## Conceptual design approach

A skilled designer blends knowledge of materials, an understanding of manufacturing processes, and imagination of new or innovative designs. It is the prediction of performance in its broadest sense, including all the characteristics and properties of materials that are essential and relate to the processing of the plastic. To the designer, an example of a strict definition of a design property could be one that permits calculating of product dimensions from a stress analysis. Such properties obviously are the most desirable upon which to base material selections. These correlative properties, together with those that can be used in design equations, generally are called engineering properties. They encompass a variety of stress situations over and above the basic static strength and rigidity, such as impact, fatigue, high and low temperature capability, flammability, chemical resistance, and arc resistance.

Recognize that there are many stresses that cannot be accurately analyzed in plastics, metals, aluminum, etc. Thus one relies on properties that correlate with performance requirements. Where the product has critical performance requirements, such as ensuring safety to people, production prototypes will have to be exposed to the requirements it is to meet in service.

### Design Analysis

The designer starts by one visualizing a certain family of material, makes approximate calculations to see if the contemplated idea is practical to meet requirements that includes cost, and, if the answer is favorable, proceeds to collect detailed data on a range of materials that may be considered for the new product. When plastics are the candidate materials, it must be recognized from the beginning that the available test data require understanding and proper interpretation before an attempt can be made to apply them to the initial product design. For this reason, an explanation of data sheets is required in order to avoid anticipating product characteristics that may not exist when merely applying data sheet information without knowing how such information was derived. The application of appropriate data to product design can mean the difference between the success and failure of manufactured products made from any material (plastic, steel, etc.).

In structural applications for plastics, which generally include those in which the product has to resist substantia] static and/or dynamic loads, it may appear that one of the problem design areas for many plastics is their low modulus of elasticity. The moduli of unfilled plastics are usually under 7 X 103 MPa (1 X 106 psi) as compared to materials such as metals and ceramics where the range is usually 7 to 28 X 104 MPa (10 to 40 x 106 psi). However with reinforced plastics (RPs) the high moduli of metals are reached and even surpassed as summarized in Fig. 2.3.

Since shape integrity under load is a major consideration for structural products, low modulus plastic products are designed shapewise for efficient use of the material to afford maximum stiffness and overcome their low modulus. These type plastics and products represent most of the plastic products produced worldwide.

With the structural analysis reviewed characteristics or behaviors of plastics are included. These characteristics or behaviors are reviewed throughout this book. The following information provides examples of what could apply in a design.

The value of heat insulation is fully appreciated in the use of plastic drinking cups and of plastic handles on cooking utensils, electric irons, and other devices where heat can cause discomfort or burning. In electrical devices the plastic material's application is extended to provide not only voltage insulation where needed, but also the housing that would protect the user against accidental electrical grounding. In industry the thermal and electrical uses of plastics are many, and these uses usually combine additional features that prove to be of overall benefit.

Corrosion resistance and color are extremely important in many products. Protective coatings for most plastics are not required owing to their inherent corrosion-resistant characteristics. The eroding effects of rust are well known with certain materials, and materials such as certain plastics that do not deteriorate offers distinct advantages. Colors for esthetic appearance are incorporated in the material compound and become an integral part of the plasdc for the life of the product.

Those with transparency capabilides provide many different products that include transportation vehicle lighting, camera lenses, protective shields (high heat resistance, gunfire, etc.), etc. When transparency is needed in conjunction with toughness and safety, plastic materials are the preferred candidates. Add to the capability of providing simple to very complex shapes.

Other important properties for certain products include coefficient of friction, chemical resistance, and others. Many plastic materials inherendy have a low coefficient of friction. Other plastic materials can incorporate this property by compounding a suitable ingredient such as graphite powder into the base material. It is an important feature for moving products, which provides for self-lubrication. Chemical resistance is another characteristic that is inherent in most plastic materials; the range of this resistance varies among materials.

Materials that have all these favorable properties also have their limitations. As with other materials, every designer of plastic products has to be familiar with their advantages and limitations. It requires being cautious and providing attention to all details - nothing new since this is what designers have been doing for centuries with all kinds of materials if they want to be successful.

### Pseudo-Elastic Method

As reviewed viscoelastic behavior relates to deformations that are dependent on time under load and the temperature. Therefore, when structural components are to be designed using plastics it must be remembered that the standard engineering equations that are available (Figs 2.31 and 2.32) have been derived under the assumptions that (1) the strains are small, (2) the modulus is constant, (3) the strains are independent of the loading rate or history and are immediately reversible, (4) the material is isotropic, and (5) the material behaves in the same way in tension and compression.

These equations cannot be used indiscriminately. Each case must be considered on its merits, with account being taken of the plastic behavior in time under load, mode of deformation, static and/or dynamic loads, service temperature, fabrication method, environment, and others. The traditional engineering equations are derived using the relationship that stress equals modulus times strain, where the modulus is a constant. The moduli of many plastics are generally not a constant. Several approaches have been reviewed permitting use of these type igure 2 3 1 Engineering equations (na = neutral axis).

bH i rbr

F Itotal load)

FL 4Z

F (total load)

far support)

(at Support)

I92EI

I92EI

3s4ei plastics. The drawback is that these methods can be quite complex, involving numerical techniques that may not be attractive to designers. However, one method has been widely accepted, the so-called pseudo-elastic (PE) design method.

