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Elastodynamic stress intensity factors are computed for diffraction of antiplane shear waves by a crack in a layered composite. The crack is parallel to the layering. The problem is formulated by means of integral transforms, and reduced to the solution of a singular integral equation. The special case when the direction of the wave motion is perpendicular to the layering is studied numerically, and stress intensity factors are obtained for several values of frequency, material constants, and geometrical parameters.Subject Classification: 40.55; 20.30.

Elastodynamic stress intensity factors are computed for diffraction of antiplane shear waves by a crack in a layered composite. The crack is normal to and bisected by the midplane of the layer. Both cases of a partially broken layer and a completely broken layer are studied. Integral transform techniques are used to formulate the problem as a singular integral equation. The propagation of symmetric modes (Love waves) is studied numerically, and stress intensity factors are obtained for several values of frequency, geometrical parameters, and material constants. The amplitude ratios of the incident waves to incident plus scattered waves at a large distance from the crack are also calculated.

The antiplane shear problem of two bonded elastic half planes containing a crack perpendicular to the interface is considered. The cases of a semi-infinite crack terminating at the interface, a finite crack away from and terminating at the interface, two cracks one on each side of the interface, and a finite crack crossing the interface are separately investigated. The nature of the stress singularity for the crack terminating at and going through the interface is studied, and it is shown that at the irregular point on the interface, for the former the power of singularity is not -1/2 and for the latter the stresses are bounded. For a material pair of aluminum-epoxy some numerical results giving the stress intensity factors, the density functions, and the crack opening displacements are presented.

Strike slip generated by wave motions and wave motions generated by strike slip are analyzed for vertical surface faults on which motion is opposed by a frictional shear stress, which is assumed to increase linearly with depth. The fault is a plane of discontinuity in a homogeneous, isotropic, linearly elastic half-space. The half-space is subjected to normal stresses that increase linearly with depth and to spatially uniform antiplane shear stresses. The horizontally polarized shear motions occurring in these two problems can be treated by a single mathematical analysis, which is presented in some detail. The results of this paper include an expression for the rate of advance of the leading edge of the zone of sliding in the initial stages of the sliding process and an expression for the maximum depth of penetration of the zone of sliding. Shear stresses in the fault plane have also been computed, and an upper bound has been established for the relative displacement at the surface trace of the fault.

This article examines the equilibrium configuration of dislocation arrays in anisotropic bimaterial plates. Both components in the plate are assumed to be orthotropic with respect to plate axes. Forces on dislocations due to external loadings are found in closed form.Image forces due to phase boundary and free surfaces are also taken into consideration.Discussions on the behavior of screw dislocation arrays can be easily extended to the behavior of antiplane shear cracks. The crack opening displacements for several biomaterial systems have been calculated. In these systems, the crack opening displacements are found to be insensitive to the variation of plate thickness. However, they are strongly affected by the relative magnitude of elastic constants of the component phases. This is demonstrated in several diagrams.

The problem of diffraction of normally incident longitudinal and antiplane shear waves by two parallel and coplanar rigid strips embedded in an infinite, isotropic and homogeneous elastic medium is solved. Approximate formulas are derived for the displacement field, stress tensor, far-field amplitudes and the scattering cross section when the wave lengths are large compared to the distance between the outer edges of the two strips. The limiting results for the corresponding problem of a single strip are also derived and are presented here for the first time.

Hydrogen embrittlement is shown to occur very easily in notched-round bars under opening modeI (tension) but not under antiplane shear modeIII (torsion). The stress tensor invariants under modeI,II, andIII loadings and how these affect interstitial diffusion are discussed. It is suggested that long range diffusion of hydrogen down orthogonal trajectories to the vicinity of the crack tip, which can occur under modeI but not modeIII, is a key part of any hydrogen embrittlement mechanism. This premise was evaluated with AISI 4340 steel heat treated to ultrahigh strength levels. It was found that an initial modeI stress intensity level of 17,000 psi-in.1/2 produced failure in several minutes. ModeIII stress intensity levels three times this produced no crack initiation in 300 min. Further analysis of the time-dependent hydrogen concentrating effect utilized a stress wave emission technique. This produced plausible critical hydrogen concentrations even though the present elastic analysis is a first order approximation of the stress field.

