A new method for predicting multi-crack fracture mechanism in the finite plate of red sandstone

Abstract

A novel theoretical approach was put forth to forecast multi-crack propagation trajectories in a finite plate. First, a weighted residual approach and complex function are used to create the formula for computing the maximum (stress intensity factor) SIF of multi-crack in the finite plate. And then, three cracks were then chosen as a model for computation to determine how the plate size affects the SIF. The formula of multi-branch crack in finite plate is derived and the crack initiation and propagation criterion of multi-crack in finite plate was established. Finally, the propagation paths of three cracked red sandstone in a finite plate were predicted and verified by the uniaxial compression test. It demonstrates that the SIF of multiple cracks in a finite plate is consistently larger than that of an infinite plate. Under the uniaxial compression test, the first crack initiation point is often A2 or B2, and each specimen’s first crack initiation time increases and subsequently reduces when the relative horizontal spacing (Ds’) of cracks varies. The crack initiation stress increases and the unstable stress first increases and then decreases with Ds’. The total crack extension length initially goes down and then goes up. All of the fracture initiation and propagation mechanisms are Mode I. The effectiveness of the multi-crack propagation theory in finite plates is established by the good agreement between predicted and test findings.