On the computation method for the stress intensity factor of a stationary crack in mode~I under dynamic loading

A. V. Malik ; I. M. Lavit

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 54 (2018), pp. 88-102

Résumé

A method for calculating the time dependence of the stress intensity factor of a dynamic loaded body with a stationary crack in mode I is proposed. The method represents a modified method of lines developed for solving the problems of dynamic fracture mechanics. Time integration is performed using the finite difference method. The Crank–Nicolson implicit scheme is applied. Boundary problems obtained at each step of time integration are solved by the finite element method. For each time instant, the stress intensity factor is determined by the calculated value of specific energy release. For this purpose, the special cohesive finite elements ensured by the implementation of Barenblatt's postulates are used. Addition of the degrees of freedom for the mesh points arranged along the crack line enables to provide a smooth joining of the edges at the crack tip. This is equivalent to the absence of stress singularity in the tip of crack. The results of calculations are compared with those obtained by other researchers and with experimental data. A satisfactory agreement ensures the efficiency of the method applied. The latter can also be used to solve the problems of growing and branching cracks. Moreover, it admits taking into account plastic deformation.

Détail

Keywords: dynamic fracture, method of lines, cohesive finite elements.