A dynamic crack problem with finite crack length subject to antiplane shear is solved. The medium is viscoelastic in shear and the two tips are allowed to extend as arbitrary functions of time; hence it represents a more realistic physical condition. On the other hand, the solution is interesting in itself because of the lack of the elastic-viscoelastic correspondence principle. The solution is obtained from a system of recursive Abel's integral equations which are derived from an integral representation, slightly different from Poisson's formula for the wave equation.

The scattering of polarized harmonic shear waves by a sharp crack of finite length under antiplane strain is considered. Use is made of integral transforms, which reduce the problem to the evaluation of a system of coupled integral equations. Special emphasis is placed on obtaining the detailed structure of the crack‐front stress and displacement fields, which control the instability behavior of cracks in brittle materials. While the dynamic stresses around the singular crack point are found to be qualitatively the same as those encountered under statical loading, they differ quantitatively in that the intensity of the dynamical stress field, which may be regarded as a measure of the force tending to cause crack propagation, depends on the incident wavelength. At certain wavelengths, this intensification is shown to be larger than the static case. The method of solution in this paper applies equally well to boundary value problems in electromagnetic and acoustic theory.

A perturbation theory of antiplane elastic-plastic deformations is presented based on a total or deformation theory of plasticity. A complete formal solution is given. A circular hole in a body under uniform antiplane shear is considered for illustration purposes.

Double-ended dislocation pileups and the three modes of cracks at a bimaterial interface have been studied. The elastic field of the cracks are represented by that of a continuous distribution of infinitesimal dislocations. Analytical solutions are obtained for antiplane shear cracks. It is found that the stress intensity at the tip of a double-ended screw dislocation pileup is smaller than that of a single-ended pileup by the factor of (1—a) wherea = (2/π) sin-1√(l-k)/2 andk = (G2-G1)/(G2 + G1). G2 and G1 are the shear moduli of the two constituent phases. Numerical techniques are used to discuss double-ended edge dislocation pileups and tensile and in-plane shear cracks. The crack opening displacements for various bimaterial systems have been determined.

The problem of the diffraction of normally indicent longitudinal and antiplane shear waves on a Griffith crack located in an infinite, isotropic elastic medium is considered. A Fredholm integral equation of the second kind is derived in each case for the determination of diffracted field. From the integral equation an asymptotic development of the solution is obtained which is valid for wavelength long compared to the crack length. For wavelengths comparable with the size of the crack the integral equation is solved numerically. The stress and the displacement fields in the vicinity of the crack as well as the radiation field at points far away from the crack are computed for a range of values of the frequency.

The problem of diffraction of normally incident longitudinal and antiplane shear waves by two parallel and coplanar Griffith cracks embedded in an infinite, isotropic and homogeneous elastic medium is solved. Approximate formulas are derived for the displacement field, stress tensor, stress intensity factors, farfield amplitudes and scattering cross section when the wave lengths are large compared to the distance between the outer edges of the two cracks. By taking appropriate limits we derive various interesting and new results. Furthermore, we derive the solution of the corresponding problem of diffraction of a plane acoustic wave by two rigid coplanar and parallel strips.

The two dimensional problem of the diffraction of normally incident compressional and antiplane shear waves by a Griffith crack in an infinite isotropic elastic medium is considered. For wavelengths long compared to the crack length, the stress intensity factors as well as the maximum crack openings are expressed in series of ascending powers of the normalized wave number. The approximate solutions are compared with exact solutions obtained in a previous paper[1], for a Poisson's solid. The results indicate that a five term expansion of each of the series solutions is sufficiently accurate for most problems of practical interest.

