On the dynamic stress and displacement field associated with a crack propagating across the interface between two media

Two half-spaces with different elastic constants are wellled together and subjected to a longitudinal shear strain at infinity so that the whole system is in a state of anti-plane strain. Suddenly the weld breaks and a crack begins to propagate at right angles to the interface into each of the two media simultaneously with a different velocity in each. This paper attempts to calculate the resulting stress and displacement fields.     

Elastic wave propagation with kinematic discontinuity along a non-ideal interface between two isotropic elastic half-spaces

The problem of wave propagation along the interface between two elastic, isotropic, and homogeneous half-spaces is studied when the half-spaces are coupled through a vanishingly thin layer of Voigt material. It is assumed that the separation, 2H, between the half-spaces, and the complex rigidity-modulus, , of the layer are both vanishingly small, but the complex quantity /2H remains finite.In a series of experiments in which two blocks of elastic materials with or without lubricant/couplant at the interface are subjected to an external load normal to the interface, the variation of the speed and attenuation of interfacial waves, generated and detected by piezoelectric transducers, was measured as a function of external load. Assuming a nonlinear relation between external load and /2H, the experimental data is interpreted theoretically, and the best-fit parameters of the nonlinear relation are determined.For the 13 cases of interfaces studied, with or without lubricant/couplant, satisfactory agreement was found between experiment and theory, except in one case. Even in this case, the agreement is satisfactory in the lower range of load. It is hoped that this study will be useful in developing nondestructive methods of testing the bonding conditions at an interface between elastic materials by means of interfacial wave properties.     

Finite elements with embedded displacement discontinuity: a generalized variable formulation

This paper is intended to bring a contribution towards a satisfactory simulation of those fracture phenomena which result in the appearance and development of discrete cracks. To this purpose, a general mixed finite element formulation is proposed, based on the concept of generalized variables in Prager's sense. The displacement field inside an element is modelled by the sum of two contributions: a regular (continuous) part which is governed by standard shape functions, and a possibly discontinuous one which is introduced soon after a suitable criterion is satisfied. The formulation is first specialized to a one‐dimensional case, then a triangular element for two‐dimensional problems is described in detail. Analytical and numerical examples are presented in order to clarify the formulation and to point out the essential role of inter‐element conformity. Copyright © 2000 John Wiley & Sons, Ltd.     

The stress distribution around a crack perpendicular to an interface between materials

The plane strain problem of a crack terminating perpendicular to a planar interface between two isotropic half spaces with different elastic constants is solved to obtain the distribution of stress in the vicinity of the crack tip. The relative elastic constants are shown to strongly affect the relative magnitudes of the various stress components as well as their radial drop off with distance from the crack tip. The implications of the results with regard to failure modes in composite materials are discussed.     

The interaction between capillary waves near a charged liquid-liquid interface with a tangential discontinuity of the velocity field

The evolution of capillary waves in a system of two liquid layers with a charged interface and the upper layer with a free surface and finite thickness translating at a constant velocity parallel to the semi-infinite lower layer is studied numerically within the framework of a linear mathematical model of capillary wave motion. The interacting waves generated at the free surface of the upper layer and at the interface give rise to an oscillatory instability of the interface, in addition to the Kelvin-Helmholtz instability. The new instability arises if the upper layer velocity is sufficiently small. The increment of oscillations depends on the density ratio of the liquids, velocity magnitude, and the charge at the interface.     

Characteristics of the relation between wavelength and displacement in monochromators with a sine drive

In this paper, we analyze the wavelength variation as the structural parameters of monochromators with a sine drive and describe the procedures for wavelength calibration by the fitting method. It will be helpful to understand and to use the wavelength calibration method in synchrotron radiation beamlines commissioning and other grating scanning spectrometers.     

The solution of a displacement discontinuity for an anisotropic half-plane and its applications to fracture mechanics

By imaginal method the solution of displacement discontinuity for anisotropic half-plane is derived in this paper. According to the Betti's reciprocal theorem, the relationship between the stress intensity factor K_I and the increment Δv/Δa is established and numerical results of K_I are obtained by the twice calculation method. Furthermore, the problem of edge crack chopping is studied in great detail, and the area of contaction and stress intensity factor K_I are found. These results are very worthwhile for research of chopping fracture in theory.     

Thermal stress intensities at an interface crack between two elastic layers

The thermal stress intensities (energy release rate and stress intensity factors) due to temperature changes are derived in closed-form for an interface crack between two elastic layers of dissimilar materials. The solutions are two-dimensional and tabulated over a wide range of material and layer thickness combinations. The tables serve as rapid evaluations of the thermal stress intensities for given temperature changes. A strain gauge technique is given for determining constraint coefficients which reflect the constraint conditions during the temperature changes. The solutions are compared with results from the literature. The stress intensities due to thermal and mechanical loads are generally superimposed. As an example of application, the solutions are utilized to obtain the complete thermal and mechanical stress intensities for a four-point bend specimen.     

Unsymmetric composite laminate with a discontinuity of the in-plane displacement or of the slope

Summary A discontinuity of the in-plane displacements and slopes in an infinitely extended anisotropic laminate is considered under coupled bending and stretching. The laminate is supposed to the thin with arbitrary anisotropy of the constitutive plies. Using the classical 2-D theory of laminates and techniques of complex potentials, a family of exact solutions is obtained for the case of a static problem. As it follows from the analysis, the energy of dislocations does not depend on their orientation. A few numerical results for real laminates are considered.     

