## Sandwich

The same or different materials are combined in the form of sandwich structures (Fig. 4.10). They can be used in products with an irregular distribution of the different materials, and in the form of large structures or sub-structures. A sandwich material composed of two skins and a different core material is similar to RP laminates. Overall load-carrying capabilities depend on average local sandwich properties, but materials failure criteria depend on local detailed stress and strain distributions. Design analysis procedures for sandwich materials composed of linear elastic constituents are well developed. In principle, sandwich materials can be analyzed as composite structures, but incorporation of viscoelastic properties will be subject to the limitations discussed throughout this book.

Structures and sub-structures composed of a number of different components and/or materials, including traditional materials, obey the same principles of design analysis. Stresses, strains, and displacements within individual components must be related through the characteristics (anisotropy, viscoelasticity, and so on) relevant to the particular materia], and loads and displacements must be compatible at component

Figure 4 Honeycomb core sandwich structure (Courtesy of Plastics FALLO)

Figure 4 Honeycomb core sandwich structure (Courtesy of Plastics FALLO)

interfaces. Thus, each individual component or sub-component must be treated.

Load and support conditions for individual components depend on the complete structure (or system) analysis, and are unknown to be deter mined in that analysis. As an example, if a plasdc panel is mounted into a much more rigid structure, then its support conditions can be specified with acceptable accuracy. However, if the surrounding structure has comparable flexibility to the panel, then the interface conditions will depend on the flexural analysis of the complete structure. In a more localized context, structural stiffness may be achieved by ribbing and relevant analyses may be carried out using available design formulae (usually for elastic behavior) or finite element analysis, but necessary anisotropy or viscoelasticity complicate the analysis, often beyond the ability of the design analyst.

### Design

A structural sandwich is a specially shaped product in which two thin facings of relatively stiff, hard, dense, strong material is bonded to a relatively thick core material. With this geometry and relationship of mechanical properties, facings are subjected to almost all the stresses in transverse bending or axial loading. The geometry of the arrangement provides for high stiffness combined with lightness, because the stiff facings are at a maximum distance from the neutral axis, similar to the flanges of an I-beam. Overall load-carrying capabilities depend on average local sandwich properties, but material failure criteria depend on local detailed stress and strain distributions. Design analysis procedures and fabricating procedures for sandwich materials composed of linear elasdc constituents are well developed and reported in the literature. In principle, sandwich materials can be analyzed as RP composites.

The usual objective of a sandwich design is to save weight, increase stiffness, use less expensive materials, or a combination of these factors, in a product. Sometimes, other objectives are also involved such as reducing tooling and other costs, achieving smooth or aerodynamic smoothness, reducing reflected noise, or increasing durability under exposure to acoustic energy. The designers consider factors such as getting the loads in, getting the loads out, and attaching small or large load-carrying members under constraints of deflection, contour, weight, and cost. To design properly, it is important to understand the fabrication sequence and methods, use of the correct materials of construction, the important influence of bond between facing materials and core, and to allow a safety factor that will be required on original, new developments. Use of sandwich panels are extensively used in building and, construction, aircraft, containers, etc.

The primary function of the face sheets is to provide the required bending and in-plane shear stiffness, and to carry the axial, bending, and in-plane shear loading. In high-performance structures, facings most commonly chosen are RPs (usually prepreg), solid plastic, aluminum, titanium, or stainless steel.

The primary function of a core in structural sandwich parts is that of stabilizing the facings and carrying most of the shear loads through the thickness. In order to perform this task efficiently, the core must be as rigid and as light as possible, and must deliver uniformly predictable properties in the environment and meet performance requirements. Several different materials are used such as plastic foam, honeycomb [using RP, film (plastic, steel, aluminum, paper, etc.), balsa wood, etc.].

Different fabricating processes are used. These include bag molding, compression molding, reinforced reaction rejection molding (RRIM), filament winding, corotational molding, etc. There is also the so-called structural foam (SF) that is also called integral skin foaming or reaction injection molding. It can overlap in lower performance use with the significantly larger market of the more conventional sandwich. Up until the 1980s in the U.S., the RIM and SF processes were kept separate. Combining them in the marketplace was to aid in market penetration. During the 1930s to 1960s, liquid injection molding (LIM) was the popular name for what later became RIM and SF (Chapter 1).

