Non-linear elastic analysis of delamination in two-dimensional functionally graded multilayered beams

Article type: Research Article

Authors: Rizov, V.^a;

Affiliations: [a] Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, Sofia, Bulgaria

Correspondence: [*] Address for correspondence: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., Sofia, Bulgaria. Tel.: +(359-2) 963 52 45/664; Fax: +(359-2) 86 56 863; E-mail: v_rizov_fhe@uacg.bg

Abstract: An analytical study of delamination fracture in two-dimensional functionally graded multilayered non-linear elastic split cantilever beam configurations is carried out. The beam is made of an arbitrary number of adhesively bonded longitudinal vertical layers, which have different thicknesses and material properties. Besides, the material is two-dimensional functionally grade in the cross-section of each layer. A vertical delamination crack is located arbitrary along the beam width. The beam is loaded eccentrically in tension by a force applied at the free end of the right-hand crack arm. The delamination fracture is studied in terms of the strain energy release rate. A comparison with the J-integral approach is carried out for verification. The results, yielded by the two analyses, are identical. The solutions obtained are used to evaluate the influences of crack location, material gradients and non-linear behaviour of material on the delamination fracture in the split cantilever beam under consideration. The distribution of the J-integral value along the crack front is analyzed too. It is found that the strain energy release rate can be reduced by appropriate selection of the material gradients in the design stage of two-dimensional functionally graded multilayered beams.

Keywords: Multilayered beam, two-dimensional functionally graded material, delamintion crack, material non-linearity

DOI: 10.3233/SFC-180233

Journal: Strength, Fracture and Complexity, vol. 11, no. 4, pp. 319-335, 2018