Computation of SIFs for cracks in FGMs and TBC under mechanical and thermal loadings
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ORIGINAL PAPER
Computation of SIFs for cracks in FGMs and TBC under mechanical and thermal loadings Yazid Ait Ferhat1 · Abdelkader Boulenouar1 Received: 9 December 2019 / Accepted: 23 July 2020 © Springer-Verlag France SAS, part of Springer Nature 2020
Abstract The objective of this study is to present a numerical modeling of mixed-mode fracture in isotropic functionally graded materials (FGMs), under mechanical and thermal loading conditions. In this paper, a modified displacement extrapolation technique DET was proposed to calculate the stress intensity factor (SIFs) for isotropic FGMs. Using the Ansys Parametric Design Language, the continuous variations of the material properties are incorporated by specified parameters at the centroid of each element. Four numerical examples are presented to evaluate the accuracy of SIFs calculated by the proposed method. Comparisons have been made between the SIFs predicted by the DET and the available reference solutions in the current literature. A good agreement is obtained between the results of the DET and the reference solutions. Keywords Functionally graded materials · Displacement extrapolation · Stress intensity factor · Thermal loading
1 Introduction Functionally graded materials (FGMs) are nonhomogeneous composites that possess continuous variations in the thermomechanical properties. Due to their potential usage in high temperature applications as protective coatings and interlayers, fracture mechanics and thermal stress analyses of FGMs have been considered by many researchers in the past. Various techniques have been developed in order to study the behavior of cracks in FGMs under mechanical and thermal loading conditions. For crack problems subjected to mechanical loading, Anlas et al. [1] have evaluated SIFs in FGMs for an edge-cracked plate under uniform mechanical loading, using both the strain energy release rate and the J-contour integral. Rao and Rahman [2] present a Galerkinbased meshless method for calculating SIFs for a stationary crack in two-dimensional FGMs of arbitrary geometry. Kim and Paulino [3–5] extended various finite elements based * Yazid Ait Ferhat [email protected] Abdelkader Boulenouar [email protected] 1
Materials and Reactive Systems Laboratory, Mechanical, Engineering Department, University Djillali Liabes of Sidi-Bel-Abbes, BP 89, 22000 City Larbi Ben Mhidi, Sidi‑Bel‑Abbes, Algeria
approaches for fracture mechanics analysis of FGMs such as modified crack closure method, mixed-mode J-integral and interaction integral. Gu et al. [6] have proposed a finite element based method for calculating SIFs of graded materials, using the equivalent domain integral (EDI) technique. Guo et al. [7] considered mode I crack problems in a finite width graded orthotropic strip under static loading. Shojaee and Daneshmand [8] applied the extended isogeometric analysis with orthotropic approach for numerical modeling of stationary cracks in FGM plane bodies. Martinez-Paneda and Gallego [9] evaluated the performance of numerical tools
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