Modeling approach to evaluating reduction in stress intensity factor in center-cracked plate with piezoelectric actuator patches

Abstract

Active repairs using piezoelectric actuators can play a significant role in reducing the crack damage propagation in thin plate structures. Mode-I crack opening displacement is the most predominant one in tension, and it is responsible for the failure which in turn affects the load carrying capability of the cracked structure. In addition, there are limited studies that investigated the effect of the piezoelectric actuator over mode-I active repair. In this study, the mode-I stress intensity factor for a plate with a center crack, and a bonded piezoelectric actuator was modeled using the linear elastic fracture mechanics. For this, an analytical closed-form solution is developed using the virtual crack closure technique taking into account mode-I as the only effective mode, coupling effects of the piezoelectric patch, and the singular stress at the crack tip. In addition, the total stress intensity factor was obtained by the superposition of the stress intensity factor obtained from the stresses produced by the piezoelectric actuators on the crack surfaces as the only external loads on the cracked plate and the stress intensity factor due to the far-field tension load. The proposed analytical model for mode-I stress intensity factor was verified by a finite element–based approach using ANSYS finite element software. The results demonstrated a good agreement between the analytical and finite element models with a relative error of less than 4% in all the cases studied. The results illustrated that the piezoelectric patch is efficient in reducing stress intensity factor when an extension mode of the actuator is applied. However, applying a contraction mode of the piezoelectric actuators produced negative strain which increased the stress intensity factor and thus the severity of the cracked structure and could lead to damage propagation.

Evaluating the Reduction of Stress Intensity Factor in Center-Cracked Plates Using Piezoelectric Actuators

“…In fact, the compression stress generated by the piezoelectric actuator counteracted the external loading and resulted in SIF mitigations. The finite element model was validated with the theoretical results through two phases: validation of SIF in cracked plate without piezoelectric patch and validation of the displacement of the piezoelectric actuator operating in extension mode with a certain electric voltage [23]. Furthermore, making specimens with center crack has its own certain limitation, i.e., creating centered cracks in metals.…”

“…In the active repair of a cracked structure, the main objective is to decrease the singular stress at Furthermore, previous works had proved that the thickness ratio and stiffness ratio of piezoelectric patches and host plate have an effect on the reduction of stress intensity factor. Indeed, Abuzaid et al [23] showed that to achieve the best result in reduction in the SIF, it is better to use a thin actuator with relatively high voltage. Fesharaki et al [33] compared the capability of the piezoelectric actuators with different stiffness/thickness ratios in reducing the stress concentration factor in a plate with a hole.…”

“…An investigation to study the influence of adhesive properties on active repair under Mode-I fracture [22] showed that a higher adhesive shear modulus is desired for repairing cracks, as it allows the transfer of the stress induced by the piezoelectric actuator to the host structure. Recently, Abuzaid et al [23] studied mode I active repair using a piezoelectric actuator. The authors developed an analytical closed-form solution using the virtual crack closure technique, coupling effects of the piezoelectric patch, and singular stress at the crack tip of a center cracked plate.…”

“…First, the stress intensity factor (SIF) for the center-cracked plate due only to the piezoelectric actuation is analytically modeled. Compared to the previous work [23] which was based on the energy release rate to derive the analytical SIF for the center crack plate, the current work uses the weight functions approach to derive the analytical SIF for the center crack plate. In the second step, the solution is found for the center-cracked plate due to external loading from known linear elastic fracture mechanics.…”

Investigation of crack repair using piezoelectric material under thermo-mechanical loading

“…In this work, the lifecycle improvement has been achieved in active mode repair. In d 31 -mode, the effectiveness of active repair is measured in terms of stress intensity factor (SIF) (Abuzaid et al, 2017). It is evaluated by analytical and finite element modelling of a repaired finite plate under mechanical loading.…”