Determination of Mechanics Properties of a Piezoelectric Material Using Indentation Method with a Cylindrical Indenter

2011 ◽  
Vol 335-336 ◽  
pp. 1014-1020 ◽  
Author(s):  
Bin Zhao
Keyword(s):  
Piezoelectric Materials ◽  
Contact Stiffness ◽  
Transversely Isotropic ◽  
Indentation Load ◽  
The Finite Element Method ◽  
Poling Direction ◽  
Piezoelectric Effects ◽  
Piezoelectric Strain ◽  
Piezoelectric Solids

The Finite Element Method (FEM) was used for axisymmetric indentation to investigate mechanics properties of piezoelectric solids (PZT-5H). Since piezoelectric materials are usually treated as transversely isotropic elastic materials, a simple linear relationship between indentation load P and indentation displacement h was presented under a cylindrical indenter. Three different cases (uncouple mechanical case, poled substrate-insulating indenter and poled substrate-conducting indenter) were taken into consideration to study indentation responses. The results showed that polarization could more easily damage the poled substrate than the uncoupled case. At the same displacement the highest indentation load existed in the poled/insulating case and the lowest one was in the uncoupled case because of the polarization influence. Electric potential distributions were given to study the direct piezoelectric effects and the electromechanical phenomena. In addition elastic modulus, contact stiffness, and piezoelectric strain constant were calculated directly through the use of the FEM. The determination of the poling direction is another use for the indentation technique, and the discussion of indentation size effect shows that a bigger indenter is followed by a larger indentation load.

scholarly journals Dynamic Analysis of a Rod Vibro-Impact System with Intermediate Supports

2018 ◽  
Vol 12 (2) ◽  
pp. 127-134 ◽  
Author(s):  
Volodymyr Gursky ◽  
Igor Kuzio
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Strain State ◽  
Natural Frequencies ◽  
Contact Stiffness ◽  
Free Oscillations ◽  
The Finite Element Method ◽  
Rod System ◽  
Design Diagram

Abstract The two-mass resonant vibro-impact module is presented as the rod system with cylindrical intermediate supports. The corresponding design diagram is constructed. Based on the finite element method, the frequency of free oscillations is defined for the corresponding location of the intermediate supports. A stress-strain state of the elastic element is considered. The stiffness of the intermediate supports is defined by solving the contact problem between the cylindrical rod supports and the flat spring. The dynamics of the vibro-impact rod system with multiple natural frequencies is analyzed taking into account the contact stiffness of the intermediate supports. The determination of contact and equivalent stresses occurring during the operation of the vibro-impact rod system is performed.

Indentation of Piezoelectric Ceramics: Theory, Experiments and Applications

1999 ◽  
Vol 604 ◽  
Author(s):  
Subra Suresh ◽  
Antonios E. Giannakopoulos ◽  
S. Sridhar ◽  
U. Ramamurty
Keyword(s):  
Piezoelectric Materials ◽  
Indentation Load ◽  
Electrical Measurements ◽  
Depth Sensing ◽  
Depth Of Penetration ◽  
Electrical Boundary Conditions ◽  
Theoretical Predictions ◽  
Characterization Of Properties ◽  
Piezoelectric Solids

AbstractA new method is proposed for the characterization of properties of piezoelectric materials using depth-sensing indentation involving both mechanical and electrical measurements. First, a rigorous general theory is presented for axisymmetric indentation of piezoelectric solids with anisotropic properties. The theoretical results facilitate the prediction of the indentation load versus the depth of penetration of indenter into the substrate, as well as some transient electrical effects for different electrical boundary conditions. Used in conjunction with instrumented indentation experiments at the nanoscopic, microscopic or macroscopic size scales, these results lead to the prediction of some of the elastic, dielectric and piezoelectric constants as well as the activation energy for depolarization. The predictions of the theory as well as the validity of the approach have been substantiated further with detailed indentation experiments on PZT-4 and barium titanate using either a conducting indenter or an insulated indenter. The theoretical predictions of the coupled electrical-mechanical indentation of piezoelectric solids have also been checked with finite element analyses. The implications of the proposed method for the design and characterization of piezoelectric materials and for quality control in commercial production are also addressed.

scholarly journals Exploitation of Nanoindentation and Statistical Tools to Investigate the Behavior of Materials

2016 ◽  
Vol 6 (4) ◽  
pp. 1089-1092
Author(s):  
L. Aminallah ◽  
S. Habibi
Keyword(s):  
Polynomial Regression ◽  
Contact Stiffness ◽  
Characteristic Curve ◽  
Indentation Test ◽  
Statistical Processing ◽  
Indentation Load ◽  
Contact Depth ◽  
Characterization Of Materials

The determination of the performance of materials requires the characterization of materials at scales: macro, micro and nanoscale. Among the most common experimental methods one can find the instrumented indentation test for determining the contact stiffness and contact depth and analyzing the characteristic curve by nanoindentation load on the penetration of the indentor. Through statistical processing of the experimental results, the rigidity of contact on the contact depth is investigated, depending on the indentation load, for bronze, brass and copper. A mathematical model is adopted to describe the polynomial regression by the method of least squares growth rigidity with one or more geometric parameters representative of the size of the footprint. This study allows us to identify factors that influence the rigidity of the materials examined and the sensitivity of the used indenters.

