PSI - Issue 31

M.L. Larsen et al. / Procedia Structural Integrity 31 (2021) 70–74 M.L Larsen, V. Arora, H.B. Clausen / Structural Integrity Procedia 00 (2019) 000–000

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the model as shown in Fig. 2. In total 100,000 load cycles are applied to the structure in the S-N curve fatigue damage calculation. A stress ratio of R=-1 has been considered, to remove effects from mean stresses. Furthermore, the thickness effect in the S-N curves is neglected.

Fig. 2. Sinusoidal load applied in the FE optimization study.

The load cycles are in the optimization framework considered using a Markov matrix approach, which requires only a single unit load case to be performed by finite element analysis. The stress states are then predicted by linear matrix calculations from the unit stress states. This considerably reduces the finite element computations but requires a linear model. This assumption is valid in the case of high cycle fatigue, where the stress states are well below the yield limit of the material. 3.1. Fatigue criteria In the optimization framework, four different fatigue criteria have been implemented. The criteria are listed in Tab. 1. The different fatigue estimation approaches in this paper can each be formulated using equivalent stresses which can be compared to the uniaxial normal fatigue curve, see e.g. Pedersen (2016). Only the Modified Wöhler Curve Method (MWCM) cannot be formulated as an equivalent stress and needs to be considered using a modified shear stress, Susmel (2009). In this paper, the FAT-90 curve with m = 3 is considered for normal stresses and the FAT-80 curve with m = 5 is considered for shear stresses. Only a single slope is considered for both S-N curves to simplify the analysis. The Findley and MWCM methods are shear-based criteria’s and require the critical plane approach for the stress estimation. This has been implemented in the optimization framework by checking planes each rotated by 5 degrees, resulting in a total of 36 planes which needs to be investigated. An example of the investigated planes can be seen in Fig. 4. Each FE node at the weld in the FE model is checked for fatigue damage. As the model is simple, with a simple stress state, all nodes will observe the same damage with only small differences due to numerical rounding’s. However, as this paper aims to validate the developed optimization framework, all possible nodes at the weld have been considered. Table 1: Fatigue criteria used on the optimization framework. Δ � and Δ �� denotes the stresses (ranges) occurring in the investigated plane. Δ � and Δτ � are the fatigue strength of the normal and shear stress. is the Findley sensitivity factor and � and � are the slopes of the S-N curves. CV is the comparison value which for proportional and constant amplitude loading is equal to 1. Criteria Equivalent stresses IIW � Δ � Δ � � � � � Δ �� Δ � � � � � Δ ��� � √ 1 �Δ �� � � Δ �� � � Δ �� Δ �� EC3 � Δ � Δ � � � � � Δ �� Δ � � � � 1 � Δ ��� � �Δ �� � � Δ �� � � � Δ �� Δ �� Findley Δ ������� � Δ �� � 2 ��� 1 2 � � √1 � � � � ��� MWCM Δ �� � ��� � � � Δ � 2 � Δ � � ��� � Δ � & � � ��� � � � � � � � ��� � � ��� � ��� �