Sheet Deformation

As the sheet is stretched into the shape of the part, it thins and cools. As soon as the sheet touches the mold surface, dramatic cooling takes place and the change in dimensions of that portion of the part is nearly stopped. Drawing of the sheet involves three-dimensional deformation, because as the planar dimensions increase, the thickness decreases, as shown in Fig. 10.5. Thus, the choice between use of male and female molds has implications for the characteristics of the final part. Imagine a bowl shape as the final package. If this shape is produced with a male mold, the first contact between the mold and the sheet will occur at the base of the bowl, so this will be the first to stop deforming, and consequently the thickest section. If that same part is produced with a female mold, the first contact is at the rim of the bowl, and the last at the base. Consequently, the thickest section of the bowl will be at the rim. 

The plastic at its forming temperature can behave as an elastic solid, a viscoelastic fluid, or a combination of the two. Modeling of thermoforming has been done using all of these models. On a molecular scale, things are just as complex. For an amorphous material, such as polystyrene or PMMA, the forming temperature determines the chain mobility and the ease of flow. For semicrystalline materials, such 

There are methods for estimating the pressures necessary for forming and the optimum temperatures. However, these techniques are based on constant strain rates and constant temperatures, neither of which exists in real thermoforming applications. For that reason, the final processing parameters are usually determined by experimentation. 

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The major vibrational bands in graphite are separated into four main groups which can be approximately described as local in-plane stretches at 1400-1600 cm", local in-plane bends at 600-900 cm", sheet deformations at 400-500 cm" and the rigid sheet modes below 100 cm". ... 

While the composite sheet deforms, the melted thermoplastic matrix can flow among the fibres in axial and transverse directions. 

Although elastic stress-strain behavior describes sheet stretching for most thermoforming processes, sheet deformation during plug-assist prestretching is... 

Kivisild (1969), and Peyton (1966, 1968 a, b) that the force oscillations observed were due to the velocities and vibrations of the ice-floes (whose natural frequencies were usually less than one Hz) rather than due to the structure. Kivisild (1969) estimated that the fundamental frequencies of fluid-supported ice sheets, deforming laterally in dish form, were less than one... 

In summary, then, design with polymers requires special attention to time-dependent effects, large elastic deformation and the effects of temperature, even close to room temperature. Room temperature data for the generic polymers are presented in Table 21.5. As emphasised already, they are approximate, suitable only for the first step of the design project. For the next step you should consult books (see Further reading), and when the choice has narrowed to one or a few candidates, data for them should be sought from manufacturers data sheets, or from your own tests. Many polymers contain additives - plasticisers, fillers, colourants - which change the mechanical properties. Manufacturers will identify the polymers they sell, but will rarely disclose their... 

Deformation of low molecular weight polymer or polymer precursor such as in the casting of acrylic sheet and preparation of glass-reinforced laminates. 

The finite size effects in the contact between a spherical lens of polyurethane and a soft flat sheet of crosslinked polyfdimethyl siloxane) (PDMS) has been addressed by Falsafi et al. [37]. They showed that for deformations corresponding to contact diameters larger than the sheet thickness, the compliance of the system was affected by the glass substrate supporting the soft sheet. In order to minimize the finite size effects in the adhesion measurement of small elastomeric lenses, Falsafi et al. [38] and Deruelle et al. [39] used relatively thick elastic sheets to support their samples. 

Thin sheets of mica or polymer films, which are coated with silver on the back side, are adhered to two cylindrical quartz lenses using an adhesive. It may be noted that it is necessary to use an adhesive that deforms elastically. One of the lenses, with a polymer film adhered on it, is mounted on a weak cantilever spring, and the other is mounted on a rigid support. The axes of these lenses are aligned perpendicular to each other, and the geometry of two orthogonally crossed cylinders corresponds to a sphere on a flat surface. The back-silvered tbin films form an optical interferometer which makes it possible... 

Of obvious importance to aircraft is the smoothness of exterior surfaces. Smooth aerodynamic surfaces reduce aerodynamic drag, resulting in higher airspeeds and increased efficiency. Mechanical fasteners, even countersunk flush fasteners, introduce disruptions in the airflow over the exterior surface. Even the slight deformation of thin sheets around fasteners produces drag. Adhesively bonded structure has no fasteners to disrupt airflow and is more capable of producing the smooth continuous contours that are so common on aircraft. 

Since the first bracket on the right-hand side is a constant and the second is an integer, it is evident that, for any particular /, some leeway must exist in the value of the ratio rj/G for the equality to be satisfied. Here too, the presence of screw helicity must affect either / , or G, or both. In view of the fairly small variations of G allowed if the hybridization of the C atoms is to remain sp, and since the deformation of the C orbitals decreases as the radius of the cylindrical sheets increases, the distance between successive cylinders must decrease and probably tend towards a value characteristic of turbostratic graphite. 

Two-piece food cans may be made by a draw-redraw process, in which lacquer is first applied to and cured on sheet. Blanks are then cut from the sheet and the can is drawn from the blank in two or three stages. The lacquer deforms with the drawing process and lubricates the draw. It then becomes the interior protective coating. Although epoxy-phenolic solvent-borne lacquers are used, even better drawing properties are obtained from organosols. These are dispersions of colloidal polyvinyl chloride powder in solutions of other mixed resins in solvent, e.g. chosen from epoxy, polyester, vinyl and phenolic. 

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