EM 388F Term Paper: Discussion of Fracture Criterions under Impermeable and Permeable Crack Surface of Piezoelectric Materials RONG JIAO April 27, 2008.

Slides:



Advertisements
Similar presentations
Lecture 1. How to model: physical grounds
Advertisements

Radially Polarized Piezoelectric Transducer
ELECTROMAGNETICS AND APPLICATIONS
CHAPTER 4: FRACTURE The separation or fragmentation of a solid body into two or more parts, under the action of stresses, is called fracture. Fracture.
3 – Fracture of Materials
(Introduction to) Earthquake Energy Balance
Analytical Expressions for Deformation from an Arbitrarily Oriented Spheroid in a Half- Space U.S. Department of the Interior U.S. Geological Survey Peter.
PH0101 UNIT 2 LECTURE 31 PH0101 Unit 2 Lecture 3  Maxwell’s equations in free space  Plane electromagnetic wave equation  Characteristic impedance 
Tine Porenta Mentor: prof. dr. Slobodan Žumer Januar 2010.
ECEN5341/4341Bioelectromagnetics Spring 2015 Frank S. Barnes Contact Info: (303) ECOT 250
Maxwell’s equations constitutive relations D =  E  B =  H j =  E.
HRR Integral Recall with is the integration constant.
Model: Shear Bender.
2.5 Conductors Basic Properties of Conductors Induced Charges The Surface Charge on a Conductor; the Force on a Surface Charge
The relation between the induced charge density σ p and the polarisation, P is Where is a unit vector along the outward normal to the surface. P is along.
Fundamentals of Elasticity Theory
6.2 CTOD as yield criterion
Magnetostatics Magnetostatics is the branch of electromagnetics dealing with the effects of electric charges in steady motion (i.e, steady current or DC).
Review of Work Work Done on a Point Charge by a Point Charge
Computational Fracture Mechanics
Theory of Elasticity Theory of elasticity governs response – Symmetric stress & strain components Governing equations – Equilibrium equations (3) – Strain-displacement.
Computational Fracture Mechanics
Electrostriction Effects During Defibrillation by Michelle Fritz Oakland University SMaRT Program July 28, 2006.
EEE340Lecture Helmholtz’s Theorem Helmholtz’s Theorem: A vector field (vector point function) is determined to within an additive constant if.
3-6. Conductors in Static Electric Field
CHAP 6 FINITE ELEMENTS FOR PLANE SOLIDS
Electrical Potential Energy Chapter Electrical Potential Energy Electrical Potential Energy – Potential energy associated with an object due to.
Work and Energy Definition of Work Kinetic Energy Potential Energy
The Electromagnetic Field. Maxwell Equations Constitutive Equations.
Smart Materials in System Sensing and Control Dr. M. Sunar Mechanical Engineering Department King Fahd University of Petroleum & Minerals.
1 Initiation of joint research projects on  Piezoelectric composites (M. Chafra, N. Chafra, Z. Ounaies)  Fracture mechanics of Functionally Graded MagnetoElectroElastic.
ME 520 Fundamentals of Finite Element Analysis
Chapter 6 Energy and Energy Transfer. Introduction to Energy The concept of energy is one of the most important topics in science Every physical process.
Chapter 7 Energy of a System. Introduction to Energy A variety of problems can be solved with Newton’s Laws and associated principles. Some problems that.
AMML Effect of rise, peak and fall characteristics of CZM in predicting fracture processes.
Plate acoustic waves in ferroelectric wafers V. A. Klymko Department of Physics and Astronomy University of Mississippi.
Dr. Hugh Blanton ENTC Energy & Potential Dr. Blanton - ENTC Energy & Potential 3 The work done, or energy expended, in moving any object.
三維壓電彈性力學 Chien-Ching Ma Ru-Li Lin 內容大綱 三維問題 二維問題 _ 平面問題 二維問題 _ 反平面問題 二維問題 _ 壓電問題 二維問題 _ 解的架構 二維問題 _ 全平面的基本解 二維問題 _ 半平面的解函數.
Example: Radially Polarized Tube. Introduction This is a 2D static axisymmetric piezoelectric benchmark problem A radially polarized piezoelectric tube.
Conservative Forces: The forces is conservative if the work done by it on a particle that moves between two points depends only on these points and not.
ELECTROMAGNETICS AND APPLICATIONS Lecture 5 Normal Incidence at Media Interfaces Luca Daniel.
1 3D Exact Analysis of Functionally Graded and Laminated Piezoelectric Plates and Shells G.M. Kulikov and S.V. Plotnikova Speaker: Svetlana Plotnikova.
1 Chapter 6 Energy and Energy Transfer 2 3 Introduction to Energy The concept of energy is one of the most important topics in science Every physical.
So far, we have considered plane waves in an infinite homogeneous medium. A natural question would arise: what happens if a plane wave hits some object?
1 ENE 325 Electromagnetic Fields and Waves Lecture 5 Conductor, Semiconductor, Dielectric and Boundary Conditions.
1/61/6 M.Chrzanowski: Strength of Materials SM1-08: Continuum Mechanics: Stress distribution CONTINUUM MECHANICS (STRESS DISTRIBUTION)
Chapter 6 Overview. Maxwell’s Equations In this chapter, we will examine Faraday’s and Ampère’s laws.
Work Readings: Chapter 11.
1 Chapter 6 Energy and Energy Transfer 2 3 Introduction to Energy The concept of energy is one of the most important topics in science Every physical.
1 Non-Linear Piezoelectric Exact Geometry Solid-Shell Element Based on 9-Parameter Model Gennady M. Kulikov Department of Applied Mathematics & Mechanics.
What charge exists on a 30 μF capacitor (fully charged) with a 120 V potential difference between its plates and what is the energy stored? Ans: 3.6.
An electric field is said to exist in a region of space if an electric charge placed in that region is subject to an electric force.
Engineering Electromegnetic. SUB : Engineering Electromagnetic Topic : Conductors Department : Electronics and communication Name : Parmar Taruna M. Enroll.
Electrical Energy and Capacitance Electrical Potential Energy.
Fracture of Solids Theoretical tensile strength of a solid U(r) a r
The Tri-harmonic Plate Bending Equation
Continuum Mechanics (MTH487)
Basic principles of metallic fracture
In the name of GOD.
Christopher Crawford PHY
Continuum Mechanics (MTH487)
Christopher Crawford PHY
ENE 325 Electromagnetic Fields and Waves
Review for Mid-Term Exam
What charge exists on a 30 μF capacitor (fully charged) with a 120 V potential difference between its plates and what is the energy stored? Ans: 3.6.
Fracture of Solids Theoretical tensile strength of a solid U(r) a r
Related OSE's.
Mechanics of Materials Lab
Electrical Energy & Capacitance Pgs
L.V. Stepanova Samara State University
Presentation transcript:

