PSI - Issue 5

Chmelko Vladimír et al. / Procedia Structural Integrity 5 (2017) 825–831 Chmelko, V., Margetin, M./ Structural Integrity Procedia 00 (2017) 000 – 000

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determines the fatigue life of the entire structure. That is why to an issue of notch effects in terms of fatigue has been paying a lot of attention for many decades. Nowadays, there are known analytical solutions for several types of notches. For the most other notches the values of notch effects are determined experimentally (e.g. Neuber, Petterson, Taylor etc.), the critical distance method approach (Susmel, Taylor 2003) is used to determine the fatigue strength of a component with a notch. These approaches are developed for use in engineering practice and developed for multi axial cases of loading and allow determination of fatigue strength of the structure i.e. its components. In practice, there are frequent cases where it is necessary to determine the fatigue life of the structure or parts with a notch. The real operation in most cases leads to loadings which have time-depending stochastic character. In these cases, the use of approaches to estimate fatigue strength, i.e. the fatigue limits are problematic because we need to know the loading process in the notch in the form of a time-depending stress or strain. At present, there are several experimental techniques for measuring and sensing strains, including non-contact methods , in e.g. Padevět (2016), Halama (2015). Let us note, that direct measuring of stress i.e. strain in the notch, is in many cases very difficult and sometimes is technically impossible. It is also difficult to use computer models using e.g. FEM analysis when dealing with a complex construction. In addition, the stress-strain state in the root of the notch is in most cases in the elastic plastic region, which requires the use of non-linear material models. If necessary, to consider the fatigue life of the structure or its component with an existing notch for the time-depending loading process, this can be realized in two steps:  obtaining a nominal loading process near the notch (e.g. direct measuring of the strain by strain gauge)  transformation of the nominal loading into the root of the structural notch Next will be the discussed the methodology of such a computational transformation to obtain the relevant time depending stress or strain process at the root of the structural notch with non-uniform character of loading.

2. The stress-strain relationships at the root of the notch in the elastic-plastic area

There are a number of methods that allow the calculation of the stress-strain relationships at the root of the notch in the elastic-plastic state. The Crews-Hardrath method is based on Stowel's relationships for the theoretical coefficient of the stress concentration and strain deflection for an orifice in a plate loaded by tensile stress. These were extended by Hardrath-Ohman for the real elastic-plastic coefficient of stress concentration with the ultimate dimensions in the following form

) E S 1

( 1      

(1)

E

where  is “ elastic ” coefficient of stress concentration and Es is a secant modulus of strain material characteristic. Eq. (1) was used by Crews with Hardrathom while determining the stress in the root of the notch  S at the nominal stress loading  n in the following form

     ( n

 

) E S 1      1

.



(2)

S n



E

If the deformation characteristic of the material is well-know σ = f(ε) then the equation is possible to solve by iteration method for σ S and E S . Similarly, it is possible to calculate the strain in the notch ε S by using the coefficient  ε . The Eq. (2) has been adjusted by Kliman in the form