Machinery's Handbook, 31st Edition
210
Fatigue
Alternating Fatigue Strength, S Goodman Line
Ductile Metal
S ax
Goodman Line
S mx
Brittle Metal
Mean Tensile Stress, S m
Tensile Stress, S u
S u
Fig. 3a. Goodman Diagram Fig. 3b. Mean Tensile Stress For ductile materials, the Goodman law is usually conservative, since approximately 90 percent of actual test data for most ferrous and nonferrous alloys fall above the Good- man line, even at low endurance values where the yield strength is exceeded. For many brittle materials, however, actual test values can fall below the Goodman line, as illus- trated in Fig. 3b. As a rule of thumb, materials having an elongation of less than 5 percent in a tensile test may be regarded as brittle. Those having an elongation of 5 percent or more may be regarded as ductile. Cumulative Fatigue Damage.— Most data are determined from tests at a constant stress amplitude. This is easy to do experimentally, and the data can be presented in a straightforward manner. In actual engineering applications, however, the alternating stress amplitude usually changes in some way during service operation. Such changes, referred to as “spectrum loading,” make direct use of standard S-N fatigue curves inap- propriate. A problem exists, therefore, in predicting the fatigue life under varying stress amplitude from conventional, constant-amplitude S-N fatigue data. The assumption in predicting spectrum loading effects is that operation at a given stress amplitude and number of cycles will produce a certain amount of permanent fatigue dam age and that subsequent operation at different stress amplitude and number of cycles will produce additional fatigue damage and a sequential accumulation of total damage, which at a critical value will cause fatigue failure. Although the assumption appears simple, the amount of damage incurred at any stress amplitude and number of cycles has proven difficult to determine, and several “cumulative damage” theories have been advanced. One of the first and simplest methods for evaluating cumulative damage is known as Miner’s law or the linear damage rule , where it is assumed that n 1 cycles at a stress of S 1 , for which the average number of cycles to failure is N 1 , causes an amount of damage n 1 / N 1 . Failure is predicted to occur when n i N ∑ = 1 The term n / N is known as the “cycle ratio” or the damage fraction. N i --- 1 The greatest advantages of the Miner rule are its simplicity and prediction reliability, which approximates that of more complex theories. For these reasons the rule is widely used. It should be noted, however, that it does not account for all influences, and errors are to be expected in failure prediction ability. Modes of Fatigue Failure.— Several modes of fatigue failure are: Low/High-Cycle Fatigue: This fatigue process covers cyclic loading in two significantly different domains, with different physical mechanisms of failure. One domain is charac terized by relatively low cyclic loads, strain cycles confined largely to the elastic range, and long lives, that is, a high number of cycles to failure; traditionally, this has been called “high-cycle fatigue.” The other domain has cyclic loads that are relatively high, signifi- cant amounts of plastic strain induced during each cycle, and short lives, that is, a low
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