Interaction between crack and arbitrarily shaped hole with stress and displacement boundaries

The interaction between a crack and an arbitrarily shaped hole under stress and displacement boundaries in an infinite plane subjected to a remote uniform load is studied. The Green's functions of a point dislocation for the problems are derived and are then used to analyze the interaction problem. The superposition principle is employed to reduce the original problem to two subsidiary problems. The complex stress functions of each problem are composed of two parts, in which the second parts are always holomorphic. Using analytical continuation in conjunction with rational mapping function, the stress functions are obtained in closed form. The interaction of a hole or an inclusion with a crack is solved using dislocations to model the crack and solving a system of singular integral equations. Stress intensity factors for crack tips and stress concentration factors for inclusion corner are determined and plotted for various cases. The affecting ranges of hole and inclusion are investigated.     

An experiment on stress intensity factors for an interface crack between epoxy and aluminum plates

A teflon tape (0.07 mm thickness) is placed at the center of an edge of an epoxy plate. The plate is used to fabricate a mold, and epoxy resin is cast in the mold so as to produce a cracked epoxy plate. A tensile test is conducted so as to determine the fracture toughness value of the epoxy plate. Next, a mold is fabricated from an aluminum plate having a teflon tape placed along its edge, and epoxy resin is cast in the mold so as to produce an epoxy-aluminum composite weakened by an interface crack. Tensile testing reveals that the crack always propagates into the epoxy plate at an angle measured from the interface. The stress intensity factor for an interface crack is defined in a manner similar to that for a crack in a homogeneous material, and is obtained for several values of a/h, 2a being the crack length and 2h being the width of the epoxy-aluminum composite.     

On the stress intensity factors associated with cracks interacting with an interface between two elastic media

Closed form expressions are obtained for the stresses at a crack tip when a crack is approaching a welded boundary (or a free surface) and when it has just passed through the interface. The solutions which are obtained in terms of a small parameter, the distance from or through the interface, are given in explicit form for the mode 3 situation and for some mode 1 and 2 cases. The importance of the change of stress singularity when the crack meets the interface is demonstrated.     

Elastic and plastic stress analysis of an interface crack between two dissimilar layers

In the present paper, the mixed-mode Dugdale model is applied to investigate the plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers. In the analysis, both normal and shear stresses are assumed to exist in the plastic zones and satisfy the Von Mises yield criterion. The plastic zone sizes can be determined on condition that the stress intensity factors caused by the stresses in the plastic zones and applied loading are zero. Then, the crack tip opening displacement can be obtained by dislocation theories. In numerical examples, the plane stress condition is considered. The plastic zone size and the crack tip opening displacement of an interface crack between two dissimilar layers under a uniform load are examined. The effects of Dundurs’ parameters and the thickness of materials on the plastic zone size and the crack tip opening displacement are investigated in detail. Numerical results show that in the case of small thickness, the values of the normalized plastic zone size and the normalized crack tip opening displacement decrease with increasing Dundurs’ parameters, α and β, while, in the case of infinite thickness, the value of the normalized plastic zone size is independent of α, and the value is symmetric about the axis on which β = 0.     

Relations between incompatible displacement model and hybrid stress model

An examination of the variational formulations confirms the similarity between the incompatible displacement model and the assumed stress hybrid model that was pointed out by Irons in 1972. But the basic differences between the two are also identified. For 8-node solid elements the assumed stress terms obtained through a rational procedure also agree with those deduced by Irons purely from his physical insight.     

Singularity of dynamic stress fields around an interface crack between viscoelastic bodies

The singular nature of the dynamic stress fields around an interface crack located between two dissimilar isotropic linearly viscoelastic bodies is studied. A harmonic load is imposed on the surfaces of the interface crack. The dynamic stress fields around the crack are obtained by solving a set of simultaneous singular integral equations in terms of the normal and tangent crack dislocation densities. The singularity of the dynamic stress fields near the crack tips is embodied in the fundamental solutions of the singular integral equations. The investigation of the fundamental solutions indicates that the singularity and oscillation indices of the stress fields are both dependent upon the material constants and the frequency of the harmonic load. This observation is different from the well-known −1/2 oscillating singularity for elastic bi-materials. The explanation for the differences between viscoelastic and elastic bi-materials can be given by the additional viscosity mismatch in the case of viscoelastic bi-materials. As an example, the standard linear solid model of a viscoelastic material is used. The effects of the frequency and the material constants (short-term modulus, long-term modulus and relaxation time) on the singularity and the oscillation indices are studied numerically.     

Interaction between an interface and cracks

The elastic field of edge dislocation embedded in one of two well bonded blocks is easily given by combining the edge dislocation solution in infinite plane and the method of analytic function. Using the elementary field and the principle of superposition, the problem of interaction between multi-cracks and interface is converted into a group of singular integral equations which can be numerically solved with the aid of the Chebyshev polynomial. The analytical results show that the connection between the stress intensity factors (SIF) and the Dunders' parameters depends on the bimaterial system. Furthermore, the depth beneath the interface is presented where the effect of the interface on SIF of cracks is reduced to a specified small scale. The authors point out that the depth is largely dependent on load phase angle and the distribution of cracks, but a little dependent on the orientation of the crack when there exists only one.