PSI - Issue 5

Amal ben Ahmed et al. / Procedia Structural Integrity 5 (2017) 524–530 Amal ben Ahmed et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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Where: R: the defect radius. r: Distance from the defect center to a considered point in the HLP. −1 and −1 are respectively fatigue limit under fully reserved tension and torsion loading and can be expressed, for the A356-T6 alloy, as a function of 2 as following [IbenHouriya et al.(2015)]: −1 ( 2 ) = 3 0 exp(− 2 0 ) 0 exp(− 2 0 )+√3 (6) −1 ( 2 ) = 0 exp(− 2 0 ) (7) 3.3. Computation of HCF Reliability In this section, a probabilistic approach for evaluatingHCF behavior of A356-T6 cast alloy, under fully reserved tension and torsion loadings is implemented. The main procedure for developing the probabilistic model using FE analysis and Monte Carlo simulation method is summarized as follows: (i) In the first stage, a FE model is developed upon ABAQUS commercial code. An elastic-plastic analysis using the non-linear isotropic/kinematic hardening model is used to evaluate stress distribution around the defect. It was shown that can be interpolated by mathematical expressions depending on the SDAS and ( ) ratio (eq.4and eq.5). (ii) The new expression of (eq.4and eq.5) are inserted in the DSG approach to predict A356-T6 fatigue response under alternate tension/torsion loading. (iii) Due to the significant fatigue data scatter of the A356-T6 HCF response, the proposed approach was carried out to simulate the fatigue limit for various defect sizes and load conditions by taking into account the random aspect of the Al Matrix (SDAS). The SDAS is assumed to be normally distributed with a standard deviation equals to 5 m. The reliability is computed using the Monte Carlo simulation method. (iv) The reliability fatigue response curves are plotted for different defect sizes. (v) The iso-probabilistic Kitagawa-Tkahashi Diagrams are determined at 5%, 50% and 95% of reliabilityunder fully reserved tension/torsion loadings. A probabilistic framework is developed to generatethe KTDs by taking into consideration the SDAS dispersion. Monte Carlo method coupled with DSG approach (using the new expressions of σ eC qr ) is implemented to compute reliability. Fig.2 and fig.3 present the obtained iso-Probabilistic Kitagawa Tkahashi Diagrams for 5%, 50% and 95% reliabilities under fully reserved tension and torsion loadings. It is observed that numerical results are coherent with experimental [IbenHouriya et al.(2015)].In the both load cases, it is worth noticingthat, under the same load amplitude, the reliability decreases when the SDAS increases and vice versa. 4. Results and discussion (i)

(ii) Under alternate tension (fig.2), it is observed that the fatigue response is normally distributed and the numerical results converge for big defect sizes. Under alternate torsion (fig.3), fatigue limit becomes