Delayed Fracture of the Piezoelectric Ceramics Under Electric Fields in Three-Point Bending

2007 ◽  
Author(s):  
Fumio Narita ◽  
Yasuhide Shindo ◽  
Mitsuru Hirama
Keyword(s):  
Energy Release Rate ◽  
Energy Release ◽  
Electric Fields ◽  
Lead Zirconate Titanate ◽  
Release Rate ◽  
Open Crack ◽  
Element Analysis ◽  
Delayed Fracture ◽  
Pzt Ceramics ◽  
Dc Electric Fields

This paper investigates experimentally and analytically the delayed fracture in lead zirconate titanate (PZT) ceramics under electromechanical loading. Delayed fracture tests were conducted on single-edge precracked-beam specimens, and time-to-failure and fracture load under different DC electric fields were obtained. Possible mechanisms for delayed fracture were also discussed by scanning electron microscope (SEM) examination of the fracture surface of the PZT ceramics. Further, a nonlinear finite element analysis was employed to calculate the energy release rate for the permeable, impermeable and open crack models, and the effects of applied DC electric fields and localized polarization switching on the energy release rate are examined.

Fracture Properties of Surface Modification Layers Via a Modified Bi-Layer Beam Model

2018 ◽  
Vol 35 (4) ◽  
pp. 499-511
Author(s):  
H. T. Liu ◽  
M. H. Zhao ◽  
J. W. Zhang
Keyword(s):  
Residual Stress ◽  
Surface Modification ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Fracture Process ◽  
Beam Model ◽  
Element Analysis ◽  
Fracture Properties ◽  
Proposed Model

ABSTRACTA modified bi-layer beam model is proposed to study the fracture-dominated scratch process of the brittle material with surface modification layer considering residual stress. The nonlinear analytical solution of the energy release rate is derived considering the graded distribution of the elastic modulus and residual stress. Finite element analysis is also conducted. Both analytical and numerical results show that the graded distribution of the material properties and residual stress plays an important role in the fracture process. Based on the inverse analysis, the proposed model could provide a convenient way to determine the energy release rate of materials possessing a surface modification layer.

scholarly journals Shear and foundation effects on crack root rotation and mode-mixity in moment- and force-loaded single cantilever beam sandwich specimen

2018 ◽  
Vol 52 (18) ◽  
pp. 2537-2547 ◽  
Author(s):  
Vishnu Saseendran ◽  
Leif A Carlsson ◽  
Christian Berggreen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Cantilever Beam ◽  
Release Rate ◽  
Beam Specimen ◽  
Mode Mixity ◽  
Element Analysis ◽  
Fracture Specimens

Foundation effects play a crucial role in sandwich fracture specimens with a soft core. Accurate estimation of deformation characteristics at the crack front is vital in understanding compliance, energy release rate and mode-mixity in fracture test specimens. Beam on elastic foundation analysis of moment- and force-loaded single cantilever beam sandwich fracture specimens is presented here. In addition, finite element analysis of the single cantilever beam specimen is conducted to determine displacements, rotations, energy release rate and mode-mixity. Based on finite element analysis, a foundation modulus is proposed that closely agrees with the numerical compliance and energy release rate results for all cases considered. An analytical expression for crack root rotation of the loaded upper face sheet provides consistent results for both loading configurations. For the force-loaded single cantilever beam specimen (in contrast to the moment-loaded case), it was found that the crack length normalized energy release rate and the mode-mixity phase angle increase strongly as the crack length decreases, a result of increased dominance of shear loading.

Measurement of the Total Energy Release Rate for Cracks in PZT Under Combined Mechanical and Electrical Loading

2007 ◽  
Vol 74 (6) ◽  
pp. 1197-1211 ◽  
Author(s):  
H. Jelitto ◽  
F. Felten ◽  
M. V. Swain ◽  
H. Balke ◽  
G. A. Schneider
Keyword(s):  
Total Energy ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Electric Fields ◽  
Release Rate ◽  
Total Energy Release ◽  
Custom Made ◽  
Poling Direction ◽  
Total Energy Release Rate

