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Coupled Systems Mechanics
  Volume 9, Number 4, August 2020, pages 381-396

Investigation of two parallel lengthwise cracks in an inhomogeneous beam of varying thickness
Victor I. Rizov

    Analytical investigation of the fracture of inhomogeneous beam with two parallel lengthwise cracks is performed. The thickness of the beam varies continuously along the beam length. The beam is loaded in three-point bending. Two beam configurations with different lengths of the cracks are analyzed. The two cracks are located arbitrary along the thickness of the beam. Solutions to the strain energy release rate are derived assuming that the material has non-linear elastic mechanical behavior. Besides, the beam exhibits continuous material inhomogeneity along its thickness. The balance of the energy is analyzed in order to derive the strain energy release rate. Verifications of the solutions are carried-out by considering the complementary strain energy stored in the beam configurations. The influence of the continuous variation of the thickness along the beam length on the lengthwise fracture behavior is investigated. The dependence of the lengthwise fracture on the lengths of the two parallel cracks is also studied.
Key Words
    lengthwise fracture; inhomogeneous beam; material non-linearity; three-point bending; variable thickness
Victor I. Rizov: Department of Technical Mechanics, University of Architecture, Civil Engineering and Geodesy,
1 Chr. Smirnensky blvd., 1046 - Sofia, Bulgaria

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