Issue 41

V. Rizov, Frattura ed Integrità Strutturale, 41 (2017) 491-503; DOI: 10.3221/IGF-ESIS.41.61 491 Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity Victor Rizov Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, 1 Chr. Smirnensky blvd., 1046 – Sofia, Bulgaria. v_rizov_fhe@uacg.bg A BSTRACT . An analytical study of longitudinal fracture in two-dimensional functionally graded cantilever beam configurations is carried-out with taking into account the non-linear behavior of material. A longitudinal crack is located arbitrary along the beam cross-section height. The material is functionally graded along the width as well as along the height of beam. The external loading consists of a bending moment applied at the free end of lower crack arm. Fracture is studied in terms of the strain energy release rate by considering the beam complementary strain energy. The solution derived is verified by analyzing the longitudinal crack with the help of the J -integral. The distribution of J -integral value along the crack front is studied. The effects of crack location, material gradients and non-linear behavior of material on the fracture are elucidated. The analysis reveals that the material non-linearity has to be taken into account in fracture mechanics based safety design of structural members and components made of two-dimensional functionally graded materials. K EYWORDS . Functionally graded beam; Crack; Material non-linearity; Analytical solution. Citation: Rizov, V., Analysis of longitudinal cracked two-dimensional functionally graded beams exhibiting material non-linearity, Frattura ed Integrità Strutturale, 41 (2017) 491-503. Received: 23.04.2017 Accepted: 28.05.2017 Published: 01.07.2017 Copyright: © 2017 This is an open access article under the terms of the CC-BY 4.0, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. I NTRODUCTION he functionally graded materials are new inhomogeneous materials produced by mixing of two constituent materials in different proportions in order to satisfy the requirements of material properties in different parts of a structural member [1-12]. Since the composition of constituent materials varies continuously along one or more spatial coordinates during manufacturing without sudden changes of material properties, the interfaces and stress concentrations are largely avoided in contrast to laminated composite materials [13-15]. Besides, the performance of functionally graded structural members and components to the external load can be optimized by tailoring the variation of material properties in a desired way during manufacturing. Therefore, the functionally graded materials have been widely applied as advanced structural materials in aeronautics, electronics, nuclear energy, optics, engineering and biomedicine for T