Safety Factor Example

Due to the unpredictable scheduling and high dollar costs of all weather natural testing, much of the environmental testing has been brought into laboratories or other such testing centers. Artificial conditions are provided to simulate various environmental phenomena and thereby aid in the evaluation of the test item before it goes into service under natural environments. This environmental simulation and testing does require extensive preparation and planning. It is generally desirable to obtain generalizations and comparisons from a few basic tests to avoid prolonged testing and retesting.

The type and number of tests to be conducted, natural or simulated, as usual are dependent on such factors as end item performance requirements, time and cost limitations, past history, performance safety factors, shape of specimens, available testing facilities, and the environment. Specifications, such as ASTMs' provide guidelines.

Since GRPs (glass reinforced plastics) tend not to exhibit a fatigue limit, it is necessary to design for a specific endurance, with initial safety factors in the region of 3 to 4 being commonly used. Higher fatigue performance is achieved when the data are for tensile loading with zero mean stress. In other modes of loading, such as flexural, compression, or torsion, the fatigue behavior can be worse than that in tension due to potential abrasion action between fibers if debonding of fiber and matrix occurs. This is generally thought to be caused by the setting up of shear stresses in sections of the matrix that are unprotected by some method such as having properly aligned fibers that can be applied in certain designs. Another technique, which has been used successfully in products such as high-performance RP aircraft wing structures, incorporates a very thin, high-heat-resistant film such as Mylar between layers of glass fibers. With GRPs this construction significantiy reduces the self-destructive action of glass-to-glass abrasion and significantly increases the fatigue endurance limit.

With certain plastics, particularly high performance RPs, there can be two or three moduli. Their stress-strain curve starts with a straight line that results in its highest E, followed by another straight line with a lower S, and so forth. To be conservative providing a high safety factor the lowest E is used in a design however the highest E is used in certain designs where load requirements are not critical.

In many plastics, particularly the unreinforced TPs, the straight region of the stress-strain curve is not linear or the straight region of this curve is too difficult to locate. It then becomes necessary to construct a straight-line tangent to the initial part of the curve to obtain a modulus called the initial modulus. Designwise, an initial modulus can be misleading, because of the nonlinear elasticity of the material. For this reason, a secant modulus is usually used to identify the material more accurately. Thus, a modulus could represent Young's modulus of elasticity, an initial modulus, or a secant modulus, each having its own meaning and safety factors. The Young's modulus and secant modulus are extensively used in design equations.

The example of a building roof structure represents the simplest type of problem in static loading in that the loads are clearly long term and well defined. Creep effects can be easily predicted and the structure can be designed with a sufficiently large SF to avoid the probability of failure.

A seating application is a more complicated static load problem than the building example just reviewed because of the loading situation. The self-load on a chair seat is a small fraction of the normal load and can be neglected in the design. The loads are applied for relatively short periods of time of the order of 1 to 5 hours, and the economics of the application requires that the product be carefully designed with a small safety factor.

Overall, it can be stated that plastic products meet the following criteria: their functional performance meets use requirements, they lend themselves to esthetic treatment at comparatively low cost, and, finally, the finished product is cost competitive. Examples of their desirable behaviors can start with providing high volume production. Plastic conversion into finished products for large volume needs has proven to be one of the most cost-effective methods. Combining bosses, ribs, and retaining means for assembly are easily attained in plastic products, resulting in manufacturing economies that are frequendy used for cost reduction. It is a case where the art and technology of plastics has outperformed any other material in growth and prosperity.

Their average weight is roughly one-eighth that of steel. In the automotive industry, where lower weight means more miles per gallon of gasoline, the utilization of plastics is increasing with every model-year. For portable appliances and portable tools lower weight helps people to reduce their fatigue factor. Lower weight is beneficial in shipping and handling costwise, and as a SF to humans (no broken glass botdes, etc.).

Throughout this book as the viscoelastic behavior of plastics has been described it has been shown that deformations are dependent on such factors as the time under load and the temperature. Therefore, when structural components are to be designed using plastics it must be remembered that the standard equations that are available for designing springs, beams, plates, and cylinders, and so on have all 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.

Since these assumptions are not always justifiable when applied to plastics, the classic equations cannot be used indiscriminately. Each case must be considered on its merits, with account being taken of such factors as the time under load, the mode of deformation, the service temperature, the fabrication method, the environment, and others. In particular, it should be noted that the traditional equations are derived using the relationship that stress equals modulus times strain, where the modulus is a constant. From the review in Chapters 2 and 3 it should be clear that the modulus of a plasdc is generally not a constant. Several approaches have been used to allow for this condition. The drawback is that these methods can be quite complex, involving numerical techniques that are not attractive to designers. However, one method has been widely accepted, the so-called pseudo-elastic design method.

In this method appropriate values of such time-dependent properties as the modulus are selected and substituted into the standard equations. It has been found that this approach is sufficiendy accurate if the value chosen for the modulus takes into account the projected service life of die product and/or the limiting strain of the plastic, assuming that the limiting strain for the material is known. Unfortunately, this is not just a straightforward value 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 SF. If no history exists a high value will be required. In time with service condition inputs, the SF can be reduced if justified.

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