IWPDF2023

Considering the Time Factor in Longitudinal Fracture Analysis of Functionally Graded Constructions

V. Rizov ∗

Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy, Sofia 1046, Bulgaria

∗ v_rizov_fhe@uacg.bg

Keywords: time factor, bending, longitudinal fracture.

The current theoretical paper aims to explore how the longitudinal fracture in beam-type func tionally graded engineering constructions is biased by the time factor. As known, there is a clear tendency of increasing the usage of functionally graded materials in various spheres of engineering [1]. The beam studied here has non-linear viscoelastic behavior. Besides, the beam is functionally graded through its thickness. The beam is subjected to static loading. The theoretical model used for dealing with viscoelastic behavior is set-up by linear as well as non-linear springs and dashpots. Two parameters of the model (the modulus of elasticity and the coefficient of viscosity of the non-linear spring and dashpot) are continuously varying with time (actually the basic mo tive for the present study consists in the fact that previous studies dealing with time-dependent modulus of elasticity [2] or coefficient of viscosity [3] use linear viscoelastic models). Also, all of the model parameters are distributed continuously through the beam thickness. The first step in the analysis consists in extracting of the time-dependent non-linear relation between stress and strain by treating the stressed and strained state of the components of the viscoelastic model when the latter is subjected to a constant stress. Then this relation is used when extracting of the time-dependent strain energy release rate. The solution of the strain energy release rate is confirmed by analyzing the time-dependent strain energy in the beam. It is found that the strain energy release rate is biased in a significant degree by the factor of time. In particular, the strain energy release rate-time curve has rising mode. Another issue that is clarified as a result of the present study is the effect of the variation of the modulus of elasticity and the coefficient of viscosity with time on the strain energy release rate. It is found that the strain energy release rate reduces when the values of the parameters used for treating the dependency of the modulus of elasticity and the coefficient of viscosity on time rise. References [1] Mahamood, R. C., Akinlabi, E. T. (2017). Functionally Graded Materials, Springer. [2] Rizov, V. I. (2022). Analysis of the strain energy release rate for time-dependent delamination in multilayered beams with creep. Advances in Materials Research, 11, 41-57. [3] Rizov, V. I. (2021). Continuously inhomogeneous beam structure with creep: a longitudinal crack study. Structural Monitoring and Maintenance, 8, 111-124.

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