This rapid overload fracture is the third stage of fatigue failure. Factors Affecting Fatigue Life In order for fatigue cracks to initiate, three basic factors are necessary. First, the loading pattern must contain minimum and maximum peak values with large enough variation or fluctuation. The peak values may be in tension or compression and may change over time but the reverse loading cycle must be sufficiently great for fatigue crack initiation. Secondly, the peak stress levels must be of sufficiently high value.

If the peak stresses are too low, no crack initiation will occur. Thirdly, the material must experience a sufficiently large number of cycles of the applied stress. The number of cycles required to initiate and grow a crack is largely dependant on the first to factors. In addition to these three basic factors, there are a host of other variables, such as stress concentration, corrosion, temperature, overload, metallurgical structure, and residual stresses which can affect the propensity for fatigue.

Since fatigue cracks generally initiate at a surface, the surface condition of the component being loaded will have an effect on its fatigue life. Surface roughness is important because it is directly related to the level and number of stress concentrations on the surface. The higher the stress concentration the more likely a crack is to nucleate. Smooth surfaces increase the time to nucleation. Notches, scratches, and other stress risers decrease fatigue life.

Surface residual stress will also have a significant effect on fatigue life. Compressive residual stresses from machining, cold working, heat treating will oppose a tensile load and thus lower the amplitude of cyclic loading. The figure shows several types of loading that could initiate a fatigue crack.

The upper left figure shows sinusoidal loading going from a tensile stress to a compressive stress. For this type of stress cycle the maximum and minimum stresses are equal. The physic shows that a process volume is needed probably to store the necessary energy for starting and propagating the phenomenon.

This is a rupture of the traditional "strength of material" school which always give the prior importance of the local maximum stress.

- Killer in the Rain.
- Notch Effects in Fracture and Fatigue | SpringerLink.
- The Moonstone?

This concept of process volume was strongly affirmed during this workshop. If fatigue fracture does not occur in all the surface elements, the notched specimen would not be broken by the microcrack.

## Ali Fatemi, Ph. D. - Mechanical Engineering - The University of Memphis

Here, n S is the number of surface elements. The stress relaxation effect was introduced into the method to make it applicable to a metal containing dense inhomogeneous particles. Because the fatigue crack that originates from a defect propagates on the plane perpendicular to the first principal radial stress, a spherical particle of radius R is projected onto this plane and assumed to be a penny-shaped crack.

If the projected area is denoted by area R , its square root is related to R as follows:. The stress intensity factor K IR of the small interior crack is given by [ 20 , 35 ]. If the fatigue fracture does not occur in all the solid elements, the notched specimen would not be broken by the small interior defect.

Here, n V is the number of solid elements. The stress intensity factor K IP of a small surface crack of size area P is given by the following equation [ 20 , 35 ]:. The age-hardened aluminum cast alloy is identified as AC4B-T6. Table 2 shows its mechanical properties. Figure 6 shows the configurations of the specimens.

The fatigue life N f was defined as the total number of stress cycles to failure. Figure 7 shows S - N curves obtained from the results of the tests. The present aluminum cast alloy AC4B-T6 contains three main types of inhomogeneous particles, namely, eutectic Si and Fe compounds and porosity. Surrounding an irregular cross section with a smooth convex curve as shown in Figure 12 , the area is defined as area A.

The values of r are obtained from area A by the following equation [ 12 , 37 ]:. Figure 13 shows the measured M A 0 values of eutectic Si and Fe compounds and porosity. The relationship between M V 0 and M A 0 is as follows [ 12 , 37 ]:. Considering the assumption that M V 0 R 0 is given by Eqs. The line of Eq. Figure 14 shows the values of M V 0 for porosity, Fe compounds, and eutectic Si.

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Figure 15 shows the values of M S 0 for the porosity, Fe compounds, and eutectic Si. In this study, the Vickers hardness was measured at the position of 2.

Figure 16 shows the results plotted on a normal probability paper. Because a microcrack often grows radially, it is approximated by the semielliptical crack shown in Figure The approximation of the microcrack by the semielliptical macrocrack is such that the crack non-propagation limits are equal. F P is approximated to be 1. Because g R and g P can be calculated using Eqs. The fatigue limit reliability of the notched specimen shown in Figure 6 was predicted by the present method. In this case, the region was ring-like.

In other words, the inhomogeneous particles have almost no effect on the fatigue limit reliability in terms of initiating a fatigue crack. Instead, the eutectic Si actually strengthens the matrix. This study proposed a nondestructive method for predicting the fatigue limit reliability of notched specimens of a metal containing inhomogeneous particles densely. The fatigue limits predicted by the present method were in good agreement with the experimental ones.

## Notch Effects in Fatigue and Fracture

The method is not only convenient for use in predicting fatigue strength reliability for the reliable design of machine and structures, but it is also time effective and can be applied to the economic development of materials. Licensee IntechOpen. This chapter is distributed under the terms of the Creative Commons Attribution 3.

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