Singular stresses due to adhesion defect on intersection line along which a semi-infinite thin plate is attached to an infinite thin plate by eigenfunction expansion method

Abstract

In this paper, the stress singularity due to adhesion defect on intersection line along which a semi-infinite thin plate (Plate 1) is attached to an infinite thin plate (Plate 2) is studied by the eigenfunction expansion method. For Plate 1 the stress is approximated as plane stress state, and for Plate 2 the stress is treated as a two-dimensional problem, in which the anti-plane deformation is also taken into account besides the plane stress. The eigenequation for the asymptotic behavior of stresses around the defect tip is given in an explicit form. This eigenequation is different from the analysis where the anti-plane deformation of Plate 2 is ignored. Specifically, it is found that the eigenvalue in consideration of the anti-plane deformation becomes a complex value with a real part equal to 0.5. Also, the singular stress around the defect tip is given in an explicit form. The obtained results are verified through comparison with numerical results of the finite element method.