Issue 41

V. Rizov, Frattura ed Integrità Strutturale, 41 (2017) 491-503; DOI: 10.3221/IGF-ESIS.41.61 492 the last three decades [16]. Fracture behavior is crucial for structural integrity and functionality of members and components made of functionally graded materials. Therefore, considerable attention has been paid to fracture in these novel materials by the international research community [17-22]. The present paper is concerned with a longitudinal fracture analysis of a two-dimensional functionally graded cantilever beam configuration with taking into account the non-linear behavior of material. Fracture is analyzed in terms of the strain energy release rate. The material is functionally graded along the height as well as along width of the beam. The mechanical behavior of material is described by a power-law stress-strain relation. An additional fracture analysis is carried-out by applying the J -integral approach and the results obtained are compared with the strain energy release rate. The effects of material gradients, crack location and material non-linearity on the fracture behavior are elucidated. A NALYSIS OF THE STRAIN ENERGY RELEASE RATE he present paper analyses the longitudinal fracture in the two-dimensional functionally graded cantilever beam configuration shown schematically in Fig. 1. Figure 1 : The geometry and loading of the two-dimensional functionally graded cantilever beam. A longitudinal crack of length, a , is located arbitrary along the beam cross-section height (it should be mentioned that the present paper is motivated also by the fact that functionally graded materials can be built up layer by layer [16] which is a premise for appearance of longitudinal cracks between layers). The lower and upper crack arms have different thicknesses denoted by 1 h and 2 h , respectively. The beam is loaded by one bending moment, y M , applied at the free end of lower crack arm (Fig. 1). Thus, the upper crack arm is free of stresses. The beam has a rectangular cross-section of width, b , and height, 2 h . The beam is clamped in section, D . The beam non-linear mechanical behavior is described by the following power-law stress-strain relation [23]: m B    (1) where σ is the longitudinal normal stress, ε is the longitudinal strain, B and m are material properties. Zircona-titanium is one of the functionally graded materials which exhibit non-linear mechanical behavior. Data for mechanical properties of zircona-titanium can be found in [24]. The material is functionally graded along the width as well as along the height of the beam (Fig. 1). The distribution of material property, B , in the beam cross-section is expressed as a function of 3 y and 3 z by the following quadratic law: T