Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading

Abstract

A cracked plate subjected to a sinusoidal loading perpendicular to its plane is considered, and the analytical solution of the dynamic vibration behavior of a plate, which allowed the determination of the stress field near the crack tip, is developed. A mixed mode of loading near the crack tip has been established and described with dynamic stress intensity factors K I (z,t) and K II (z,t) associated with modes I and II crack openings, respectively. To validate the analytical results, a finite element analysis (FEA) of a 1 9 1 m square plate with a thickness of 1 cm, having a middle crack of 10 cm in length, is made. The results have shown significant agreement between analytical and FEA findings.

Current challenges in modelling vibrational fatigue and fracture of structures: a review

“…In many situations, the stress intensity factor (SIF) is used to predict the stress state near the crack tip [122][123][124][125]. In dynamic loading, SIF is reinstated by the dynamic stress intensity factor (DSIF) [126][127][128][129][130][131][132][133]. In thermal loading condition, several literatures [123,[134][135][136][137][138][139][140][141][142][143][144][145][146][147][148] used thermal stress intensity factor (TSIF) to determine the thermal stress state.…”

“…A formula was developed from the path-independent J-integral by taking the effect of inertia. Aloui et al [127] studied the dynamic vibration behaviour of a cracked plate subjected to sinusoidal loading and analysed the stress field and dynamic stress intensity factor. Rokach [132] numerical investigation on the accuracy in the determination of dynamic stress intensity.…”