Kuldeep Sharma

Numerical simulation of crack propagation under fatigue loading in piezoelectric material using extended finite element method

Piezoelectric materials due to their electromechanical coupling characteristics are being widely used in actuators, sensor, transducers, etc. Considering wide application it is essential to accurately predict their fatigue and fracture under applied loading conditions. The present study deals with analysis of fatigue crack growth in piezoelectric material using the extended finite element method (XFEM). A pre-cracked rectangular plate with crack at its edge and center impermeable crack-face boundary conditions is considered for simulation. Fatigue crack growth is simulated using extended finite element method under plane strain condition and mechanical, combined (mechanical and electrical) cyclic loading. Stress intensity factors for mechanical and combined (mechanical and electrical cyclic loadings) have been evaluated by interaction integral approach using the asymptotic crack tip fields. Crack propagation criteria have been applied to predict propagation and finally the failure.

X-FEM Studies on an Inclined Crack in a 2-D Finite Piezoelectric Media

An inclined crack problem is investigated for a poled finite two-dimensional piezoelectric plate using X-FEM. Intensity factors and energy release rate make the subject matter of investigations. The parametric studies for these are presented with respect to angle of inclination and length of the crack, and electromechanical loadings. It is noted that mechanical intensity factors are independent of electric loading while electric displacement intensity factor depends on electromechanical loading. The study shows that local energy release rate may be considered as a fracture criteria for 2-D piezoelectric media.

Numerical Solution of an Edge Cracked 2-D Piezoelectric Media Using Extended Finite Element Method

The numerical solution for an edge crack problem in a two-dimensional (2-D) finite piezoelectric media has been discussed using extended finite element method. The four-fold standard enrichment functions are taken in conjugation with the interaction integral to evaluate the intensity factors (IFs). The intensity factors as well as the mechanical energy release rate and the total energy release rate has been analyzed for different electro-mechanical boundary conditions. It is observed that the IFs results are coupled and contrary to analytic solution which shows uncoupled behaviour.

Numerical prediction of plastic zone length in straight edge cracked plate using XFEM

This Paper combines the Dugdale’s Approach with Extended finite element method (XFEM) in order to estimate the Plastic zone length (PZL) for a straight edge cracked plate (SECP) under uniaxial tensile loading condition. Dugdale utilized a different approach to evaluate the PZL by nullifying the effect of singularity at the tip of the virtually extended crack by the applying a uniform pressure which is equal to the yielding stress. XFEM is utilized for analyzing SECP as it is more efficient and accurate as compared to other conventional numerical tools. In XFEM, crack can be extended without any re-meshing because elements near crack interface need not to conform the crack geometry.PZL for SECP is evaluated for crack length, a, varying in the range of 0.01 to 0.05 (m) in steps of 0.01 and load intensity (σ0/Y) ranging from 0.1 to 0.5 in steps of 0.1. Crack Position (h/H) is also varied ranging from 0 to 0.8 in step of 0.2 in order to analyse its effect on PZL. MATLAB is employed for Extended Finite element analysis of SECP under Plane stress condition. Four node Quadrilateral elementsare used for extended finite element analysis. The numerical results are validated by the experimental results from the available literature.This Paper combines the Dugdale’s Approach with Extended finite element method (XFEM) in order to estimate the Plastic zone length (PZL) for a straight edge cracked plate (SECP) under uniaxial tensile loading condition. Dugdale utilized a different approach to evaluate the PZL by nullifying the effect of singularity at the tip of the virtually extended crack by the applying a uniform pressure which is equal to the yielding stress. XFEM is utilized for analyzing SECP as it is more efficient and accurate as compared to other conventional numerical tools. In XFEM, crack can be extended without any re-meshing because elements near crack interface need not to conform the crack geometry.PZL for SECP is evaluated for crack length, a, varying in the range of 0.01 to 0.05 (m) in steps of 0.01 and load intensity (σ0/Y) ranging from 0.1 to 0.5 in steps of 0.1. Crack Position (h/H) is also varied ranging from 0 to 0.8 in step of 0.2 in order to analyse its effect on PZL. MATLAB is employed for Extended Finite element...

Numerical Studies of Some Modified Polarization Saturation Models in 2-D Semipermeable Piezoelectric Media Using Distributed Dislocation Method

In this paper, some modified polarization saturation models are proposed and studied numerically in 2-D semipermeable piezoelectric media using distributed dislocation technique (DDT). The polarization saturation (PS) model is modified here by varying the saturated condition imposed on the electrically saturated strip, i.e. a constant saturated condition to linear, quadratic and cubic varying electric displacement saturated condition. Numerical studies for these proposed models are simulated by considering their equivalent forms based on the principle of superposition. A centre-cracked problem in 2-D semipermeable piezoelectric media under arbitrary poling direction and in-plane electromechanical loadings is considered for these analyzes. To validate the developed numerical codes and iterative numerical approach for finding the unknown saturated zone length, the obtained results for PS model are compared with the analytical results available in literature. Thereafter, the results are presented for modified PS models, they show the effect of variation in saturation condition on saturated zone length, critical applied electric displacement loading and crack opening potential (COP), whereas no significant effect has been observed on local intensity factor (LIF) and crack opening displacement (COD). Further, saturated zone length increases with respect to increase in degree of variation of saturation condition, i.e. from constant to cubic. Moreover, the variation shows the effect on implication of applied electric loading and defines the critical applied electric loading corresponding to each model. It is observed that the critical value of applied electric loading significantly decreases with the increase in degree of variation of saturation condition. Here, a significant effect of poling direction is also found in all the parameters such as saturated zone length, LIF, COD and COP.

Griffith's crack in a 2-D piezoelectric domain with an arbitrary polarization direction: Analytical/X-FEM solution

The analytic solution for Griffiths crack in an infinite 2-D piezoelectric domain is obtained for arbitrary polarization direction. The analytical approach considered here is simple and different from the existing methodology (where the solutions are firstly obtained for an elliptical void and then degenerated to Griffiths crack solution). The obtained results have shown that intensity factors (IFs) are independent of the polarization direction for Griffiths crack in an infinite 2-D piezoelectric domain. The solution for a polarization perpendicular to the crack is also obtained and validated with existing results. The results of IFs are also obtained numerically using extended finite element method (X-FEM). It is observed that IFs for a finite specimen is polarization direction dependent.