Design of a notched shaft

A shaft with a circumferential round notch (see figure 4.3) with dimensions D = 20 mm, d = 16 mm, and q = 4 mm is loaded in tension. It has to be checked whether it can be used at a service load oi F = 40 kN. The shaft is made of an aluminium alloy with Young s modulus oi E = 68000 MPa and the stress-strain curve shown in figure 12.2 (J2p = 202 MPa, Rm = 280 MPa). 

The stress in front of the crack tip shows a singularity. In this exercise, we investigate why the material does not fail immediately although the stress is numerically infinite. 

To do so, we consider a sodium chloride crystal as in exercise 3. The crystal contains a crack of length a. Assume that, even on the atomic scale, the stress field at the crack tip can be described by equation (5.1). The crack is assumed to propagate in the [100] direction. 

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