PSI - Issue 26

Victor Rizov et al. / Procedia Structural Integrity 26 (2020) 86–96 Rizov / Structural Integrity Procedia 00 (2019) 000 – 000

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manufacturing process, the properties of continuously inhomogeneous materials can be formed, so as to meet the various performance requirements in different parts of a structural member. Since the macrostructure varies gradually, the mismatch of material properties and interfacial stress concentrations in continuously inhomogeneous materials are significantly reduced compared with laminated composites. Thus, it is not surprising that in the recent years these materials have found a wide application as advanced materials in aerospace, electronics, engineering, optics and civil infrastructure. In structural applications, fracture is the most common failure mode of continuously inhomogeneous materials. Therefore, analyzing fracture behaviour of these novel structural materials is of great importance for the practical engineering. The present paper is concerned with analyzing the effects of aging on lengthwise fracture in an inhomogeneous double cantilever beam configuration that exhibits elastic-plastic behaviour of material. The paper is motivated by the fact that certain class of continuously inhomogeneous materials as functionally graded ones can be built-up layer by layer (Mahamood and Akinlabi (2017)) which is a premise for appearance of lengthwise cracks between layers. The mechanical behaviour of the material is treated by using a power-law stress-strain relation. It should be mentioned that lengthwise fracture of continuously inhomogeneous beams has already been analyzed (Rizov (2017), Rizov (2018), Rizov (2019)). However, in (Rizov (2017), Rizov (2018), Rizov (2019)), the lengthwise fracture has been studied without considering the aging of the material. Therefore, the basic purpose of the present paper is to develop a lengthwise fracture analysis with considering the aging. The fracture is studied in terms of the strain energy release rate by using the beam complementary strain energy. The solution derived is verified by analyzing the balance of the energy. The two solutions produce identical results. The effects of aging on the strain energy release rate are evaluated by using the time-dependent solution derived. 2. Solution to the strain energy release rate with considering the aging The present paper deals with an investigation of lengthwise fracture in continuously inhomogeneous double cantilever beam that exhibits elastic-plastic behaviour of material. The beam considered is shown schematically in Fig.1.

Fig. 1. The geometry and loading of continuously inhomogeneous double cantilever beam.

A lengthwise crack of length, a , is located in the beam mid-plane. The external loading consists of two bending moments, 1 M and 2 M , applied at the free ends of the lower and upper crack arms, respectively. The beam has a rectangular cross-section of width, b , and height, 2 h . The beam is clamped in section, B .