# Crack Initiation and Propagation Fatigue Life of Ultra High-Strength Steel Butt Joints
## 1 Introduction
### Effect of Local Weld Geometry on Fatigue Performance  
Modern welding technologies involving highly automated processes enable the production of high-quality welds exhibiting a very smooth transition at the weld toe. Nevertheless, variations in weld geometry due to the dynamic welding processes cannot be eliminated entirely. These very local discontinuities often govern the fatigue performance of welds due to its locally pronounced notch effects. Due to the increasing demands on quality of the welds of high-strength structural components, the effect of local weld geometry on the fatigue performance is of particular relevancy. Therefore,an assessment of such variations is essential in order to determine the maximum allowable size and extension. In [31; 32; 33], the linear elastic stress concentration factor is utilized to take weld geometry into account. Thereby, Ref. [31; 32] determine the stress concentration factor by the aid of linear elastic FE-analysis, whereas [33] uses analytical equations. In general, this procedure is prone to overestimating the effect of the actual geometry, as support effects are not considered. However, a local fatigue notch factor can be obtained by evaluating the local notch stress course, the stress gradient and, finally, the corresponding supporting factor [34]. [PERSON] proposed to replace the actual weld toe transition radius by a fictitious radius \(\rho_{f}\) in order to take support effects into account [9] (see Equation (1)). In [33], this procedure leads to better matching results than the use of the actual transition radius. \[\rho_{f}=\ \rho+1\text{mm} \tag{1}\]  
The effective notch stress concept [9; 35; 36; 37] proposes a reference notch radius of \(\rho_{\textit{ref}}=1\) mm independent of the actual geometry. Thereby, a crack-like weld toe exhibiting an actual weld toe radius of \(\rho=0\) mm is assumed leading to a fictitious radius \(\rho_{f}=\rho_{\textit{ref}}=1\) mm in Equation (1). This concept is part of the International Institute of Welding (IIW) guideline [38], verified and consistent for structural steels and aluminium alloys. However, it does not consider the actual weld toe geometry. Therefore, it tends to deliver conservative results especially for high-quality high-strength welds with extremely shallow weld toes. In [39], the critical distance approach developed by [PERSON] [10] is applied. Thereby, the fatigue notch factor \(K_{f}\) is calculated from the stress concentration factor \(K_{t}\) using the Peterson formula. The required parameter \(a^{*}\), the critical distance, is related to the ultimate tensile strength of the material. [PERSON] proposed in [8] an evaluation method based on stress averaging in order to consider microstructural support. Hereby, the fatigue assessment is performed using an effective stress \(\sigma_{\textit{eff}}\) obtained by averaging of the stress distribution in depth \(\sigma(x)\) over the microstructural support length \(p^{*}\) at the surface layer instead of the linear elastic stress maximum (see Equation (2)). The fraction of \(\sigma_{\textit{eff}}\) and the nominal stress \(\sigma_{n}\) gives the fatigue relevant effective stress concentration factor \(K_{f}\) (see Equation (3)). \[\sigma_{\text{eff}}(\rho^{*})=\ \frac{1}{\rho^{*}}\int_{y_{0}}^{y_{0}+\rho^{*} }\sigma(y)dy \tag{2}\]  
\[K_{t}(\rho^{*})=\ \frac{\sigma_{\text{eff}}(\rho^{*})}{\sigma_{\text{n}}} \tag{3}\]  
Values for the key parameter \(\rho^{*}\) are provided by [PERSON] himself for various materials in [8]. For welded structural steels exhibiting a microstructure similar to steel castings a microstructural support length of \(\rho^{*}=0.4\) mm is suggested leading to the effective notch stress concept with a fictitious transition radius of \(\rho_{\textit{ref}}=1\) mm, which is mentioned above in [PERSON]'s concept. In [40], comprehensive investigations on the effect of weld geometry on the fatigue strength under consideration of the microstructural support length are published.