PSI - Issue 25

Victor Rizov / Procedia Structural Integrity 25 (2020) 112–127

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Author name / Structural Integrity Procedia 00 (2019) 000–000

widespread use of the functionally graded materials in the up-to-date engineering (Gasik (2010), Hirai and Chen (1999), Kawasaki and Watanabe (1997), Miyamoto et al. (1999)). The functionally graded materials are continuously inhomogeneous composites with smooth spatial variation of their macroscopic properties. One of the important advantages of the functionally graded material over the conventional structural materials is the fact that the variation of their properties in one or more spatial directions in the solid can be tailored technologically during the manufacturing process in order to meet specific performance requirements. Therefore, it is not surprising that the functionally graded materials have gained significant attention in such areas of the practical engineering as aerospace, nuclear power stations, aircrafts, microelectronics, optics and biomedicine (Nemat-Allal et al. (2011), Saiyathibrahim et al. (2016), Shrikantha and Gangadharan (2014)). An adequate analysis of the fracture behaviour of the inhomogeneous (functionally graded) structural members and components is quite important for assessment of their operations performance and load-bearing capacities. Thus, the fracture behaviour of continuously inhomogeneous materials and structures presents a great deal of interest for researchers around the globe. One of the specific physical features that have to be taken into account in the development of efficient theoretical models and methods for fracture analysis of inhomogeneous materials is the dependence of the material properties on the coordinates (Erdogan (1995), Gan-Yun Huang et al. (2003), Jin and Batra (1996), Tilbrook et al. (2005)). Various works on fracture behaviour of composite materials with functionally graded material properties have been reviewed in (Tilbrook et al. (2005)). Analyses of the influence of microstructural gradation on fracture have been presented. Studies of cracks oriented parallel or perpendicular to the material gradient direction have been discussed. Effects of various geometrical parameters and material properties on the failure resistance of graded composites have been analyzed. Solutions of different crack problems in functionally graded composite materials by applying methods of linear-elastic fracture mechanics have been considered. Fracture behaviour of graded composites under static as well as fatigue crack loading conditions has been investigated. The influence of the thermal stresses on the fracture has been studied too. Some basic problems of fracture mechanics of inhomogeneous (functionally graded) materials have been identified and discussed in (Erdogan (1995)). The debonding of functionally graded coatings has been analyzed. Various topics concerning surface crack problems in functionally graded materials have been considered. General problems of fracture behaviour of functionally graded materials have been studied in (Jin and Batra (1996)). The fracture toughness of functionally graded materials has been investigated by applying the crack bridging concept. The strength behaviour of functionally graded materials with an edge crack has been evaluated. A model for fracture analysis of functionally graded materials with arbitrary varying properties has been developed in (Gan-Yun Huang et al. (2003)). Plane deformation has been assumed. A crack problem of a functionally graded coating under normal and shearing loading has been solved by applying the model developed and discussed in detail. It should be noted that certain kinds of continuously inhomogeneous materials, such as functionally graded materials, can be built-up layer by layer (Mahamood and Akinlabi (2017)). Such materials are highly prone to appearance of lengthwise cracks between layers. The lengthwise fracture affects the structural integrity and is one of the dominant failure modes of the inhomogeneous structural members and components. Recently, several works on lengthwise fracture behaviour of continuously inhomogeneous beam structures have been published (Rizov (2017), Rizov (2018), Rizov (2019)). The influence of various factors such as crack length and location, material gradients, loading conditions and others on the lengthwise fracture have been evaluated. The present paper is focused on the effects of the beam cross-section geometry on the lengthwise fracture of inhomogeneous beams. Fracture behaviour is analyzed in terms of the strain energy release rate by applying methods of linear-elastic fracture mechanics. The effects of four beam cross-section geometries (isosceles triangle, antiparallelogram, T-shape and circle) on the lengthwise fracture behaviour are evaluated. 2. Methodology for calculation of the strain energy release rate A beam configuration that exhibits continuous material inhomogeneity in both height and length directions is under consideration. Thus, the material properties vary continuously in both length and directions of the beam. The material has linear-elastic mechanical behaviour. The beam is loaded by an arbitrary system of mechanical loading.