scholarly journals Indentation Modulus, Indentation Work and Creep of Metals and Alloys at the Macro-Scale Level: Experimental Insights into the Use of a Primary Vickers Hardness Standard Machine

Materials ◽  
2021 ◽  
Vol 14 (11) ◽  
pp. 2912
Author(s):  
Alessandro Schiavi ◽  
Claudio Origlia ◽  
Alessandro Germak ◽  
Andrea Prato ◽  
Gianfranco Genta
Keyword(s):  
Contact Stiffness ◽  
Calculation Model ◽  
Indentation Load ◽  
Indentation Creep ◽  
Indentation Modulus ◽  
Indentation Curve ◽  
Metrological Research ◽  
Macro Scale ◽  
Applied Forces

In this work, the experimental method and the calculation model for the determination of indentation moduli, indentation work, and indentation creep of metallic materials, by means of macroscale-level forces provided by a primary hardness standard machine at the National Institute of Metrological Research (INRIM) at the at room temperature were described. Indentation moduli were accurately determined from measurements of indentation load, displacement, contact stiffness and hardness indentation imaging and from the slope of the indentation unloading curve by applying the Doerner-Nix linear model; indentation work, representing the mechanical work spent during the force application of the indentation procedure, was determined by calculating the areas under the loading–unloading indentation curve, through fitting experimental data with a polynomial law. Measurements were performed with a pyramidal indenter (Vickers test). The applied force was provided by a deadweight machine, and the related displacement was measured by a laser interferometric system. Applied forces and the occurring indentation depths were simultaneously measured: the resulting loading–unloading indentation curve was achieved. Illustrative tests were performed on metals and alloy samples. Discussion and comments on the suitability of the proposed method and analysis were reported.

Macrocrack-Microcrack Interaction in Piezoelectric Materials, Part I: Basic Formulations and J-Analysis

1999 ◽  
Vol 66 (2) ◽  
pp. 514-521 ◽  
Author(s):  
Y.-H. Chen ◽  
J.-J. Han
Keyword(s):  
Piezoelectric Materials ◽  
Process Zone ◽  
Electric Displacement ◽  
Transversely Isotropic ◽  
Numerical Results ◽  
Fredholm Integral Equations ◽  
Electric Displacement Intensity Factor ◽  
Poling Direction ◽  
Microcrack Interaction ◽  
Interaction Problem

The macrocrack-microcrack interaction problem in transversely isotropic piezoelectric materials is studied. The microcracks near a macrocrack tip in the process zone are assumed to be parallel to the latter, while the poling direction of the piezoelectric materials is assumed to be perpendicular to the cracks. Three kinds of elementary solutions with different crack configurations and under different loading conditions are given, from which the interaction problem is reduced to a system of Fredholm integral equations by using the pseudo-traction electric displacement method (abbreviated PTED). After the equations are solved numerically, the traditional mode I and mode II stress intensity factors and the electric displacement intensity factor are evaluated. In order to confirm the proposed method as well as the numerical results, a consistency check is proposed which is based on the J-integral analysis and provides a powerful tool to examine the numerical results. Thus, any mistakes are avoided since they would certainly lead to unsatisfied numerical results contrary to the check. It is concluded also that the disturbance of the near-tip electric field provides another source of shielding.

scholarly journals Determination of Transverse Shear Stiffness of Sandwich Panels with a Corrugated Core by Numerical Homogenization

Materials ◽  
2021 ◽  
Vol 14 (8) ◽  
pp. 1976
Author(s):  
Tomasz Garbowski ◽  
Tomasz Gajewski
Keyword(s):  
Transverse Shear ◽  
Shear Stiffness ◽  
The Finite Element Method ◽  
Homogenization Procedure ◽  
Plate Structures ◽  
Corrugated Board ◽  
Energy Equivalence ◽  
The Stability ◽  
Global Stiffness Matrix

Knowing the material properties of individual layers of the corrugated plate structures and the geometry of its cross-section, the effective material parameters of the equivalent plate can be calculated. This can be problematic, especially if the transverse shear stiffness is also necessary for the correct description of the equivalent plate performance. In this work, the method proposed by Biancolini is extended to include the possibility of determining, apart from the tensile and flexural stiffnesses, also the transverse shear stiffness of the homogenized corrugated board. The method is based on the strain energy equivalence between the full numerical 3D model of the corrugated board and its Reissner-Mindlin flat plate representation. Shell finite elements were used in this study to accurately reflect the geometry of the corrugated board. In the method presented here, the finite element method is only used to compose the initial global stiffness matrix, which is then condensed and directly used in the homogenization procedure. The stability of the proposed method was tested for different variants of the selected representative volume elements. The obtained results are consistent with other technique already presented in the literature.

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