Four-point-bending V-notched specimens of lead zirconate titanate (PZT) poled parallel to the long axis are fractured under conditions of controlled crack growth in a custom-made device. In addition to the mechanical loading electric fields, up to 500V∕mm are applied parallel and anti-parallel to the poling direction, i.e., perpendicular to the crack surface. To determine the different contributions to the total energy release rate, the mechanical and the piezoelectric compliance, as well as the electrical capacitance of the sample, are recorded continuously using small signal modulation/demodulation techniques. This allows for the calculation of the mechanical, the piezoelectric, and the electrical part of the total energy release rate due to linear processes. The sum of these linear contributions during controlled crack growth is attributed to the intrinsic toughness of the material. The nonlinear part of the total energy release rate is mostly associated to domain switching leading to a switching zone around the crack tip. The measured force-displacement curve, together with the modulation technique, enables us to determine this mechanical nonlinear contribution to the overall toughness of PZT. The intrinsic material toughness is only slightly dependent on the applied electric field (10% effect), which can be explained by screening charges or electrical breakdown in the crack interior. The part of the toughness due to inelastic processes increases from negative to positive electric fields by up to 100%. For the corresponding nonlinear electric energy change during crack growth, only a rough estimate is performed.

An Application of Finite Element-Based Fracture Mechanics Analysis to Cord-Rubber Structures

1996 ◽  
Vol 24 (3) ◽  
pp. 220-235 ◽  
Author(s):  
T. G. Ebbott
Keyword(s):  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Crack Growth ◽  
Release Rate ◽  
Fatigue Behavior ◽  
Internal Crack ◽  
Materials Testing ◽  
Element Analysis ◽  
Rate Evaluation

Abstract A finite element-based method to analyze the severity of internal cracks in cord-rubber structures is presented. The method includes materials testing to characterize rubber fatigue behavior, a global-local finite element analysis to provide the detail necessary to model explicitly an internal crack, and use of the J-integral and virtual crack closure techniques for energy release rate evaluation. Analysis of the multiaxial and cyclic fracture situation is carried out by considering the cycle of each mode of fracture separately and then combining the effect of each mode to determine the total effect. Crack growth rates in the structure are assumed to be the same as the crack growth rate in a laboratory specimen at the same level of cyclic energy release rate. Results are presented for a material change in a critical tire region.

scholarly journals Finite Element Analysis for Interfacial Crack in Piezoelectric Composite under Impact Loading

2012 ◽  
Vol 21 (1) ◽  
pp. 096369351202100
Author(s):  
Liang Wang ◽  
Rui-Xiang Bai ◽  
Hao-Ran Chen
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Energy Release Rate ◽  
Energy Release ◽  
Release Rate ◽  
Impact Loading ◽  
Crack Surface ◽  
Piezoelectric Composite ◽  
Element Analysis ◽  
Piezoelectric Composites

In this paper, a nonlinear finite element analysis of impact interfacial fracture for a piezoelectric composite is provided. The Newmark method was used to solve the dynamics equation. Virtual crack closure technique is to evaluate the energy release rate of crack tip. Contact elements were set up on crack surface and in the area in contact under impact loading to prevent the penetration between PZT and composite. The response curves of the energy release rate are obtained for piezoelectric composites. Numerical results are provided to show the effect of the piezoelectricity, the applied voltage, the stack sequence of composites and the contact of crack surface on the resulting dynamic energy release rate of piezoelectric composites.

Stress and Electric Fields in a Rectangular Piezoelectric Body with a Center Crack under Anti-Plane Shear Loading

2004 ◽  
Vol 261-263 ◽  
pp. 99-104
Author(s):  
Shu Hong Liu ◽  
Z.Z. Zou ◽  
B.Q. Xu ◽  
Han Yun Li
Keyword(s):  
Electric Field ◽  
Energy Release Rate ◽  
Energy Release ◽  
Electric Fields ◽  
Release Rate ◽  
Crack Tip ◽  
Shear Loading ◽  
Crack Face ◽  
Piezoelectric Body ◽  
Center Crack

The problem involving a center crack in a rectangular piezoelectric body under anti-plane mechanical shear loading and plane electrical loading is analyzed for the permeable crack face conditions. The so-called general solutions of stress and electric fields are obtained, which is satisfied both the governing equations of anti-plane problems and the boundary conditions of the crack face. It is shown that electric field is nonsingular near right crack tip, while strain, stress and electric displacement have crack-tip singular behavior, the energy release rate has the same form as that without the electromechanical interaction, which is always positive. At last, the boundary collocation method is used to calculate the energy release rate. Numerical values are obtained to show the influence of the material properties and the electric field. The results show that the method of half analytical and half numeral is simple, accurate and widely applicable.

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