These structures are characterized as a plastic structure with nearly uniform density foam core and integral near-solid skins (facings). When these structures are used in load-bearing applications, the foam bulk density is typically 50 to 90% of the plastic's unfoamed bulk density. Most SF products (90wt%) are made from different TPs, principally PS, PE, PVC, and ABS. Polyurethane is the primary TS plastic. Unfilled and reinforced SFs represents about 70% of the products. The principal method of processing (75%) is modified low-pressure injection molding. Extrusion and RIM account for about 10% each.

In a sandwich design, overall proportions of structures can be established to produce an optimization of face thickness and core depth which provides the necessary overall strength and stiffness requirements for minimum cost of materials, weight of components, or other desired objectives. Competing materials should be evaluated on the basis of optimized sandwich section properties that take into account both the structural properties and the relative costs of the core and facing materials in each combination under consideration. For each combination of materials being investigated, thickness of both facings and core should be determined to result in a minimum cost of a sandwich design that provides structural and other functional requirements.

Sandwich configurations are used in small to large shapes. They generally are more efficient for large components that require significant bending strength and/or stiffness. Examples of these include roofs, wall and floor panels, large shell components that are subject to compressive buckling, boat hulls, truck and car bodies, and cargo containers. They also provide an efficient solution for multiple functional requirements such as structural strength and stiffness combined with good thermal insulation, or good buoyancy for flotation.

Sandwich materials can be analyzed as composite structures. Structures and sub-structures composed of a number of different components and/or materials, including traditional materials, obey the same principles of design analysis. Stresses, strains, and displacements within individual components must be related through the characteristics (anisotropy, viscoelasticity, etc.) relevant to the particular material; also loads and displacements must be compatible at component interfaces. Thus, each individual component or sub-component must be treated using the relevant methods.

Load and support conditions for individual components depend on the complete structure (or system) analysis. For example, if a panel is mounted into a much more rigid structure, then its support conditions can be specified with acceptable accuracy However, if the surrounding structure has comparable flexibility to the panel, then the interface conditions will depend on the flexural analysis of the complete structure.

In a more localized context, structural stiffness may be achieved by ribbing, and relevant analyses may be carried out using available design formulae (usually for elastic behavior) or finite element analysis. But necessary anisotropy or viscoelasticity complicate the analysis, often beyond the ability of the design analyst.

Primary structural role of the face/core interface in sandwich construction is to transfer transverse shear stresses between faces and core. This condition stabilizes the faces against rupture or buckling away from the core. It also carries loads normally applied to the panel surface. They resist transverse shear and normal compressive and tensile stress resultants. For the most part, the faces and core that contain all plastics can be connected during a wet lay-up molding or, thereafter, by adhesive bonding. In some special cases, such as in a truss-core pipe, faces and core are formed together during the extrusion process, resulting in an integral homogeneous bond/connection between the components. Fasteners are seldom used to connect faces and core because they may allow erratic shear slippage between faces and core or buckling of the faces between fasteners. Also, they may compromise other advantages such as waterproofing integrity and appearance.

For RP-faced sandwich structures the design approaches includes both the unique characteristics introduced by sandwich construction and the special behavior introduced by RP materials. The overall stiffness provided by the interaction of the faces, the core, and their interfaces must be sufficient to meet deflection and deformation limits set for the structures. Overall stiffness of the sandwich component is also a key consideration in design for general instability of elements in compression.

In a typical sandwich constructions, the faces provide primary stiffness under in-plane shear stress resultants (2^,), direct stress resultants (Nx, Ny), and bending stress resultants (Mx, My). Also as important, the adhesive and the core provide primary stiffness under normal direct stress resultants (Nz), and transverse shear stress resultants (Qg Q^). Resistance to twisting moments (Txz) Tyz), which is important in certain plate configurations, is improved by the faces. Capacity of faces is designed not to be limited by either material strength or resistance to local buckling.

The stiffness of the face and core elements of a sandwich composite must be sufficient to preclude local buckling of the faces. Local crippling occurs when the two faces buckle in the same mode (antisymmetric). Local wrinkling occurs when either or both faces buckle locally and independendy of each other. Local buckling can occur under either axial compression or bending compression. Resistance to local buckling is developed by an interaction between face and core that depends upon the stiffness of each.