The self-consistent model is used to derive an expression for the effective longitudinal shear modulus of a unidirectional filamentary composite reinforced with curvilinear fibers. It is found that shaped fibers result in a higher effective shear modulus than circular ones. Furthermore, the antiplane shear problem for an elastic curvilinear inclusion is solved.

If an obstacle exists in the vicinity of the free surface of a half‐space and a stress field is applied in such a manner that dislocations are pushed towards the obstacle, an array of dislocations then piles up into an equilibrium distribution against the obstacle. The distributions of dislocations are obtained by the Wiener‐Hopf technique for the edge and screw dislocations. The total strength of dislocations (Burgers vector multiplied by the number of dislocations) distributed in the distance L is calculated as 0.92π(1−v)σAL/G for edge dislocations and 2σAL/G for screw dislocations, where G, v are the shear modulus and Poisson ratio respectively and σA is the applied stress. The result can be applied to crack problems. The above two numbers for the total strength of dislocations give the crack openings at the free surface for the extensional mode and the antiplane shear mode of fracture, respectively.

A rigid rectangular foundation, embedded at an arbitrary depth below the surface of an elastic half space is subjected to a plane, transient SH-wave. The Laplace and Kantorovich-Lebedev transforms are applied to derive the equation of motion for the foundation during the initial time period required for an SH-wave to traverse the base width. The peak impulse response is found to occur during this time and the response there-after appears to be valid based on a comparison with the known, long-time limit. Consequently, the results presented here can be convolved with an earthquake accelerogram to yield an accurate foundation earthquake response.

The extension of a crack formed by cutting at a high velocity into the surface of an elastic solid is investigated. The solid is assumed to be in a state of uniform antiplane shear before the cut is induced. The anti-plane wave motion which is generated by the cutting process is analyzed through a Green's function technique. This technique leads to an integral equation for the stress in the plane of the crack. The stress intensity and velocity intensity functions are obtained, and the propagation of the crack after the cutting process has been terminated is analyzed by means of the balance-of-rates-of-energy criterion. It is shown that the proclivity towards propagation beyond the length of the cut-induced crack shows a significant dependence on the speed of cutting.

The continuous distribution of screw dislocations for a single‐layered double‐ended pileup in a soft lamella embedded between two rigid phases is studied. Explicit expressions are obtained for the distribution function, the number of dislocations, the relative displacement, and the strain energy. The stress concentration at the tips is calculated by using Moutier's theorem. When compared with a similar case in a homogeneous medium under the same stress, all these quantities are smaller by about 30%. The present solution is applicable also to the case of a slit crack under an antiplane shear stress.

Symmetry considerations are of no use for the reflection of more general types of wave motions, except if the physically less realistic mixed conditions are assumed to hold at the reflecting surface. Consequently, it is rather complicated to determine the transient wave motion in simple waveguides such as layers and rods where a myriad of reflections take place. This chapter explains the transient waves in a layer and a rod. It presents an analysis of two-dimensional antiplane shear motions in a layer. For shear waves, the expressions for the field variables, which are simple in form, provide some interesting insights in the forced motions of waveguides. The chapter further reviews the more complicated cases of wave motions in plane strain in a layer and axially symmetric wave motions in a rod. The dynamic response of the layer can be computed from the response of an unbounded medium by invoking symmetry considerations.

The problem of a semi-infinite crack suddenly arising in a loaded strip of finite width and then propagating with a constant velocity is considered. The analysis is carried out within the realm of the classical theory of elasticity and a state of antiplane shear is assumed. By using integral transform methods the problem is reduced to an equation of the Wiener—Hopf type, which can be solved by a standard technique involving the infinite product theory. In order to determine the stress state in the vicinity of the crack tip, i.e. the stress intensity factor, asymptotic expansions are employed. The time-dependence of this quantity is calculated numerically and exposed in diagrams. The influence of various parameters is discussed and it is shown that the stress intensity factor oscillates with a decreasing amplitude and tends to a steady-state value.