Numerical investigations of maximum stress concentration at elliptic holes in finite thickness piezoelectric plates

The through-thickness variations of stress-concentration factors along the wall of elliptic holes in finite thickness plates of transversely isotropic piezoelectric materials subjected to uniaxial remote tensile stress and applied electric field have been systematically analyzed using the finite element method. The three-dimensional stress concentration factor K_t is found to be a function of the thickness to root radius ratio B/ρ and the aspect ratio t (short to long axial length) of the elliptic holes under tensile loading. It is found that the maximum stress-concentration factor through the thickness, (K_t)_max, is 20-150% higher than the value on the free surface (K_t)_surf when t changes from 1 to 0.01, and the ratio of the surface value (K_t)_surf to the corresponding planar solution (K_t)_p-σ at the roots is only 0.84-0.44 when t ranges from 1 to 0.01 if B/ρ is large enough. When B/ρ is decreasing to 1, both the ratios are approaching unity. Simple empirical formulae for the relationships between the three values were obtained by fitting the numerical results with good engineering accuracy for large range of B/ρ (from 1 to 100,000) and t (from 0.01 to 1). The proposed formulae will be useful for strength and fatigue designs of engineering structures with notches and holes. Additional applied electric field can cause higher opening stress in the interior and lower opening stress at the free surface of the plate near the hole, and enhance the out-of-plane constraint significantly. Therefore, the three-dimensional effects can be much stronger in piezoelectric ceramics than in metallic materials.