Analysis of Delamination in Two-Dimensional Functionally Graded Multilayered Beam with Non-Linear Behaviour of Material

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Authors

  • Victor Iliev RIZOV University of Architecture, Civil Engineering and Geodesy, Bulgaria

Abstract

An analytical study of delamination fracture in a two-dimensional functionally graded multilayered beam exhibiting material non-linearity is carried-out. The beam is made of adhesively bonded horizontal layers. The material is two-dimensional functionally graded in the cross-section of each layer. A delamination crack is located symmetrically with respect to the beam mid-span. The delamination is studied in terms of the strain energy release rate. The solution derived is compared with the J-integral for verification. The effects of material gradients, the crack location along the beam height and the material non-linearity on the delamination fracture are investigated. The distribution of the J-integral value along the crack front is analysed too.

Keywords:

two-dimensional functionally graded material, multilayered beam, delamination, material non-linearity, analytical solution

References

1. Bohidar S.K., Sharma R., Mishra P.R., Functionally graded materials: A critical review, International Journal of Research, 1(7): 289–301, 2014.

2. Tilbrook M.T., Moon R.J., Hoffman M., Crack propagation in graded composites, Composite Science and Technology, 65(2): 201–220, 2005.

3. Upadhyay A.K., Simha K.R.Y., Equivalent homogeneous variable depth beams for cracked FGM beams; compliance approach, International Journal of Fracture, 144(3): 209–213, 2007.

4. Panigrahi B., Pohit G., Nonlinear modelling and dynamic analysis of cracked Timoshenko functionally graded beams based on neutral surface approach, Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 230(9): 1468–1497, 2016.

5. Rizov V.I., Analytical study of elastic-plastic longitudinal fracture in a functionally graded beam, Strength, Fracture and Complexity, 10(1): 11–22, 2017.

6. Rizov V.I., Delamination fracture in a functionally graded multilayered beam with material nonlinearity, Archive of Applied Mechanics, 87(6): 1037–1048, 2017.

7. Szekrenyes A., Nonsingular crack modelling in orthotropic plates by four equivalent single layers, European Journal of Mechanics – A/Solids, 55: 73–99, 2016.

8. Hsueh C.H., Tuan W.H., Wei W.C.J., Analyses of steady-state interface fracture of elastic multilayered beams under four-point bending, Scripta Materialia, 60(8): 721–724, 2009.

9. Lubliner J., Plasticity theory (Rev. Ed.), University of California, Berkeley, CA, 2006.

10. Petrov V.V., Non-linear incremental structural mechanics, Infra-Injeneria, M., 2014.

11. Hutchinson J.W., Suo Z., Mixed mode cracking in layered materials, Advances in Applied Mechanic, 29: 63–191, 1991.

12. Broek D., Elementary engineering fracture mechanics, Springer, 1986.