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Fluctuating Stress Introduction Some machine parts are subjected to static loading. Since many of the machine parts (such as axles, shafts, crankshafts, connecting rods, springs, pinion etc.) are subjected to variable or alternating loads (also known as fluctuating or fatigue loads), therefore we shall discuss, in this chapter, the variable or alternating stresses.. For example in below figure the fiber on the surface of a rotating shaft subjected to a bending load, undergoes both tension and compression for each revolution of the shaft.

Any fiber on the shaft is therefore subjected to fluctuating stresses. Machine elements subjected to fluctuating stresses usually fail at stress levels much below their ultimate strength and in many cases below the yield point of the material too. These failures occur due to very large number of stress cycle and are known as fatigue failure. These failures usually begin with a small crack which may develop at the points of discontinuity, an existing subsurface crack or surface faults. Once a crack is developed it propagates with the increase in stress cycle finally leading to failure of the component by fracture. There are mainly two characteristics of this kind of failures: (a) Progressive development of crack. (b) Sudden fracture without any warning since yielding is practically absent. Fatigue failures are influenced by (i) Nature and magnitude of the stress cycle. (ii) Endurance limit. (iii) Stress concentration. (iv) Surface characteristics. These factors are therefore interdependent. For example, by grinding and polishing, case hardening or coating a surface, the endurance limit may be improved. For machined steel endurance limit is approximately half the ultimate tensile stress.

Stress cycle A typical stress cycle is shown in below figure using standard specimen. The maximum, minimum, mean and variable stresses are indicated. In order to find the mean stress for completely reversed cycle the mean stress is zero. The stress verses time diagram for fluctuating stress having values σmin and σmax is shown in fluctuating stress Fig. The variable stress, in general, may be considered as a combination of steady (or mean or average) stress and a completely reversed stress component σv. There are three types of mathematical models for cyclic stresses –(1) fluctuating or alternating stresses; (2) repeated stresses; (3) reversed stresses

Methods of Reducing Stress Concentration: We have already discussed that, whenever there is a change in cross-section, such as shoulders, holes, notches or keyways and where there is an interference fit between a hub or bearing race and a shaft, then stress concentration results. The presence of stress concentration cannot be totally eliminated but it may be reduced to some extent. A device or concept that is useful in assisting a design engineer to visualize the presence of stress concentration and how it may be mitigated is that of stress flow lines.

Fatigue Stress Concentration Factor: When a machine member is subjected to cyclic or fatigue loading, the value of fatigue stress concentration factor shall be applied instead of theoretical stress concentration factor. Since the determination of fatigue stress concentration factor is not an easy task, therefore from experimental tests it is defined as Fatigue stress concentration factor.

Fatigue strength formulations: Fatigue strength experiments have been carried out over a wide range of stress variations in both tension and compression below figure shows a schematic diagram of experimental plots of variable stress against mean stress and Gerber, Goodman and Soderberg lines. But the following are important from the subject point of view: 1. Goodman method 2. Soderberg method.

References 1. http://nptel.ac.in/courses/Webcoursecontents/IIT%20Kharagpur/Machine%20design1/pdf/Module-3_lesson-3.pdf

2. https://www.coursera.org/learn/machine-design1/lecture/g4Iyw/module-38-fatigue-fluctuating-stress