With the structural foam (SF) construcdon, large and complicated parts usually require more critical structural evaluation to allow better prediction of their load-bearing capabilities under both static and dynamic conditions. Thus, predictions require careful analysis of the structural foam's cross-section.

The composite cross-section of an SF part contains an ideal distribution of material, with a solid skin and a foamed core. The manufacturing process distributes a thick, almost impervious solid skin that is in the range of 25% of overall wall thickness at the extreme locations from the neutral axis where maximum compressive and tensile stresses occur during bending.

When load is applied flatwise the upper skin is in compression while the lower one is in tension, and a uniform bending curve will develop. However, this happens only if the shear rigidity or shear modulus of the cellular core is sufficiently high. If this is not the case, both skins will deflect as independent members, thus eliminating the load-bearing capability of the composite structure. In this manner of applying a load the core provides resistance against shear and buckling stresses as well as impact (Fig. 4.11). There is an optimum thickness that is critical in designing this structure.

When the SF cross-section is analyzed, its composite nature still results in a twofold increase in rigidity, compared to an equivalent amount of solid plastic, since rigidity is a cubic function of wall thickness. This

Core thickness vs. density impact strength

Thickness:

Impact Strangih

% Oensily Reduction

Figure 4.12 Sandwich and solid material construction

Figure 4.12 Sandwich and solid material construction

increased rigidity allows large structural parts to be designed widi only minimal distortion and deflection when sd'essed within die recommended values for a particular core material. When analyzing rigidity and the moment of inertia (/) can be evaluated three ways. In the first approach, the cross-section is considered to be solid material (Fig. 4.12).

The moment of inertia (Ix) is then equal to:

This commonly used approach provides acceptable accuracy when the load-bearing requirements are minimal. An example is the case of simple stresses or when time and cost constraints prevent more exact analysis.

The second approach ignores the strength contribution of the core and assumes that the two outer skins provide all the rigidity (Fig. 4.13).

The equivalent moment of inertia is then equal to:

This formula results in conservative accuracy, since the core does not

■ Sandwich and I-beam Cross-section

■ Sandwich and I-beam Cross-section

contribute to the stress-absorbing function. It also adds a built-in safety factor to a loaded beam or plate element when safety is a concern.

A third method is to convert the structural foam cross-section to an equivalent I-beam secdon of solid resin material (Fig. 4.14).

The moment of inerda is then formulated as:

where i>, = b(Ec)/(EJ, Ec= modulus of core, Es ts = skin thickness, and = core height

modulus of skin,

This approach may be necessary where operating conditions require stringent load bearing capabilities without resorting to overdesign and thus unnecessary costs. Such an analysis produces maximum accuracy and would, therefore, be suitable for finite element analysis (FEA) on complex parts. However, the one difficulty with this method is that the core modulus and the as-molded variations in skin thicknesses cannot be accurately measured.

The following review relates to the performance of sandwich constructions such as those with RP skins and honeycomb core. For an isotropic material with a modulus of elasticity (£), the bending stiffness factor (EI) of a rectangular beam b wide and ¿deep is:

A rectangular structural sandwich with the same dimensions whose facings and core have moduli of elasticity £y and En respectively, and a core thickness c, the bending stiffness factor EI becomes:

This equation is OK if the facings are of equal thickness, and approximate or approximately equal, but the approximation is close if the facings are thin relative to the core. If, as is usually the case, Ef is much smaller than E^ the last term in the equation is deleted.

Asymmetrical sandwich structures with different materials or different thicknesses in their facings, or both, the more general equation for El may be used. With isotropic materials, the shear modulus G is high compared to the elastic modulus £, and the shear distortion of a transversely loaded beam is so small that it can be neglected in calculating deflection. Sandwich core shear modulus G is usually so much smaller than Ef of the facings that the shear distortion of the core may be large and therefore contribute significantiy to the deflection of a transversely load. The total deflection of a sandwich beam involves the two factors of the deflection caused by the bending moment alone and the deflection caused by shear, that is;

where 8 = total deflection, Sm = moment deflection, and 5S = shear deflection.

Under transverse loading, bending moment deflection is proportional to the load and the cube of the span and inversely proportional to the stiffness factor, EI.

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