PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 97–105 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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Miyamoto (1997), Shrikantha and Gangadharan (2014)). By gradually changing the properties in one or more directions during manufacturing, one can optimize the material structure to achieve high performance of the structural member. This fact is one of the basic advantages of continuously inhomogeneous materials over the traditional structural materials. Initiation and growth of cracks drastically reduces the strength of material and can, in some cases, cause catastrophic failure of the structure. Therefore, understanding the fracture behavior is an important factor for improving the performance of continuously inhomogeneous materials and for further development of smart structures technology. Advancement of fracture mechanics can aid in the design and optimization of structures composed by continuously inhomogeneous materials. The considerable role of fracture in the failure mechanism is reflected by a number of articles published in this filed around the world (Jin and Batra (1996), Joshi et al. (2015), Rousseau and Tippur (2001), Tilbrook et al. (2005)). In these articles, fracture behavior of different continuously inhomogeneous (functionally graded) systems has been investigated by using mainly beam type configurations subjected to bending. The fracture behavior has been studied by applying the methods of linear-elastic fracture mechanics. The basic assumption of linear-elastic fracture mechanics is that the relationship between stresses and strains can be expressed by the Hook’s law. One specific problem is the lengthwise fracture of continuously inhomogeneous beam structures. Appearance of lengthwise cracks is due to the fact that certain kinds of continuously inhomogeneous materials such as functionally graded materials can be built-up layer by layer (Mahamood and Akinlabi (2017)). It should be noted that the works on lengthwise fracture of continuously inhomogeneous beam structures published recently do not consider the influence of the aggressive environment on the fracture behavior (Rizov (2017), Rizov (2018), Rizov (2019)). Therefore, the main purpose of present paper is to develop an analysis of lengthwise fracture in a continuously inhomogeneous beam configuration in aggressive environment. For this purpose, a time-dependent solution to the strain energy release rate which considers the damage zone that appears in the beam as a result of the aggressive environment is derived by applying the compliance method. The J -integral approach is used for verification of the solution derived.

2. Analysis of the strain energy release rate

The continuously inhomogeneous beam configuration analyzed here is shown schematically in Fig. 1.

Fig. 1. The geometry and loading of beam configuration with damage zone.

The beam has a rectangular cross-section of width, b , and height, h 2 . A vertical notch is cut-out in the beam mid span in order to induce conditions for lengthwise fracture. There is a lengthwise crack with length of a 2 . The beam length is ( ) 1 2 l l + . The crack is located symmetrically with respect to the mid-span (Fig. 1). The thicknesses of the lower and upper crack arms are denoted by 1 h and 2 h , respectively. The upper crack arm is free of stresses. The