13th International Conference on Fracture June 16–21, 2013, Beijing, China -3- (a) R=0.1 (b) R=0.3 Fig. 3 Crack growth rate under different ratios for three different welding conditions 3. Numerical simulation 3.1 Numerical solution of Kres The evaluation of residual K (Kres) was considered as a mature method of predicting fatigue crack growth rates in residual stress fields. Finite element analysis was used to calculate the stress intensity factor Kres from residual stress by using ABAQUS 6.10. The models were built using C3D8R (an 8-node linear brick, reduced integration, hourglass control.) entity elements around the notch tip and along the crack lines. The unit size gradual transition from 2.5mm to 0.5mm length. The virtual crack closure technique (VCCT) [10] was used for calculating strain energy release rate for unit sample thickness. For plane stress, the relation between the strain energy release rate and stress intensity factor (SIF) was as follows: (1) (2) (3) If residual stresses were input to this model, Kres can be derived from Eqs. (1), Reff can be derived from Eqs. (2) and (3). The crack growth rate can be calculated with the Paris formula. 3.2 Fatigue life in simulation The fatigue life in weld nugget were compared to the experimental data, as shown in Fig.4 For Δ K less than 10MPa√m, the experimental data was consistent with the parent material. When ΔK grew breakthrough 10MPa√m, the experimental data was more in line with simulations.
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