Analytical study of elastic-plastic longitudinal fracture in a functionally graded beam

Article type: Research Article

Authors: Rizov, V.

Affiliations: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria. Tel.: + (359-2) 963 52 45/664; Fax: + (359-2) 86 56 863; E-mail: v_rizov_fhe@uacg.bg

Abstract: The longitudinal fracture in a functionally graded beam configuration was investigated analytically with considering the non-linear material behaviour. It was assumed that the material is functionally graded along the beam width. The mechanical behaviour of beam was modelled by a power-law stress–strain relation. The fracture was analyzed in terms of the strain energy release rate. An analytical solution for the strain energy release rate was derived by considering the beam complimentary strain energy. In order to verify the solution, the strain energy release rate was analyzed also by considering the complimentary strain energy in the beam cross-sections ahead and behind the crack front. The influence of material gradient, beam height and crack location along the beam width on the non-linear longitudinal fracture was investigated. The results obtained may be used for optimization of elastic-plastic functionally graded beams with respect to their fracture behaviour. The present paper contributes for the understanding of longitudinal fracture in functionally graded structures with non-linear material behaviour.

Keywords: Functionally graded materials, fracture, non-linear material behaviour, analytical solution

DOI: 10.3233/SFC-170197

Journal: Strength, Fracture and Complexity, vol. 10, no. 1, pp. 11-22, 2017