Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under
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TECHNICAL ARTICLE—PEER-REVIEWED
Analytical and Numerical Solution of the Stress Field and the Dynamic Stress Intensity Factors in a Cracked Plate under Sinusoidal Loading Abdessattar Aloui Æ Khemais Hamrouni Æ Tahar Fakhfakh Æ Mohamed Haddar
Submitted: 7 February 2008 / in revised form: 19 August 2008 / Published online: 17 September 2008 Ó ASM International 2008
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 KI (z,t) and KII (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. Keywords Plate Crack Dynamic loading Dynamic stress intensity factors Finite element analysis
Introduction Knowledge of the stress and deformation fields near the tip of a crack is central to the continued development of engineering fracture mechanics and is therefore important to the prevention of future failures. Many authors have developed solutions for the parallel loading problem of a plate. Several studies have investigated static and dynamic loading cases; Fedelinski et al. [1] have calculated the dynamic stress intensity factors using the quarter-point elements and path independent Jˆ-integral, while Enderlein et al. [2] have developed three methods to calculate the dynamic stress
intensity factor for the mode I loading of a stationary crack. Hosseini-Tehrani et al. [3] have presented a numerical technique for the calculation of stress intensity factors as a function of time for a coupled thermoelastic problem. Theocaris et al. [4] have used path-independent integrals around crack tips to estimate stress intensity factors at crack tips for the plane elasticity static problems. Miyazaki [5] has proposed a method based on a line-spring model to calculate the dynamic stress intensity factor of a precracked threepoint bend and a precracked four-point bend specimen. Chen [6] has used the time-dependent Lagrangian finitedifference code (HEMP) to compute the stress intensity factor for a centrally cracked rectangular bar. We are interested in the resolution of the problem of flat elastic plate supporting its own weight and subjected to a sinusoidal loading perpendicular to its plan. The goal is to determine stress field near the crack tip as well as the dynamic stress intensity factors. This plate has a crack of 2e in length, located in the middle of the plate and oriented parallel to the x axis. The dimensions of the plate are given in Fig. 1. To solve this problem, we first determined the dynamic stress field in the plate without a crack. The
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