Time-domain Boundary Integral Equation Method Research Articles

An application of the time-domain boundary integral equation method to dynamic crack propagation

Abstract An application of the time-domain boundary integral equation method (TBIEM) to the case of rapidly moving cracks in a continuum is presented. The major objective of this paper is to explore the potential of the TBIEM in solving problems in dynamic fracture where inertia effects cannot be ignored. In earlier investigations, the method proved to be accurate and efficient for stationary cracks under dynamic loading conditions. A survey of the literature indicates no attempt at applying this method to any dynamically moving crack problems. A linear superposition technique is applied to derive the solution for the case of moving cracks from that of a stationary crack under dynamic loading. Comparison of the numerical results with the exact solution for the case of a semi-infinite crack subjected to full and partial loading on the crack face shows good agreement. It is concluded that the present numerical scheme is a viable method for determining the dynamic stress intensity factors for running cracks.

Acoustic emission and near-tip elastodynamic fields of a growing penny-shaped crack

Elastodynamic fields for a growing penny-shaped crack under tension have been obtained by the time-domain boundary integral equation method. A crack of radius R1, is initially in equilibrium with a static tensile stress applied at infinity. The crack then propagates with a given rupture velocity, but stops abruptly when its radius reaches R2(> R1). Numerical results have been calculated for various values of the rupture velocity and the initial radius, R1, of the crack. Crack-opening displacements, stress intensity factors and radiated far fields are graphically presented as functions of time. The acoustic emission in terms of the radial displacement as calculated in this paper, has been compared with the usual approximation in which the acoustic emission is generated by a system of three double forces whose magnitudes are proportional to the crack-opening volume.

Dynamic fields near a collinear macrocrack-microcrack configuration under antiplane impact loading

Dynamic interaction between a macrocrack and a collinear, neighboring microcrack is investigated. The mathematical formulation presented here is two-dimensional, and for a state of antiplane strain. A time-domain boundary integral equation method is presented to calculate elastodynamic stress intensity factors generated by the incidence of stress (or displacement) pulses on single cracks and systems of two collinear cracks. As a check of the time-stepping technique presented here, numerical calculations have been carried out for pulse incidence on a single crack, and the results have been compared with those of other authors. For macrocrack-microcrack configurations the variation of the effective stress intensity factors at the tips of the macrocrack with time, with the microcrack location, and with the microcrack size will be displayed and discussed.

Time-domain boundary element analysis of dynamic near-tip fields for impact-loaded collinear cracks

Abstract A time-domain boundary integral equation method has been developed to calculate elastodynamic fields generated by the incidence of stress (or displacement) pulses on single cracks and systems of two collinear cracks. The system of boundary integral equations has been cast in a form which is amenable to solution by the boundary element method in conjunction with a time-stepping technique. Particular attention has been devoted to dynamic overshoots of the stress intensity factors. Elastodynamic stress intensity factors for pulse incidence on a single crack have been computed as function of time, and they have been compared with results of other authors. For collinear macrocrack-microcrack configurations the stress intensity factors at both tips of the macrocrack have been computed as functions of time for various values of the crack spacing and the relative size of the microcrack.

Time-domain elastodynamic scattering problems

The interaction of an ultrasonic pulse with an inhomogeneity in an elastic solid is generally analyzed by the use of the FFT over time in combination with a numerical method for the scattering problem in the frequency domain. For pulses with a high-frequency content this approach tends to be computationally intensive. In this talk the possibilities of a direct analytical time-domain approach are explored, and then there is a discussion of numerical techniques. Results are presented for a single crack (slit and penny-shaped) and for macrocrack-microcrack configurations. Some of these results have been obtained by the finite difference method. The main emphasis in this paper is, however, on the development of a time-domain boundary integral equation method. By the use of appropriate representation integrals, a system of boundary integral equations has been obtained, which has subsequently been cast in a form that is amenable to a solution by the boundary element method in conjunction with a time-stepping technique. Particular attention has been devoted to dynamic overshoots of the stress intensity factors. Elastodynamic stress intensity factors have been computed as functions of time, and they have been compared with results of other authors.

Computation of dynamic stress intensity factors by the time domain boundary integral equation method—II. Examples

Computation of dynamic stress intensity factors by the time domain boundary integral equation method—II. Examples