Plane Of Transverse Isotropy Research Articles

Boundary element analysis of orthotropic delamination specimens with interface cracks

The boundary element method (BEM) with special crack-tip elements is used to obtain the stress intensity factors, K 1 and K 2, and the strain energy release rates of interface cracks in bilayer double cantilever beam (DCB) and end-loaded-split (ELS) specimens. The material system considered is one in which an orthotropic, transversely isotropic layer is bonded to another layer of equal thickness and made of the same material, but the latter being in the plane of transverse isotropy. The effects of the mechanical properties of the orthotropic material are characterized by the parameters, η 1 and η 2, which correspond to the purely imaginary roots of the characteristic equation for the material. Calibration results showing the variations of the normalized strain energy release rates with the geometry of the specimens are presented for a range of values of these material parameters. They show the same qualitative trends as for a completely homogeneous beam specimen. To provide a complete characterization of the near-tip fields of the interface crack, the phase angle ψ = tan −1 ( K 2/ K 1), which denotes the degree of the mode mixity there, is also obtained for each case. The results show that ψ generally attains a constant value when the ratio of the crack length to the layer thickness reaches a value of less than eight.

Stress intensification near an elliptical crack border

Analyzed in this work is the stress intensification around an elliptical crack in a piezoelectric medium with transverse isotropy. The electroelastic field equations in three dimensions are expressed in terms of the displacement components and electric potential. Two potential functions are introduced to obtain the solution for an elliptical crack subjected to uniform tractions and electric disturbance. The plane of transverse isotropy is parallel to the crack. Complex interactions of the local stresses and electric displacements are found, the variations of which around the crack border are expressed in terms of the stress intensity factor. Numerical results are obtained for four different peizo-ceramic materials; they are PZT-6B, PZT-2, BaTi0 3 and PZT-5H. Enhancement of piezoelectric properties is shown to reduce the crack border stress intensification.

Analysis of borehole expansion and gallery tests in anisotropic rock masses

Closed-form solutions are used to show how rock anisotropy affects the variation of the modulus of deformation around the walls of a hole in which expansion tests are conducted. These tests include dilatometer and NX-jack tests in boreholes and gallery tests in tunnels. The effects of rock anisotropy on the modulus of deformation are shown for transversely isotropic and regularly jointed rock masses with planes of transverse isotropy or joint planes parallel or normal to the hole longitudinal axis for plane strain or plane stress condition. The closed-form solutions can also be used when determining the elastic properties of anisotropic rock masses (intact or regularly jointed) in situ.