## Design Parameter

Loads on a fabricated product can produce different types of stresses within the material. There are basically static and dynamic stresses (Fig. 3.1). The magnitude of these stresses depends on many factors such as applied forces/loads, angle of loads, rate and point of application of each load, geometry of the structure, manner in which the structure is supported, and time at temperature. The behavior of the material in response to these induced stresses determines the performance of the structure.

Examples of stresses due to loads (Courtesy of Plastics FALLO)

Examples of stresses due to loads (Courtesy of Plastics FALLO)

The behavior of materials (plastics, steels, etc.) under dynamic loads is important in certain mechanical analyses of design problems. Unfortunately, sometimes the engineering design is based on the static loading properties of the material rather than dynamic properties. Quite often this means over-design at best or incorrect design resulting in failure of the product in the worst case.

The complex nature of the dynamic behavior problem can be seen from Fig. 3.1, which depicts a wide range of interaction of dynamic loads that occurs with various materials (metals, plastics, etc.). Ideally, it would be desirable to know the mechanical response to the full range of dynamic loads for each material under all types of conditions. However, certain load-material interactions have more relative importance for engineering design, and significant as well as sufficient work on them exists already. The mechanical engineers, civil engineers, and metallurgical engineers have always found materials (includes plastic, steel, aluminum, etc.) to be most attractive to study. Even so, there is a great deal that we do not understand about these materials in spite of voluminous scientific literature existing worldwide. Each type of load response, e.g., creep, fatigue/vibratory, or impact, is a major field in itself. Data on each response is available. However there is always a desire to obtain more data.

The nature and complexity of applied loads as well as the shape requires the usual engineering calculations. For a simple engineering form like a plate, beam, or box structure the standard design formulas can be used with appropriate parameters relating to the factors of short- and long-time loadings, creep, fatigue, impact, and applying the viscoelastic plastic material behavior (Chapter 2). The term engineering formulas refers to those equations in engineering handbooks by which the stress analysis can be accomplished.

In a product load analysis the structure as a whole and each of its elements together are in a state of equilibrium. There are no unbalanced forces of tension, compression, flexure, or shear acting on the structure at any point. All the forces counteract one another, which results in equilibrium. When all the forces acting on a given element in the same direction are summed up algebraically, the net effect is no load. However the product does respond to the various forces internally.

These forces could deform the product due to internal stresses of varying types and magnitudes. This action could be immediate or to some time-temperature period based on its viscoelastic behavior and underestimating potential internal stresses. To overcome this situation different approaches are used, as explained in the engineering books.

An example is when the cross-sectional area of a product increases for a given load, the internal stresses are reduced, so make it thicker. Design is concerned with determining the stresses for a given shape and subse-quendy adjusting the shape until the stresses are neither high enough to risk fracture nor low enough to suggest that material is being wasted (cosdy).

The stress analysis design involves various factors. It requires the descriptions of the product's geometry, the applied loads and displacements, and the material's properties including its viscoelastic behavior. The result is to obtain numerical expressions for internal stresses as a function of the stress's position within the product and as a function of time-temperature as well.

With the more complex shapes the component's geometry complicates the design analysis for plastics (and other materials) and may make it necessary to carry out a direct analysis, possibly using finite element analysis (FEA) followed with prototype testing (Chapter 5).

Loads applied on products induce tension, compression, flexure, torsion, and/or shear, as well as distributing the loading modes. The product's particular shape will control the type of materials data required for analyzing it. The location and magnitude of the applied loads in regard to the position and nature of such other constraints as holes, attachment points, and ribs are important considerations that influences its shape. Also influencing the design decision will be the method of fabricating the product (Chapter 1).

Loads will generally fall into one of two categories, direcdy applied loads and strain-induced loads (Chapter 2. Isolator). Direcdy applied loads are usually easy to understand. They are defined loads that are applied to defined areas of the product, whether they are concentrated at a point, line, or boundary or distributed over an area. The magnitude and direction of these loads are known or can easily be determined. An example of a strain-induced load is when it is required that a product be deflected. The load developed is direcdy related to the strain that occurs. Unlike directly applied loads, strain-induced loads are dependent on the modulus of elasticity; when comparing TPs with TSs, the TPs will generally decrease quicker in magnitude over time. Many assembly and thermal stresses could be the result of these strain-induced loads.

Time-dependent applied loading effects the materials viscoelasticity (Chapter 2). Loads applied for short times and at normal rate cause material response that is essentially elastic in character. However, under sustained load plastics, particularly TPs, tend to creep, a factor that is

Figure 3.2 Example of intermittent loading Figure ':' 3 Loading and unloading examples

Figure 3.2 Example of intermittent loading Figure ':' 3 Loading and unloading examples

included in the design analysis.

Intermittent loading can involve creep and recovery over reladvely long dme periods. Creep deformation during one loading can be pardy recovered in the unloading cycle, leading to a progressive accumulation of creep strain as the continuous intermittent load action continues (Figs. 3.2 and 3.3). This action in an improperly designed product will probably result in creep rupture. An analogue of creep behavior is the stress-relaxation cycle that can occur under constant strain. This behavior is particularly relevant with push-fit assemblies and bolted joints that rely on maintaining their load under constant strain. Special design features or analysis may be required to counteract excessive stress-relaxation.

There are intermittent or dynamic loads that occur over short time periods that can cause failure due to creep and possibly fatigue. This type loading condition applies to products such as motion control isolators, engine mounts, and other antivibration products; panels that vibrate and transmit noise; chairs; and road surface-induced loads carried to vehicle wheels and suspension systems. Plastics' relevant properties in this regard are material stiffness and internal damping, the latter of which can often be used to advantage in design (Chapter 2). Both properties depend on the frequency of the applied loads or vibrations, a dependence that must be allowed for in the design analysis. Design engineers unfamiliar with plastics' behavior will be able to apply the information contained in this book to applicable equations that involve such analysis as multiple and complex stress concentrations. The various machine-design texts and mechanical engineering handbooks review this subject.

Products can be stressed in a manner that is more complex than simple tension, compression, flexure, or shear. Because yielding will also occur under complex stress conditions, a yield criterion can be specified that will apply in all stress states. Any complex stress state can be resolved into the usual engineering three normal components acting along three mutually perpendicular (X, Y, Z) axes and into three shear components along the three planes of those axes. By making a proper choice it is possible to find a set of three axes along which the shear stresses will be zero. These are the principal axes, with the normal stresses along them being called the principal stresses.

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