EM 388F Term Paper: Discussion of Fracture Criterions under Impermeable and Permeable Crack Surface of Piezoelectric Materials RONG JIAO April 27, 2008

Outline of this topic Fundamental equations for piezoelectric material Impermeable crack surface J-integral or Total Potential Energy Release Rate (TPERR ) Mechanical Strain Energy Release Rate ( MSERR ) Permeable crack surface Total Potential Energy Release Rate (TPERR ) Mechanical Strain Energy Release Rate ( MSERR )

Fundamental equations for piezoelectric materials Field equations: Boundary equations: Constitutive equations: Crack surface Impermeable or permeable? ~stress tensor ~body force ~ electric displacement ~body charge ~traction vector ~surface change ~elastic module ~dielectric constants ~piezoelectric constants ~electric field

Stroh’s complex potential theorem (Suo et al.,1992)

Impermeable crack surface: Boundary condition: Traction free condition: Charge free condition: Stress intensity factors (SIF) : Electric displacement intensity factor (EDIF):  SIF is not a good fracture criterion for the impermeable crack since they do not consider the influence of the electric field on fracture.

J-integral (TPERR: Total Potential Energy Release Rate) (Park and Sun,1995, International Journal of Fracture 70, 203~216) Why TPERR is not a good fracture criterion here? 1. Negative last term always block the crack growth 2. Do not agree with the experiment Mechanical Coupling Electric, Negative? ( Mode I )

MSERR (Mechanical Strain Energy Release Rate)  Fracture is mechanical process and it’s more reasonable to only use the mechanical energy release rate as the fracture criterion. (Mode I) (Park and Sun,1995,International Journal of Fracture 70, 203~216)  The negative electric term vanishes.  Positive electric field decreases the critical stress and hence accelerate crack growth while negative electric field increases the fracture stress hence blocks crack growth.  These conclusions match experimental results very well.

Permeable crack surface Boundary condition: Traction free condition: Charge continuous condition:  Stress intensity factors (SIF) :

Energy calculations for permeable crack surface: ( Xu and Rajapakse, 2001, International Journal of Solids and Structures, 38: 7643) ~distributed normal eclectic displacement ~complex coefficient in the complex potentials  Electric displacement intensity factor (EDIF):

Energy analysis for impermeable and permeable crack ( Liu and Chen, 2002, International Journal of Fracture, 116: ) Mechanical part of TPERR (MSERR) 1. It’s constant for permeable crack under different electric loading. 2. It’s always bigger than that for impermeable crack, which implies the permeable boundary enhance the crack growth. 3. For the impermeable crack, MSERR is influenced by the applied electric loading: Positive electric load increases MSERR while negative decreases MSERR.

Energy analysis for impermeable and permeable crack (Liu and Chen,2002) (Continue) Electric part of TPERR 1. It’s almost zero for permeable crack under different electric loading and this is the reason why TPERR could be used as a fracture criterion for the permeable crack. 2. For the impermeable crack, it is affected by the applied electric loading and this is the reason why TPERR could not be used as a fracture criterion for the impermeable crack.

Comments? End and thank You!