PSI - Issue 7

F. Fomin et al. / Procedia Structural Integrity 7 (2017) 415–422 Fedor Fomin and Nikolai Kashaev/ Structural Integrity Procedia 00 (2017) 000–000

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parameters are needed: ∆ σ e , ∆ K th,LC and ∆ K th,eff . The latter can be derived as the long crack threshold obtained at high R-ratio ( R > 0.7) where no crack closure is expected. Quantitative analysis based on a fracture mechanics approach requires a constitutive relationship between the rate of crack growth, da/dN , and the crack driving force, expressed by some function of the applied SIF range ∆ K ap . Additionally, the gradual build-up of crack closure and the variations of ∆ K th along the crack path should be taken into account. The effective crack driving force was calculated according to Xiulin and Hirt (1983):   ( ) . m ap th da C K K a dN     (4) The finite fatigue life at a given level of stress was estimated by integrating Equation (4) from the initial crack length a i to the final crack length a f . Following Zerbst et al. (2016), the a i parameter was estimated from the KT diagram modified for the intrinsic threshold by Equation (3) where ∆ K th,LC is substituted by ∆ K th,eff . The crack initiation period was neglected. 6. Application of the model and discussion The validation of the model was carried out on the S-N data of the laser beam welded Ti-6Al-4V butt joints in two conditions: as-welded machined and heat-treated machined. ∆ K th,LC and near threshold crack growth rates for the investigated stress ratio R = 0.1 were taken from the literature for the fine lamellar (as-welded) and coarse lamellar (PWHT) Ti-6Al-4V microstructures (Wagner and Lütjering, 1987). The da/dN - ∆ K data are shown in Fig. 5(a). The parameters C and m were determined by fitting the experimental data to Equation (4). The intrinsic fatigue propagation threshold was taken as 2.0 MPa√m for both types of investigated microstructures (Gregory, 1996). The fatigue limits were estimated based on the microhardness measurements performed in previous research (Fomin et al., 2017) assuming a linear relationship between hardness and ∆ σ e . The parameters necessary for constructing the cyclic R-curve are listed in Table 1. Table 1. Model parameters Condition ∆ K th,eff , MPa√m ∆ K th,LC , MPa√m ∆ σ e , MPa C , mm/cycle m a 0 , µm a i , µm As-welded 2.0 5.7 763 2.1·10 -10 2.07 33.6 4.2 PWHT 2.0 7.6 655 4.7·10 -11 2.40 81.6 5.7 The applied SIF range was calculated taking into account the stress concentration arising from the presence of a spherical cavity (Green, 1980). The average pore radius of 30 µm was obtained from X-ray analysis of the FZ (see Fig. 5(b)), and the depth of 500 µm was found from fractographical observations. Once the crack reaches the surface, it transforms to a surface crack and propagates much faster compared to internal cracks. Unstable crack growth and the final failure occur if the remaining cross section can no longer carry the maximum load of the loading cycle and the stress intensity factor at the crack tip is higher than the fracture toughness of the material. The estimation showed that the number of cycles spent for surface crack propagation was negligible in comparison to the number of cycles in the internal crack stage. Thus, the total life was calculated as the number of cycles for internal crack growth.

Fig. 5. (a) Near threshold da/dN - ∆ K data for Ti-6Al-4V (after Wagner and Lütjering, 1987); (b) pore diameter distribution.