Ching-Hwei Chue

Bonded repair of a plate with inclined central crack under biaxial loading

Abstract This paper is to study the performance of the bonded repairs of a plate containing an inclined central through-crack under a biaxial loading. The concept is to change the load path and to bypass the defect or crack in a structure. Consequently, the stress intensity factors or the energy level near the crack tip can be reduced. Also, the maximum adhesive shear stress and patch fibre stress have to meet the design criteria such that the structure will not fail in service. In general, the stresses and stress intensities are strongly influenced by the existence of the biaxial load. The problem of how to optimize the patch fibre orientation with single- or double-sided patching has been discussed. The interactions between the biaxial load and the ply orientation on the fracture behaviour of the inclined crack are studied numerically. For better repair efficiency, the results indicate that the fibre orientation should coincide with the maximum tensile load direction in double-sided patching and be perpendicular to the crack surface in single-sided patching.

Decoupled formulation of piezoelectric elasticity under generalized plane deformation and its application to wedge problems

Abstract This paper presents the formulation of piezoelectric elasticity under generalized plane deformation derived from the three-dimensional theory. There are four decoupled classes in the generalized plane deformation formulation, i.e. when l 3 ( μ )= l 2 * ( μ )=0, l 3 ( μ )= l 3 * ( μ )=0, l 3 * ( μ )= l 2 * ( μ )=0 or l 3 ( μ )= l 3 * ( μ )= l 2 * ( μ )=0. Only the inplane fields of the first class and the antiplane field of the second class include the piezoelectric effect. Several examples of wedge problem often encountered in smart structures, such as sensors or actuators are studied to examine the stress singularity near the apex of the structure. The bonded materials to the PZT-4 wedge are PZT-5, graphite/epoxy or aluminum (conductor). The influencing factors on the singular behavior of the electro-elastic fields include the wedge angle, material type, poling direction, and the boundary and interface conditions. The numerical results of the first case are compared with Xus graphs and some comments are made in detail. In addition, some new results regarding the antiplane stress singularity of the second class are obtained via the case study. The coupled singularity solutions under generalized plane deformation are also investigated to seek the conditions of the weakest or vanishing singular stress fields.

A general solution on stress singularities in an anisotropic wedge

Abstract This paper presents a general solution for determining the stress singularity order in an anisotropic wedge. The order depends on the wedge angle, boundary conditions and material properties. The characteristic equation, which governs the eigenvalues, is established from the Lekhnitskii’s complex function method. A domain of one-quarter circle is proposed in which the contours of singularity order are plotted for all fiber orientations and a certain wedge angle. The numerical results agree well with the open literature for special cases. To reduce to strength of stress singularity at the wedge corner, the fiber direction corresponding to minimum singularity order can be determined.

Fracture mechanics analysis of a composite piezoelectric strip with an internal semi-infinite electrode

Abstract IA piezoelectric strip with semi-infinite electrode is investigated. Two combinations of mechanical–electrical loadings are considered. They consist of the anti-plane deformation with in-plane electrical field and the in-plane electroelastic field. Based on the Fourier transform and the Wiener–Hopf technique, the electroelastic local stress fields are found to exhibit the square root singularity near the electrode tip. The energy density factor criterion is applied to examine the fracture behavior near the electrode tip.

Pitting formation under rolling contact

Abstract The mechanism of pitting caused by rolling contact is analyzed using the fracture mechanics approach. The governing factors are the initial crack length, crack angle, contact force, friction, strain hardened layer, and the hydraulic pressure of trapped fluid acting on the crack surface. Mode I and II stress intensity and the strain energy density factors are calculated by application of the two-dimensional finite element method. The strain energy density criterion is applied to show that shallow angle crack under small rolling contact force and friction enhances the probability of pitting under the roller’s running surface. The presence of a strain hardened surface layer also tends to affect the fracture behavior. The analytical results agree well with the experimental observations.

Disappearance of free-edge stress singularity in composite laminates

Abstract Based on the anisotropic elasticity theory and Lekhnitskiis complex potential functions, the r λ −1 type stress singularities occurring near the apex of free edge composite laminate are studied. The singularity order depends on wedge angles, which form a half plane, material properties and the fiber orientation. The disappearance conditions of the stress singularity can be found from the contours of λ −1 plotted in a full circular region. Numerical results regarding to zero order singularity are obtained for some α −(180°− α ) bonded wedges, such as α =45°, 60°, 75° and 90°. Also, the applications of this approach to angle-ply and cross-ply composite laminates for diminishing the stress singularity near the apex of free edge are discussed.

Stability and integrity of mechanical joints in flight vehicles: Local and global energy density

Abstract A methodology is presented for analyzing the inlfuence of mechanical joint failure on the global instability of flight vehicles. Considered are the ways with which loading, geometry and material of the vehicle can affect the structure instability and/or integrity. The peaks and valleys of the volume energy density function are assumed to coincide with failure by fracture and/or yielding while the distance between their local and global stationary values govern the structure instability. A single length parameter l can thus be applied to provide a measure of stability. The simultaneous occurrence of high energy density and large l at the same location should be avoided as it may have undesirable consequences. A flight vehicle consisting of four cylindrical shell-like structures connected by three tongue-and-groove joints is analyzed. The time-dependent load can be axisymmetric or non-axisymmetric. A semi-analytical finite element program is developed and used to solve for the transient stress and strain distribution from which contours of the volume energy density in the structure are obtained as a function of time. The magnitudes and locations of their local and global stationary values are then calculated and discussed in connection with potential failure by fracture. Stability behavior does not alter appreciably for axisymmetric flight. Considerable fluctuations in the energy density and the dynamic stability length parameter are found when non-axisymmetric loads are considered.

On stress singularities in an anisotropic wedge for various boundary conditions

This paper presents a general solution for determining the stress singularity orders of an anisotropic wedge for various boundary conditions. The characteristic equation, which governs the singularity orders, is derived from Lekhnitskiis complex function method. The order depends upon the wedge angle, boundary conditions and material properties. The contours of the singularity order are plotted in a domain of one-quarter circle for all fiber orientations and a certain wedge angle. The numerical results agree well with the open literature for special simple cases. New results come from studying the contours and provide useful information for composite structural design.

The effects of laminated composite patch with different stacking sequences on bonded repair

Abstract This paper discusses the effect of laminated composite patch with different stacking sequences on repairing an inclined central cracked plate under biaxial loads. By means of the finite element method and the strain energy density theory, the results show that the optimal ply orientations of the patch are the three directions 90° and ± 45° related to the crack direction. Also, the use of different stacking sequences for the patch does not affect the energy distribution near the crack tip significantly.

Singular electro-mechanical fields near the apex of a piezoelectric bonded wedge under antiplane shear

This paper presents the explicit forms of singular electro-mechanical field in a piezoelectric bonded wedge subjected to antiplane shear loads. Based on the complex potential function associated with eigenfunction expansion method, the eigenvalue equations are derived analytically. Contrary to the anisotropic elastic bonded wedge, the results of this problem show that the singularity orders are single-root and may be complex. The stress intensity factors of electrical and mechanical fields are dependent. However, when the wedge angles are equal (α=β), the orders become real and double-root. The real stress intensity factors of electrical and mechanical fields are then independent. The angular functions have been validated when they are compared with the results of several degenerated cases in open literatures.