Riemann–Hilbert approach-based analytical solutions for strip saturated two unequal collinear cracks in piezoelectric media

The objective of the work is to derive analytical solutions based on the Riemann–Hilbert (R–H) approach for semipermeable strip saturated two unequal collinear cracks in arbitrary polarized piezoelectric media. We particularly consider the influence of far field electromechanical loadings, poling direction and different crack-face boundary conditions. The problem is mathematically formulated into a set of non-homogeneous R–H problems in terms of complex potential functions (related to field components) using complex variable and extended Stroh formalism approach. After solving these equations, explicit solutions are obtained for the involved unknown complex potential functions and hence, the stress and electric displacement components at any point within the domain. Furthermore, after employing standard limiting conditions, explicit expressions for some conventional fracture parameters such as saturated zone lengths (in terms of nonlinear equations), local stress intensity factors and crack opening displacement are obtained. Numerical studies are presented for the PZT-4H material to analyze the effects of prescribed electromechanical loadings, inter-cracks distance, crack-face conditions and poling direction on the defined fracture parameters.

Analysis of Cracked Body Strengthened by Adhesively Bonded Patches by BEM-FEM Coupling

This paper presents an efficient numerical technique capable of handling the stress analysis of three-dimensional cracked bodies strengthened by adhesively bonded patches. The proposed technique is implemented within the framework of the coupling of the weakly singular boundary integral equation method and the standard finite element procedure. The former is applied to efficiently treat the elastic body containing cracks, whereas the latter is adopted to handle both the adhesive layers and patches. The approximation of the near-front relative crack-face displacement is enhanced by using local interpolation functions that can capture the right asymptotic behavior. This also offers the direct calculation of the stress intensity factors along the crack front. A selected set of results is reported to demonstrate the capability of the proposed technique and the influence of various parameters on the performance of the strengthening.

Nonlinear analysis of a crack in 2D piezoelectric semiconductors with exact electric boundary conditions

In this paper, taking the exact electric boundary conditions into account, we propose a double iteration method to analyze a crack problem in a two-dimensional piezoelectric semiconductor. The method consists of a nested loop process with internal and outside circulations. In the former, the electric field and electron density in governing equations are constantly modified with the fixed boundary conditions on crack face and the crack opening displacement; while in the latter, the boundary conditions on crack face and the crack opening displacement are modified. Such a method is verified by numerically analyzing a crack with an impermeable electric boundary condition. It is shown that the electric boundary condition on crack face largely affects the electric displacement intensity factor near a crack tip in piezoelectric semiconductors. Under exact crack boundary conditions, the variation tendency of the electric displacement intensity factor versus crack size is quite different from that under an impermeable boundary condition. Thus, exact crack boundary conditions should be adopted in analysis of crack problems in a piezoelectric semiconductor.

Comparative Study on Stress Intensity Factors for Surface Cracks in Welded Joint and Flat Plate by Using the Influence Function Method

Welding is an effective method for joining metallic structures which are very common in the construction of ships and offshore platforms. However, welded joints are prone to fatigue failure under cyclic loading due to the associated high residual stresses. In order to assess the fatigue crack propagation (FCP) accurately, precise evaluation of stress intensity factors (SIFs) is a key parameter. The residual stress distribution on the crack face of welded joints is usually non-uniform and also depends on boundary conditions. Therefore, an efficient technique is required to calculate SIFs for welded joints under non-uniform stress distribution. In this study, SIFs of semi-circular surface cracked welded joints are calculated by using the influence function method (IFM). The IFM has been introduced as an efficient method to evaluate SIFs under arbitrary stress distribution. The influence coefficient databases (ICDB) are developed for welded joints and flat plate models using IFM in this study. As the crack face traction (CFT) integral is employed in this developed influence coefficients (IC), the SIFs given by IFM are more accurate compared to the previously established solutions without CFT-integral. The ICDB and SIFs evaluated by using welded joint and flat plate models are compared and discussed. This study reveals the difference between ICDB of flat plates and welded joints, and estimation error of calculated SIFs for welded joints by using flat plate ICDB.

FE SOLUTIONS OF NEAR-TIP FIELD FOR MODE-I CRACKS WITH RESIDUAL SURFACE TENSION

This paper presents finite element solutions of a near-tip elastic field of a straight, nano-scale crack in a two-dimensional, linear elastic, whole plane subjected to mode-I crack-face loads. The mathematical model is formulated using a continuum-based theory of classical linear elasticity together with Gurtin-Murdoch surface model to capture the role of the residual surface tension present on the crack-face material layer. The formulation finally yields a second-order, integrodifferential equation governing the crack opening displacement. A weighted residual technique along with the regularization procedure is applied to establish a weakly singular weak-form equation with the involved kernel of O(ln )r . Galerkin strategy and the finite element procedure are then employed to discretize the weak-form equation. Various types of element shape functions, generated by standard C0 -elements, standard C1 -elements, and special elements with built-in crack-tip functions, are considered. A proper quadrature rule is selected to efficiently and accurately evaluate both nearly and weakly singular double line integrals over pairs of elements resulting from the discretization and the solution of a dense system of linear algebraic equations is obtained using an efficient indirect solver. The rate of convergence of finite element solutions is fully investigated and such information is then used to conclude the influence of the residual surface tension on the behavior of the near-tip field.