ASM Handbook: Volume 12: Fractography (Asm Handbook)

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Plotting on log paper emphasizes the bend in the curve, which might not be apparent if the results were plotted by using Cartesian coordinates. Moore rotating- beam machine.

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Figure 6—10 Low cycle High cycleAn S-N diagram plotted from Finite life Infinitethe results of completely lifereversed axial fatigue tests. Note ,December From R. Reprinted by 20permission.

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Soon we shall learn that S-N diagrams can be determined either for a test specimen or for an actual mechanical element. In the case of the steels, a knee occurs in the graph, and beyond this knee failure will not occur, no matter how great the number of cycles. The strength corresponding to the knee is called the endurance limit Se, or the fatigue limit. The graph of Fig. Figure 6—11 shows scatter bands indicating the S-N curves for most common aluminum alloys excluding wrought alloys having a tensile strength below 38 kpsi.

High-cycle fatigue, then, is concerned with failure corresponding to stress cycles greater than cycles. As noted previously, it is always good engineering practice to conduct a testing program on the materials to be employed in design and manufacture. This, in fact, is a requirement, not an option, in guarding against the possibility of a fatigue failure. Thus our primary purpose in studying fatigue is to understand why failures occur so that we can guard against them in an optimum man- ner.

For this reason, the analytical design approaches presented in this book, or in any other book, for that matter, do not yield absolutely precise results. The results should be taken as a guide, as something that indicates what is important and what is not impor- tant in designing against fatigue failure. As stated earlier, the stress-life method is the least accurate approach especially for low-cycle applications.

However, it is the most traditional method, with much published data available. It is the easiest to implement for a wide range of design applications and represents high-cycle applications adequately. For these reasons the stress-life method will be emphasized in subsequent sections of this chapter.

However, care should be exercised when applying the method for low-cycle applications, as the method does not account for the true stress-strain behavior when localized yielding occurs. The approach can be used to estimate fatigue strengths, but when it is so used it is necessary to compound several idealizations, and so some uncertain- ties will exist in the results. For this reason, the method is presented here only because of its value in explaining the nature of fatigue. A fatigue failure almost always begins at a local discontinuity such as a notch, crack, or other area of stress concentration.

When the stress at the discontinuity exceeds the elastic limit, plastic strain occurs. If a fatigue fracture is to occur, there must exist cyclic plastic strains.

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Thus we shall need to investigate the behavior of materials sub- ject to cyclic deformation. Landgraf has investigated the low-cycle fatigue behavior of a large number of very high-strength steels, and during his research he made many cyclic stress-strain plots. In this case the strength decreases with stress repetitions, as evidenced by the fact that the reversals occur at ever-smaller stress levels.

As previously noted, other materials may be strengthened, instead, by cyclic stress reversals. Note that the slope ofthe line AB is the modulus of Belasticity E. Reprinted with permission 1. The plastic-strain line begins at this point in Fig. Note in Fig. If the number of stress reversals is 2N, then N is the number of cycles.

Now, from Fig. Many more are included in the SAE J report. The question of how to determine the total strain at the bottom of a notch or discontinuity has not been answered. There are no tables or charts of strain concentration factors in the literature. Crystal slip that extends through several contiguous grains, inclusions, and surface imperfections is pre- sumed to play a role. Since most of this is invisible to the observer, we just say that stage I involves several grains.

The second phase, that of crack extension, is called stage II fatigue. The advance of the crack that is, new crack area is created does produce evi- dence that can be observed on micrographs from an electron microscope. The growth of 5J. Tavernelli and L.

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Manson, discussion, Trans. ASME, J. Basic Eng. Dowling, Mechanical Behavior of Materials, 2nd ed. Final fracture occurs during stage III fatigue, although fatigue is not involved. Stage III fatigue is associated with rapid acceleration of crack growth then fracture. Crack Growth Fatigue cracks nucleate and grow when stresses vary and there is some tension in each stress cycle.

From Eq. Cracks nucleate at or very near a free surface or large discon- tinuity. For KI below some threshold value KI th a crack will not grow. Notice the effect of the higher stress range in Fig. The three stages of crack development are observable, and the stage II data are linear on log-log coordinates, within the domain of linear elastic fracture mechanics LEFM validity.

K I th is the threshold value Increasingof K I, below which a crack stress ratiodoes not grow. From thresholdto rupture an aluminum alloy Rwill spend percent oflife in region I, percent inregion II, and percent inregion III. Barsom and S. Rolfe, Fatigue and Fracture Control in Structures, 2nd ed. Reprinted with permission. Representative, but conservative, values of C and m for various classes of steels are listed in Table 6—1. Substituting Eq. Fuchs and R. Quick Upload. Customer Service. Technical Support.

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