Machinery's Handbook, 31st Edition
Fatigue 209 patterns indicative of strain direction and magnitude, as well as color-changing coatings that indicate the amount of strain at each point, identifying areas requiring component modification. Alternatively, modern materials testing systems offer automated, multi- axial, and high-precision capabilities. Testing may involve use of specific wavelengths of light or be performed at extreme temperatures. Most of these tests have been standardized by the American Society for Testing and Ma- terials (ASTM) and are published in their Book of Standards in separate sections for met- als, plastics, rubber, and wood. Many of the test methods are also adopted by the American National Standards Institute (ANSI). Fatigue Properties.— When a material is subjected to many cycles of stress reversal or fluctuation (variation in magnitude without reversal), failure may occur, even though the maximum stress at any cycle is considerably less than the value at which failure would occur if the stress were constant. Fatigue properties are determined by subjecting test specimens to stress cycles and counting the number of cycles to failure. From a series of such tests in which maximum stress values are progressively reduced, diagrams of stress versus number of cycles until failure ( S-N diagrams) can be plotted as illustrated by the accompanying figures. The S-N diagram Fig. 2a shows the behavior of a material for which there is an endurance limit S en . Endurance limit is the stress value at which the number of cycles to failure is infinite. Steels have endurance limits that vary according to hardness, composition, and quality, but many nonferrous metals do not. The S-N diagram Fig. 2b does not have an endurance limit. For a metal that does not have an endurance limit, it is standard practice to specify fatigue strength as the stress value corresponding to a specific number of stress reversals, usually 100,000,000 or 500,000,000.
Sen
N
N, number of cycles to failure
Fig. 2a. S-N Endurance Limit Fig. 2b. S-N No Endurance Limit Influence of Mean Stress on Fatigue.— Most published data on the fatigue properties of metals are for completely reversed alternating stresses, that is, the mean stress of the cycle is equal to zero. However, if a structure is subjected to stresses that fluctuate between dif- ferent values of tension and compression, then the mean stress is not zero. When fatigue data for a specified mean stress and design life are not available for a mate rial, the influence of nonzero mean stress can be estimated from empirical relationships that relate failure at a given life, under zero mean stress, to failure at the same life under zero mean cyclic stress. One widely used formula is Goodman’s linear relationship, S S 1 a = − c m S m ⁄ S u where S a is the alternating stress associated with some nonzero mean stress S m . S is the alternating fatigue strength at zero mean stress. S u is the ultimate tensile strength. Goodman’s linear relationship is usually represented graphically on a so-called Good- man Diagram , shown in Fig. 3a. The alternating fatigue strength or the alternating stress for a given number of endurance cycles is plotted on the ordinate ( y -axis) and the static tensile strength is plotted on the abscissa ( x -axis). The straight line joining the alternating fatigue strength S and the tensile strength S u is the Goodman line. The value of an alternating stress S ax at a known value of mean stress S mx is determined as shown by the dashed lines on the diagram.
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