycomb is done with a diamond disk (peripheral speed in the order of 30 m/s). The honeycomb is kept on the table of the machine by an aluminum sheet to which it is bonded. Below the aluminum sheet, a depression anchors it to the table (see Figure 4.12). One can also deform the honeycomb. It is important to constrain it carefully, because the deformation behavior is complex. For example, a piece of honeycomb under cylindrical bending shows two curvatures as illustrated in Figure 4.13. 8 Figure 4.11 Honeycomb Figure 4.12 Processing of Honeycomb Figure 4.13 Deformation of Honeycomb 8 This phenomenon is due to the Poisson effect, particularly sensitive here (see Section 12.1.4). TX846_Frame_C04 Page 61 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC
林城 Figure 4.14 Over-Expansion of Honeycomb es0.05 mm R21.5a a≤50mm Figure 4.15 Curvature of Honeycomb adhesive film forming fabric soft membrane tightening piece partial vacuum Figure 4.16 Processing of a Sandwich Piece of a Structural Part The processing can be facilitated using the method of overexpansion which modifies the configuration of the cells as shown in Figure 4.14. At limit of curvature,R is the radius of the contour,and e is the thickness of the sheets which consitute the honeycombs (see Figure 4.15).Nomex honey- combs (sheets of bonded polyamide)must be processed at high temperature.The schematic for the processing of a structural part of sandwich honeycomb is as in Figure 4.16.For moderate loadings (for example,bulkheads),it is possible to fold a sandwich panel following the schematic in Figure 4.17. 2003 by CRC Press LLC
The processing can be facilitated using the method of overexpansion which modifies the configuration of the cells as shown in Figure 4.14. At limit of curvature, R is the radius of the contour, and e is the thickness of the sheets which consitute the honeycombs (see Figure 4.15). Nomex honeycombs (sheets of bonded polyamide) must be processed at high temperature. The schematic for the processing of a structural part of sandwich honeycomb is as in Figure 4.16. For moderate loadings (for example, bulkheads), it is possible to fold a sandwich panel following the schematic in Figure 4.17. Figure 4.14 Over-Expansion of Honeycomb Figure 4.15 Curvature of Honeycomb Figure 4.16 Processing of a Sandwich Piece of a Structural Part TX846_Frame_C04 Page 62 Monday, November 18, 2002 12:07 PM © 2003 by CRC Press LLC