PSI - Issue 18

Tintu David Joy et al. / Procedia Structural Integrity 18 (2019) 287–292

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T. D. Joy, G. Kullmer./ Structural Integrity Procedia 00 (2019) 000–000

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The assumptions used for crack initiation in C RACKINT 3D are: a) a crack is most likely to initiate at the place where the maximum principal normal stress is at its highest value b) a crack grows perpendicular to the maximum normal stress, see Haibach (2006), Läpple (2011) and Radaj (2007). So for the node with the highest value for the maximum principal stress is selected as the critical node to initiate a crack. An exception that can occur is in the case where there are multiple nodes that are having highest values for the maximum principal stress. In this situation C RACKINT 3D calculates the stress gradient on the nodes and the critical node is the node with the lowest stress gradient value. Using the stress tensor for the critical node, the crack initiation direction and the crack initiation plane are calculated. After that, python scripts are invoked to insert the crack initiation location and the crack plane in the A BAQUS TM CAE model and to sketch the technical initial crack. The new geometry of the 3D model with the initial crack is meshed to create the FE-Model necessary for the crack growth simulation. This step is also performed with the help of a python script. In addition to this, the crack initiation lifetime is calculated using the damage parameter, P SWT, see Smith et al. (1970). Equation (1) is used to calculate the crack growth lifetime, where σ a is the stress amplitude, σ m is the mean stress, ε a is the strain amplitude, E is the Young's modulus, σ ’ f is the fatigue strength coefficient, N is the crack initiation lifetime, ε ’ f is the fatigue ductility coefficient, b is the fatigue strength exponent and c is the fatigue ductility exponent. The algorithm to automatically initiate a crack in a 3D structure is given in Algorithm 1.         2 2 b b c a m a f f f E 2 N E 2 N                    (1) Algorithm 1: Initiate a crack in A BAQUS TM model automatically and calculate the crack initiation lifetime. Input : A BAQUS TM Model, FE-Model Output : A BAQUS TM FE-Model with initial technical crack 1: Simulate FE-Model in A BAQUS TM 2: Invoke Python script to find the nodes, N b , that are on the boundaries of the 3D-Model 3: Obtain Stress tensors, S(N b ) of N b from the simulation results obtained from 1 4: Sort S(N b ) according to the maximum principal stress, σ 1 in descending order 5: IF multiple nodes with highest value for maximum principal stress THEN 6: Calculate stress gradient, G(N b ) for the nodes with max( σ 1 ) 7: Node, N b (i) with max( σ 1 ) and min(G(N b )) is the origin of the initial crack 8: ELSE 9: Node, N b (i) with max( σ 1 ) is the origin of the initial crack 10: END IF 11: Calculate the direction of crack initiation and initial crack plane from S(N b (i)) 12: Invoke Python script to insert the location of crack initiation and the plane on which the crack has to be initiated 13: Invoke Python script to create the initial technical crack in the A BAQUS TM model 14: Calculate the lifetime required for a crack initiation at N b (i) using P SWT 15: Mesh the model and generate the input file for N ETADAPT 3D to start the crack growth simulation

4. Discussion of Simulation Results and Future Work

The above explained procedure in A DAPCRACK 3D was tested with various 3D models. One such 3D model which was tested is that of a knee-lever. This model was previously simulated for crack growth in Schöllmann (2003). The loading and boundary conditions of the knee-lever are also taken from Schöllmann (2003), whereas the concentrated load (cload) on the model is F=10 kN. The material data used for the simulation in A BAQUS TM and for calculating crack initiation lifetime is shown in Table 1.