Burcu Atay, 140060029, 12th week

Miner's Rule

Several attempts have been made to predict the fatigue strength for such variable stresses using S/N curves for constant mean stress conditions. Some of the predictive methods available are very complex but the simplest and most well known is "Miner's Law."

Miner postulated that whilst a component was being fatigued, internal damage was taking place. The nature of the damage is difficult to specify but it may help to regard damage as the slow internal spreading of a crack, although this should not be taken too literally. He also stated that the extent of the damage was directly proportional to the number of cycles for a particular stress level, and quantified this by adding, "The fraction of the total damage occurring under one series of cycles at a particular stress level, is given by the ratio of the number of cycles actually endured n to the number of cycles N required to break the component at the same stress level". The ratio n/N is called the "cycle ratio" and Miner proposed that failure takes place when the sum of the cycle ratios equals unity.

i.e. when ∑ n/N=1

or n1/N1+n2/N2+n3/N3+...+ etc =1 (11.14)

If equation (1 1.14) is merely treated as an algebraic expression then it should be unimportant whether we put n3/N3 before n l / N I etc., but experience has shown that the order of application of the stress is a matter of considerable importance and that the application of a higher stress amplitude first has a more damaging effect on fatigue performance than the application of an initial low stress amplitude. Thus the cycle ratios rarely add up to 1, the sum varying between 0.5 and 2.5, but it does approach unity if the number of cycles applied at any given period of time for a particular stress amplitude is kept relatively small and frequent changes of stress amplitude are carried out, i.e. one approaches random loading conditions. A simple application of Miner's rule is given in Example 11.4.

(Hearn, E. J., Mechanics of materials: an introduction to the mechanics of elastic and plastic deformation of solids and structural materials, 3rd Edition, pg. 455)

Edge Dislocations

An edge dislocation (fig. 4-5) can be illustrated by slicing partway through a perfect crystal, spreading the crystal apart, and partly filling the cut with an extra plane of atoms. The bottom edge of this inserted plane represents the edge dislocation. If we describe a clockwise loop around the edge dislocation, starting at point x and going an equal number of atoms spacing in each direction, we finish, at point y, one atom spacing from the starting point. The vector required to complete the loop is, again, The Burgers vector. In this case. The Burgers vector is perpendicular to the dislocation. By introducing the dislocation, the atoms above the dislocation line are squeezed too closely together, while the atoms below the dislocation are stretched too far apart. The surrounding region of the crystal has been disturbed by the presence of the dislocation. Unlike an edge dislocation, a screw dislocation cannot be visualized as an extra half plane of atoms.

(Askeland, D.R., Fulay, P.P, Essentials of Materials Science and Engineering, SI Edition, pg.99)