PSI - Issue 51

Victor Rizov et al. / Procedia Structural Integrity 51 (2023) 44–50 V. Rizov / Structural Integrity Procedia 00 (2022) 000–000

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4. Conclusions SERR for a beam with three parallel lengthwise cracks axially loaded in tension is analyzed. The beam is inhomogeneous along the height. The material is non-linear elastic. A vertical notch is cut-out in the mid-span. The locations of cracks along the height are arbitrary. The notch divides the three upper crack arms into symmetric parts. Therefore, the three upper crack arms are not stressed. The symmetry is taken into account in the analysis. Three solutions to the SERR are derived by differentiating the CSE. The three cracks are examined also by the J -integral. The solutions are used to evaluate the effects of the locations of the three cracks along the beam height on the lengthwise fracture behaviour by expressing of the SERR as a function of h h / 1 ,   h h h / 2 1  and   h h h h / 3 2 1   ratios. The analysis reveals that the strain energy release rate increases with increasing of h h / 1 ,   h h h / 2 1  and   h h h h / 3 2 1   ratios. When analyzing crack 2 with respect to the location of crack 1, it is found that the SERR decreases when h h / 1 ratio increases (this is explained by the decrease of the difference between the stiffness of parts, 2 3 S S and 3 4 S S , of the beam which are located, respectively, behind and ahead of the tip of crack 2). The analysis of crack 3 with respect to the location of crack 2 shows that the SERR decreases when   h h h / 2 1  increases (this is due to the decrease of the difference between the stiffness of parts, 1 2 S S and 2 3 S S , of the beam which are located, respectively, behind and ahead of the tip of crack 3). From view point of practical engineering, these results indicate clearly that the fracture behaviour is strongly influenced by the locations of the lengthwise cracks along the height of the beam configuration. Therefore, all possible locations of the cracks have to be considered in design of inhomogeneous structures axially loaded in tension. Also, it is found that the SERR decreases when h b / ratio increases. The SERR decreases also when 0 1 / D D ratio increases. The analysis indicates that the SERR for crack 1 is lower than the SERR for cracks 2 and 3. The SERR at increase of crack 3 is higher than the SERR at increase of cracks 1 and 2. The SERR for crack 2 is intermediate with respect to the SERR for cracks 1 and 3. References Broek, D., 1986. Elementary engineering fracture mechanics. Springer. Erdogan, F., 1995. Fracture mechanics of functionally graded materials. Comp. Eng. 5, 753-770. Chikh, A., 2019. Investigations in static response and free vibration of a functionally graded beam resting on elastic foundations. Frattura ed Integrità Strutturale 14, 115-126. Ignatiev, W., Ignatiev, A., Galishnikov, W., Onishtenko, E., 2014. Nonlinear structural mechanics. GASU. Kou, X.Y., Parks, G.T., Tan, S.T., 2012. Optimal design of functionally graded materials, using a procedural model and particle swarm optimization, Computer Aided Design 44, 300-310. Mahamood, R.M., Akinlabi, E.T., 2017. Functionally Graded Materials. Springer. Rizov, V.I., 2017. Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity. Frattura ed Integrità Strutturale 41, 498-510. Rizov, V.I, Altenbach, H., 2020. Longitudinal fracture analysis of inhomogeneous beams with continuously varying sizes of the cross-section along the beam length, Frattura ed Integrità Strutturale 53, 38-50. Saidi, H., Sahla, M., 2019. Vibration analysis of functionally graded plates with porosity composed of a mixture of Aluminum (Al) and Alumina (Al2O3) embedded in an elastic medium. Frattura ed Integrità Strutturale 13, 286-299. Saiyathibrahim, A., Subramaniyan, R., Dhanapl, P., 2016. Centrefugally cast functionally graded materials – review. International Conference on Systems, Science, Control, Communications, Engineering and Technology, 68-73.