PSI - Issue 41

Victor Rizov et al. / Procedia Structural Integrity 41 (2022) 134–144 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1  increases. The increase of the parameter, 2  , also leads to reduction

the strain energy release rate reduces when of the strain energy release rate (Fig. 4). The influence of parameters,

3  and 4  , on the strain energy release rate is studied too. The curves in Fig. 5

3  and 4  increases.

indicate that the strain energy release rate reduces when

5  and 6  , on the strain energy release rate is shown in Fig. 6. One can observe in 5  , causes increase of the strain energy release rate (this is due to reduction of the 5  ). It can also be seen in Fig. 6 that the strain energy release rate decreases when

The effects of parameters, Fig. 6 that increase of parameter, beam stiffness with increase of

the parameter, 6  , increases. The curves in Fig. 7 illustrate the influence of the parameter, 7  , on the strain energy release rate at three values of h h / 2 ratio. It can be observed that increase of 7  leads to increase of the strain energy release rate (Fig. 7). The strain energy release rate decreases when h h / 2 ratio increases (Fig. 7). 4. Conclusions The longitudinal fracture in a non-linear viscoelastic beam structure is analyzed. The upper crack arm is loaded in pure bending so as the angle of rotation of the free end of the upper crack arm increases continuously with time. The beam is made of inhomogeneous material whose properties change smoothly along the beam thickness. A viscoelastic model structured by linear and non-linear springs and dashpots is used for treating of the mechanical behaviour of the beam configuration. The strain energy release rate is determined. The method of the J -integral is applied to verify the strain energy release rate. The parametric study indicates that the strain energy release rate increases with increasing of v (the parameter, v , controls the change of the angle of rotation of the free end of the upper crack arm). The parametric study reveals also that the strain energy release rate reduces when the values of 1  , 2  , 3  , 4  and 6  increase. However, the increase of 5  and 7  leads to increase of the strain energy release rate (this behaviour is due to reduction of the beam stiffness with increase of 5  and 7  ). Ahmed Keddouri, Lazreg Hadji, Abdelouahed Tounsi, 2019. Static analysis of functionally gradedsandwich plates with porosities. Advances in Materials Research 8, 155-177. Broek, D., 1986. Elementary engineering fracture mechanics. Springer. Chatzigeorgiou, G., Charalambakis, G., 2005. Instability Analysis of Non-Homogeneous Materials Under Biaxial Loading, Int. J. Plast. 21, 0749 6419. Chen, Y., Lin, X., 2008. Elastic analysis for thick cylinders and spherical pressure vessels made of functionally graded materials. Computational Materials Science 44, 581-581. Chikh, A., 2019. Investigations in static response and free vibration of a functionally graded beam resting on elastic founda tions. Frattura ed Integrità Strutturale 14, 115-126. Ganapathi, M., 2007, Dynamic stability characteristics of functionally graded materials shallow spherical shells, Composite Structures 79, 338 343. Gururaja Udupa, Shrikantha Rao, S., Rao Gangadharan, K., 2014. Functionally Graded Composite Materials: An Overview. Procedia Materals Science 5, 1291-1299. Han, X., Liu, G.R., Lam, K.Y., 2001. Transient waves in plates of functionally graded materials, International Journal for Numerical Methods in Engineering 52, 851-865. Hao, Y.X, Chen, L.H., Zhang, W., Lei, J. G., 2002. Nonlinear oscillations and chaos of functionally graded materials plate. Journal of Sound and vibration 312, 862-892. Kieback, B., Neubrand, A., Riedel, H., 2003. Processing techniques for functionally graded materials. Materials Science and Engineering: A 362, 81-106. 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. Kyung-Su Na, Ji-Hwan Kim, 2004. Three-dimensional thermal buckling analysis of functionally graded materials, Composites Part B: References