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Anti-plane stress intensity, energy release and energy density at crack tips in a functionally graded strip with linearly varying properties

Kargarnovin, M. H ; Sharif University of Technology

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  1. Type of Document: Article
  2. DOI: 10.1016/j.tafmec.2011.09.003
  3. Abstract:
  4. The fracture problem of a crack in a functionally graded strip with its properties varying in a linear form along the strip thickness under an anti-plane load is considered. The embedded anti-plane crack is located in the middle of strip half way through the thickness. The third mode stress intensity factor is derived using two different methods. In the first method, by employing Fourier integral transforms, the governing equation is converted to a singular integral equation, which is subsequently solved numerically by the collocation method based on Chebyshev polynomials. Then, the problem is solved by means of finite element method in which quadrilateral 8-node singular elements around each crack tip are used. After inspecting the validity of the solution technique, effects of crack geometry and non-homogeneous material parameter on the stress intensity, energy release and energy density are studied and the results of analytical and FEM solutions are compared
  5. Keywords:
  6. Finite element method ; Functionally graded material ; Stress intensity factor ; Anti-plane ; Chebyshev polynomials ; Collocation method ; Crack geometries ; Energy density ; Energy release ; FEM solutions ; Fourier integral transforms ; Functionally graded ; Functionally graded strip ; Governing equations ; Non-homogeneous material ; Singular elements ; Singular integral equations ; Solution techniques ; Stress intensity ; Beams and girders ; Crack tips ; Cracks ; Functionally graded materials ; Stress intensity factors ; Integral equations
  7. Source: Theoretical and Applied Fracture Mechanics ; Volume 56, Issue 1 , 2011 , Pages 42-48 ; 01678442 (ISSN)
  8. URL: http://www.sciencedirect.com/science/article/pii/S0167844211000462