In the PE method time-dependent property values for the modulus (include secant modulus) are selected and substituted into the standard equations. This approach is sufficiently accurate if the value chosen for the modulus takes into account the projected service life of the product and/or the limiting strain of the plastic. This approach is not a straightforward solution applicable to all plastics or even to one plastic in all its applications. This type of evaluation takes into consideration the value to use as a safety factor (SF). If no history exists a high value will be required. In time with service condition inputs, the SF can be reduced if justified (Chapter 7).

Theory of Combined Action

### Overview

The following sections attempt only to set forth the elements of design theory of reinforced plastics (RPs). Fibrous RPs differ from most other engineering materials because they combine two essentially different materials, fibers and synthetic resin, into a single composite. In this they are somewhat analogous to reinforced concrete which combines concrete and steel, but in RPs the fibers are generally much more evenly distributed throughout the mass and the ratio of fibers to resin is much higher than the ratio of steel to concrete.

In their design it is necessary to take into account the combined action of fiber and resin. Sometimes the combination can be considered to be homogeneous and, therefore, to be similar to engineering materials like metal but in other cases, homogeneity cannot be assumed and it is necessary to take into account the fact that two widely dissimilar materials have been combined into a single unit.

In designing these reinforced plasties, certain important assumptions are made. The first and most fundamental is that the two materials act together and that the stretching, compression, and twisting of fibers and of resin under load is the same, that is, the strains in fiber and resin are equal. This assumption implies that a good bond exists between resin and fiber to prevent slippage between them and to prevent wrinkling of the fiber.

The second major assumption is that the material is elastic, that is, strains are directly proportional to the stresses applied, and when a load is removed the deformation disappears. In engineering terms the material is assumed to obey Hooke's Law. This assumption is probably a close approximation of the actual behavior in direct stress below the proportional limit, particularly in tension, if the fibers are stiff and elastic in the Hookean sense and carry essentially all of the stress. The assumption is probably less valid in shear where the resin carries a substantial portion of the stress. The resin may undergo plastic flow leading to creep or to relaxation of stress, especially when stresses are high.

More or less implicit in the theory of materials of this type is the assumption that all of the fibers are straight and unstressed or that the initial stresses in the individual fibers are essentially equal. In practice it is quite unlikely that this is true. It is to be expected, therefore, that as the load is increased some fibers reach their breaking points first. As they fail, their loads are transferred to other as yet unbroken fibers, with the consequence that failure is caused by the successive breaking of fibers rather than by the simultaneous breaking of all of them. The effect is to reduce the overall strength and to reduce the allowable working stresses accordingly, but the design theory is otherwise largely unaffected as long as essentially elastic behavior occurs. The development of higher working stresses is, therefore, largely a question of devising fabrication techniques to make the fibers work together to obtain maximum strength.

Design theory shows that the values of a number of elastic constants must be known in addition to the strength properties of the resin, fibers, and combination. Reasonable assumptions are made in carrying out designs. In the examples used, more or less arbitrary values of elastic constants and strength values have been chosen to illustrate the theory. Any other values could be used.

As more experience is gained in the design of these materials, and as more complete experimental data are forthcoming, the design procedures will no doubt be modified. This review can be related to the effects of environment.

### Stress-Strain Analysis

Any material when stressed stretches or is deformed. If the resin and the fiber in RPs are firmly bonded together, the deformation is the same in both. For efficient structural behavior high strength fibers are employed, but these must be more unyielding than the resin, therefore for a given deformation or strain, a higher stress is developed in the fiber than in the resin. If the stress to strain relationships of fiber and resin are known from their stress-strain diagrams, the stresses developed in each for a given strain can be computed, and their combined action determined.

In Fig. 2.27 stress-strain diagrams for glass fiber and for two resins are shown. Curve A, typical of glass, shows that stress and strain are very nearly directly proportional to each other to the breaking point. Stiffness, or modulus of elasticity, as measured by the ratio of stress to strain, is high. Curve B represents a hard resin. Stress is directly proportional to strain when both are low, but stress gradually levels off as strain increases. Stiffness, or modulus of elasticity, is much lower than that of glass. The tangent measures it to the curve, usually at the origin. Curve C represents a softer resin intermediate between the hard resin and the very soft plastics. Stress and strain are again directly proportional at low levels, but not when the strains become large. Modulus of elasticity, as measured by the tangent to the curve, is lower than for the hard resin.

