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Advances in Conservation Laws and Energy Release Rates Theoretical Treatments and Applications

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ISBN-10: 1402005008

ISBN-13: 9781402005008

Edition: 2002

Authors: Yi-Heng Chen

List price: $199.99
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Description:

This book summarizes two significant tendencies for application of conservation laws and energy release rates. The first is to establish a bridge between some famous invariant integrals and microcrack damage descriptions. The second is the direct extension from the understandings established in Fracture Mechanics for conventional materials to those for functional materials. In the first point it discusses the vanishing nature for both components of the Jk-integral vector when the closed contour encloses all discontinuities completely. Both mathematical manipulations and numerical examinations are given. Thus the M-integral and the L-integral are independent of coordinate shifts and, more…    
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Book details

List price: $199.99
Copyright year: 2002
Publisher: Springer
Publication date: 3/31/2002
Binding: Hardcover
Pages: 298
Size: 6.75" wide x 9.75" long x 1.00" tall
Weight: 1.430
Language: English

List of Figures
List of Tables
Preface
Acknowledgments
Historical Review and Fundamentals
Definitions and basic formulations
Definitions of the J[subscript k] integral vector, M integral, and L integral
Path selections and conservation laws
Discussion of previous investigations for invariant integrals
Physical meanings of the M integral and the L integral
Nondestructive evaluation of the J and M integrals
Techniques for experimentally evaluating J and M
Edge crack
Evaluation of the M integral
Center crack
Brief Summary
Conservation Laws in Brittle Solids
Historical reviews and engineering backgrounds
Independence of the M integral from the origin selection of the global coordinates
Application of the M integral in multiple crack interacting problems
Independence of the M integral from the origin selection of the coordinates
Numerical examples
Four regularly distributed microcracks
Randomly distributed microcracks
Short summary
Conservation laws in bimaterials
Conservation laws of the J[subscript k] vector in bimaterials
Independence of the M integral from the coordinate selection in bimaterials
M integral analysis for microcrack damage in the brittle phase
A half-plane brittle solid containing multiple cracks
Brief summary
The Projected Conservation Law of J[subscript K] Vector in Microcrack Shielding Problems
Microcrack shielding problems
A continuum theory of microcrack shielding
A discrete modelling of shielding problems
Fundamental solutions
Pseudo-traction methods and integral equations
Numerical examinations
The J integral analysis: the projected conservation law of the Jk vector
Numerical results and discussions
Effect of the T stress
What is the T stress?
What role does the T stress play in microcrack shielding problems?
Brief summary
Application of the Conservation Laws in Metal/Ceramic Bimaterials
Fundamental solutions for an interface crack and a sub-interface crack
Pseudo-traction methods and Fredholm integral equations
The J integral analysis: the projected conservation law of the J[subscript k] vector
Numerical examples and discussions
Brief summary
Macrocrack Microcrack Interaction in Dissimilar Anisotropic Materials
Fundamental formulations in dissimilar anisotropic materials
Fundamental solution for an interface crack
Fundamental solution for an edge dislocation
Remote loading conditions
Superimposing technique and singular integral equations
Decomposition of the original problem
Solution of the integral equations
Analysis of the J integral
Conservation law of the J integral
Calculation of the J[subscript 2] integral
Multiple microcracks situation
Numerical results and consistency check
Composite material properties
Crack interaction configuration and numerical results
In homogeneous anisotropic cases
Different dissimilar materials combinations
The T stress effect
Brief Summary
Macrocrack Microcrack Interaction in Piezoelectric Materials
Elementary solutions
Elementary solutions for a finite crack
Elementary solutions for a semi-infinite crack
Remote loading conditions
Pseudo-traction electric displacement method (PTED)
Conservation law and consistency check
The mechanical strain energy release rate (MSERR)
Variable tendencies of the SIF owing to microcracking
Variable tendencies of the EDIF against the location angle
Variable tendencies of the mechanical strain energy release rate (MSERR)
Oriented microcrack
Brief Summary
Microcrack Damage in Piezoelectric Materials
General description of the present problem
J[subscript k] vector in piezoelectric media: physical interpretation and conservation laws
Path independence of the two components of the J[subscript k] vector
Conservation laws: statement
Mathematical proof of conservation laws
Numerical techniques and examples
Pseudo-traction electric displacement method
Numerical results
Applications: two arbitrarily located interacting cracks
Brief Summary
Some other Developments of the Conservation Laws and Energy Release Rates
Application of the M integral to the Zener crack
Conservation laws in functional materials
Energy Momentum Tensor in piezoelectric materials
Energy momentum tensor in functional materials
Bueckner's work conjugate integral in piezoelectric materials
Application of conservation laws of invariant integrals in nanostructures
Summary
Index