PSI - Issue 57

Magnus Andersson et al. / Procedia Structural Integrity 57 (2024) 307–315 M. Andersson et al. / Structural Integrity Procedia 00 (2023) 000–000

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3.1. FEA with unit load cases

N L unit load cases are analyzed using FEA. For each weld cross section a path is created and is defined by angle v = v ref = 45 ◦ , see Fig. 6. The in-plane normal stress to the path is extracted and linearized to obtain the membrane, σ m and bending stress σ b . The linearized stress for a weld cross section for load case i : σ FEA , i = σ m , FEA , i ( v ref ) σ b , FEA , i ( v ref )

Fig. 6. (a) In-plane normal stress; (b) crack angle v ; (c) crack geometry (depth, a and width, 2 c ).

3.2. Load time signals

Corresponding to each unit load case i there is a load time signal, F i ( t ) that are created by multi body simulations.

3.3. Initial crack geometry

The initial crack is assumed to be located in the tip of the weld root and its depth is defined to a i = 0.15mm Hob bacher (2007). The crack width, 2 c , is then given by (Madia et al. (2017)): 2 c = 6 . 34 · a − 0 . 27 . The initial crack angle is set to v = 0 ◦ , see Fig. 6. The crack can grow in three directions (depth, width and angle v ).

3.4. Geometry factors

From the database the geometry factors are interpolated using the input values a and v (see Appendix A):

β I , UC ( a , v ) = β I , UCm ( a , v ) β I , UCb ( a , v ) β II , UC ( a , v ) = β II , UCm ( a , v ) β II , UCb ( a , v )

3.5. Transformation of the FE stress to angle v

In general the crack growth is not in the direction of angle v ref = 45 ◦ . Hence the stress must be transformed from v ref to the actual crack angle v . This is done by using the [2 x 2] transformation matrix A UC , ref ( v ) (which is stored in the database, see Appendix A): σ FEA , i ( v ) = A UC , ref ( v ) · σ FEA , i ( v ref ). 3.6. Calculation of stress intensity factors

The Mode I and II stress intensity factors are given by (summing up contributions from all unit load cases):

K I ( t , a , v ) = K II ( t , a , v ) =

N L i = 1 β I , UC ( a , v ) · σ FEA , i ( v ) · F i ( t ) · √ π a N L i = 1 β II , UC ( a , v ) · σ FEA , i ( v ) · F i ( t ) · √ π a