Machinery's Handbook, 31st Edition
206
Mechanical Properties of Materials STRENGTH OF MATERIALS
Strength of materials deals with the relations between elastic bodies, external forces ap- plied, and resulting deformations and stresses. In the design of structures and machines, mechanical engineering must consider the behavior of chosen materials when under load and apply strength of materials principles, including static strength and fatigue strength. Optimizing mechanical properties, load characteristics, and part shapes helps ensure ex- pected behavior and life of a part or machine. Forces are produced by the action of gravity, by accelerations and impacts of moving parts, by gasses and fluids under pressure, and by the transmission of mechanical power, among others. In order to analyze the stresses and deflections of a body, the magnitudes, directions and points of application of forces acting on the body must be known. Informa- tion given previously in the Mechanics section provides the basis for evaluating force systems. The time element in the application of a force on a body is an important consideration. Thus, a force may be static or change so slowly that its maximum value can be treated as if it were static; it may be suddenly applied, as with an impact; or it may have a repetitive or cyclic behavior. The environment in which forces act on a machine or part is also important. Such factors as high and low temperatures; the presence of corrosive gases, vapors and liquids; radia tion, etc. may have a marked effect on how well parts are able to resist stresses. Throughout this and other sections of the Handbook, both English and metric SI data and formulas are given to cover the requirements of working in either system of measurement. In many cases, formulas and text relating exclusively to SI units are given in bold-face type. Mechanical Properties of Materials.— Many mechanical properties of materials are de- termined from tests such as tensile testing, which subjects a uniform sample of a material to controlled axial tension. Strain (elongation) is measured as well as stress at the point of rupture. Engineering stress is the applied load on a tensile specimen divided by its original cross- sectional area. True stress uses the actual cross-sectional area. The maximum stress a material can withstand before breaking may be called ultimate tensile stress or breaking stress . Engineering strain is the amount by which a tensile specimen of a given mate- rial changes when the body is subjected to a load, divided by the original value of the dimension. True strain is the natural log of the ratio of current length over original length. Instead of unit strain , the simpler term strain often is used. The shape of an engineering stress-strain curve (see Fig. 1) reveals how material will be- have under tensile loading, assuming the tensile specimen has a constant cross-sectional area as loading is applied. (True stress and strain both reference the instantaneous cross- sectional area, which can be more accurate, but in practice, engineering stress-strain curves are used almost exclusively.) Values beyond the elastic limit must be used with caution, as the cross-sectional area begins to change and introduce error. Fig. 1 (1) shows the curve shape for a ductile ferrous material similar to low-carbon steel. The (upper or first) yield point is well defined and followed by some elongation with little additional stress. Then the curve turns upward again, toward an inflection point; strain hardening accounts for the increasing stress in this segment. When the curve again turns downward at the ultimate strength point, necking has begun. Fig. 1 (2) shows a curve typi- cal of a ductile non-ferrous material such as annealed copper. A well-defined yield point is absent, so an offset yield point is constructed. Fig. 1 (3) illustrates an offset yield point, as discussed below.
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