Notch stress gradient

After the specimen is loaded in tension at intermediate stress levels, an incubation period is required to initiate a crack. During this time, lattice-contained or weakly-trapped hydrogen diffuses ahead of the notches and local stress raisers, so as to equilibrate under the influence of any triaxial stress created there-this equilibration involves hydrogen redistribution associated with the equilibration of its chemical potential, under the combined influences of all factors that affect it. The first cracks will be initiated in this region after a critical hydrogen concentration has accumulated. The kinetics of the crack-initiation process are therefore dependent on the temperature and the stress gradient as they relate to the diffusion and concentration of hydrogen at the site of maximum triaxial stress in the steel. 

Whether a growing crack can be stopped in this way depends on how rapidly the stress decreases at the notch root. To quantify this decrease, we define the relative stress gradient at the notch root... 

Fig. 10.36. Dependence of the notch support fax tor on the relative stress gradient for several iron-base materials (after [147])...

The reason to subtract unity from both numerator and denominator in Eq. (7.4) is to provide a scale for q that ranges from zero for no notch effect to unity for fiiU notch effect. In this latter case kf is exactly equal to kf. A deep analysis of fatigue limit experimental data brought Peterson to make the hypothesis that fatigue damage became critical in relation to the stress level Opeak at a small distance b below the surface of notch root where the stress gradient is very steep... 

Around mid 1950s, Siebel and Stieler [19] introduced a new parameter that they indicated with the symbol x and called relative stress gradient (RSG) at notch root. The fundamental concept is always the same that is to say that fatigue is governed by the stress gradient rather than by the maximum stress at notch tip. Stress gradient means distance over which a stress level is maintained. The x parameter takes the form... 

The stress gradient da/dx, schematized in Fig. 7.6, is in turn equatable through both the theoretical stress concentration factor k, and the notch root radius p that, therefore, reenters into play... 

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