Dynamically Loaded Branched and Intersecting Cracks

Abstract

The boundary element method (BEM) is applied to analysis of statically and dynamically loaded plates with branched and intersecting cracks. The numerical solution is obtained by discretization of external boundaries and crack surfaces using quadratic three-node boundary elements. The problem of coincident crack boundaries is solved by the dual BEM in which for nodes on crack surfaces simultaneously the displacement and the traction boundary integral equations are applied. The dynamic problem is solved by using the Laplace transform method and the solution in the time domain is computed by the Durbin numerical inversion method. The Laplace transform method gives very stable and accurate results and requires small computer memory. Static stress intensity factors (SIF) are computed by the path independent J-integral and dynamic SIF by the crack opening displacement (COD) method. Numerical examples of a branched crack in a rectangular plate and a star-shaped crack in a square plate are presented. Static SIF are compared with available results presented in literature showing good agreement. The maximum dynamic SIF are approximately two times larger than the corresponding static SIF. The influences of angles between branches of the crack and dimensions of the plate for the star-shaped crack on dynamic SIF are analyzed.

A state-of-the-art review of crack branching

“…The crack propagation speed and the SIF were calculated, showing good agreement with the experimental observations. Since then, examples for BEM simulation of crack branching have been presented in the literature [64,170,171,172,173,174,175].…”

Modelling of Guillotine Cutting of a Cold-Rolled Steel Sheet

“…During the modelling of a cutting process, the failure models [19,20,21,22,23], as well as fatigue testing [4], are quite important. The crucial issue is designing new industrial machines [24], as well as the selection of an appropriate finite element model [25,26,27,28,29,30].…”

“…For example, Xiong and Xiao [31] extended the application range of the cohesive zone model, making it suitable for concrete fracture simulation both under tension and compression. Quantifying the effects of the different materials and interaction parameters studied in their paper contributes to revealing the relationship between a meso-scale fracture and microscopic behavior of concrete, which is rather quite similar to modelling fractures in metals [20,21,22,23].…”

Modelling of the Guillotine Cutting Process by Means of a Symmetrical Blade with the Defined Geometry

“…The modelling of the cutting process would not be possible without introducing the appropriate physical model concerning the propagation of fracture. In the literature, many different such physical models are proposed [25][26][27][28][29]. Currently, the cutting productivity might be increased by changing the technology of the process passing from cutting a single metal sheet into many sheets arranged in a bundle and being cut at once.…”