Abstract
The dynamic propagation of a crack in an anti-plane shear deformation field is analyzed by second-order-accurate finite differences. The finite difference equations are obtained by integrating the dynamic linear elastic equations of motion along the bicharacteristic strips in four perpendicular directions and the time axis to 0(Δt 3). The singularity in stresses around the crack is calculated by performing a global energy balance on small region containing the crack tip and approximating the stresses and velocity in this region by a one term asymptotic expansion about the crack tip. Results for stresses and stress intensity factor are presented for a semi-infinite crack propagating steadily in an infinite strip, from which errors in the numerical calculations are identified. Four cases of typical non-steady crack propagation in an infinite strip following steady propagation are also considered.
Résumé
La propagation dynamique d'une fissure dans un champ de déformation de cisaillement anti-planaire est analysée en utilisant une méthode de différence finie exacte au second ordre. Les équations de différence finie sont obtenues en intégrant les équations de mouvement dynamique linéaire et élastique le long de 4 bandes caractéristiques distribuées dans 4 directions perpendiculaires et en fonction d'un axe de temps. La singularité des contraintes autour de la fissure est calculée en procédant à un équilibre global d'énergie dans les petites régions qui contiennent l'extrémité de la fissure, et en évaluant les contraintes et la vitesse dans cette région à l'aide d'une expansion asymptotique à un terme dans la zône de l'extrémité de la fissure. Les résultats obtenus pour les contraintes et le facteur d'intensité de contrainte sont présentés dans le cas d'une fissure semi-infinie qui se propage de manière stable dans une bande infinie, un cas pour lequel les erreurs des calculs numériques sont identifiées. Quatre cas de propagation typique de fissure non stable dans une bande infinie suivie d'une fissure stable sont également pris en considération.
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Burgers, P. Dynamic linear elastic crack propagation in anti-plane shear by finite differences. Int J Fract 16, 261–274 (1980). https://doi.org/10.1007/BF00013382
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DOI: https://doi.org/10.1007/BF00013382