These stress-strain diagrams may be applied, for example, in the investigation of a rod in which half the total volume is glass fiber and half is resin. If the glass fibers are laid parallel to the axis of the rod, at any cross section, half of the total cross-sectional area is glass and half is resin. If the rod is stretched 0.5%, the glass is stressed at an intensity of 345 MPa (50,000 psi) and the resin, if resin B, at 52 MPa (7500 psi), or if resin C, at 17 MPa (2500 psi). If, for example, the rod has a total cross section of one-half square inch, the glass is one-quarter square inch, and the total stress in the glass is '4 times 50,000 or 5,675 kg (12,500 lb). Similarly, the stress in the resin, if resin B, is 850 kg (1875 lb), and in resin C is 280 kg (625 lb). The load required to stretch the rod made with resin B is therefore the sum of the stresses in glass and resin, or 6,526 kg (14,375 lb). Similarly, for a rod utilizing resin C, the load is 5,960 kg (13,125 lb). The average stress on the one-half square inch cross section is therefore 198 MPa (28,750 psi) or 180 MPa (26,250 psi), respectively.

An analogous line of reasoning shows that at a strain of 1.25% the stress intensity in the glass is 860 MPa (125,000 psi), and in resins B and C it is 87 and 31 MPa (12,600 and 4,500 psi), respectively. The corresponding loads on rods made with resins B and C are 237 and 223 MPa (34,400 and 32,375 lb), respectively.

Loading |
Beam ends |
Deflections at |
K,„ |
Ks |

Uniformly distributed |
Both simply supported |
Midspan |
5/384 |
1/8 |

Uniformly distributed |
Both clamped |
Midspan |
1/384 |
1/8 |

Concentrated at midspan |
Both simply supported |
Midspan |
1/48 |
1/4 |

Concentrated at midspan |
Both clamped |
Midspan |
1/192 |
1/4 |

Concentrated at outer | ||||

quarter points |
Both simply supported |
Midspan |
11/768 |
1/8 |

Concentrated at outer | ||||

quarter points |
Both simply supported |
Load point |
1/96 |
1/8 |

Uniformly distributed |
Cantilever, 1 free, | |||

1 clamped |
Free end |
1/8 |
1/2 | |

Concentrated at free end |
Cantilever, 1 free, | |||

1 clamped |
Free end |
1/3 |
1 |

The foregoing can be put into the form of an equation oA = ofif+oA (2-81)

where a = mean stress intensity on entire cross section Of = stress intensity in fiber a, = stress intensity in resin A = total cross-sectional area

Af = cross-sectional area of fiber Ar = cross-sectional area of resin

If the moduli of elasticity, as measured by the tangents to the stressstrain diagrams are known, the following relationships hold:

Er = modulus of elasticity of resin Ef = modulus of elasticity of fiber

Referring to Fig. 2.27, the tangent to the stress-strain curve for glass gives a value of modulus of elasticity Ej-= 10 x 106 psi. The tangents to the two resin curves give values of Erequal to 1.5 x 106 psi and 0.5 x 106 psi, respectively. Substituting these values in Eq. 2-83 and solving for the stresses in the one-half square inch rod of the previous example, gives

Resin B

Average values of modulus of elasticity of the entire cross section may be computed by dividing a by the strain. The strain is 0.5%, therefore the two average values of E of the rod, incorporating resins B and C, are 5.75 x 106 psi and 5.35 x 106 psi, respectively.

For a cross section made up of a number of different materials, Eq. 2-81 may be generalized to a A = X °¡Ai /=1

in which (7, is the tensile strength and A, the cross-sectional area of any component of the cross section. This equation can be still further generalized to include tension, compression, and shear

in which S, is the strength property of the cross-sectional area of component i, and S is the mean strength property over the endre cross secdon A.

Similarly, to find the overall modulus of elasticity of a cross-section, the equation becomes in which E is the overall modulus of elasticity, A the total cross section and E; the modulus of elasticity corresponding to the partial cross sectional area For shear modulus G the equation becomes

### Plain Reinforced Plates

Fibrous reinforced plates, flat or curved, are commonly made with mat, fabrics, and parallel filaments, either alone or in combination. Mat is usually used for good strength at minimum cost, fabrics for high strength, and parallel filaments for maximum strength in some particular direction.

Because the fibers in mat are randomly oriented, mat-reinforced materials have essentially the same strength and elastic properties in all directions in the plane of the plate, that is, they are essentially isotropic in the plane. Consequendy, the usual engineering theories and design methods employed for isotropic engineering materials may be applied. It is only necessary to know strength, modulus of elasticity, shearing modulus, and Poisson's ratio of the combined mat and resin. These can be obtained from standard stress-strain measurements made on specimens of the particular combination of fiber and resin under consideration.

In fabric and roving-reinforced materials the strength and elastic properties are different in different directions, that is, they are not isotropic, and the usual engineering equations must accordingly be modified. Because fabrics are woven with yarns at right angles (warp and fill directions), a single layer of fabric-reinforced material has two principal directions or natural axes, longitudinal (warp) and transverse (fill) at right angles to each other. This structure is called orthotropic (right-angled directions). Parallel strands of fiber, as in a single layer of roving-reinforced or unidirectional fabric-reinforced plates, also result

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