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

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 J k - 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 significantly, the M -integral presents a new description for the damage level of a microcracking brittle solid. In the second point it discusses the direct extension from the basic understandings established in Linear Elastic Fracture Mechanics to those for functional materials, e.g., piezoelectric ceramics. Owing to the mechanical and electric coupling, some new insights of energy release rates are discussed in detail. 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 Significantly, The M-integral Presents A New Description For The Damage Level Of A Microcracking Brittle Solid. In The Second Point It Discusses The Direct Extension From The Basic Understandings Established In Linear Elastic Fracture Mechanics To Those For Functional Materials, E.g., Piezoelectric Ceramics. Owing To The Mechanical And Electric Coupling, Some New Insights Of Energy Release Rates Are Discussed In Detail. List Of Figures -- List Of Tables -- Preface -- Acknowledgments -- 1. Historical Review And Fundamentals -- 2. Conservation Laws In Brittle Solids -- 3.the Projected Conservation Law Of Jk Vector In Microcrack Shielding Problems -- 4. Application Of The Conservation Laws In Metal/ceramic Bimaterials -- 5. Macrocrack Microcrack Interaction In Dissimilar Anisotropic Materials -- 6. Macrocrack Microcrack Interaction In Piezoelectric Materials -- 7. Microcrack Damage In Piezoelectric Materials -- 8. Some Other Developments Of The Conservation Laws And Energy Release Rates. By Yi-heng Chen. Front Matter....Pages i-xxi Historical Review and Fundamentals of Conservation Laws and Energy Release Rates....Pages 1-40 Conservation Laws in Brittle Solids with Strongly Interacting Cracks....Pages 41-93 The Projected Conservation Law of J K Vector in Microcrack Shielding Problems of Brittle Solids....Pages 95-133 Application of the Conservation Laws in Metal/Ceramic Bimaterials....Pages 135-169 Macrocrack Microcrack Interaction in Dissimilar Anisotropic Materials....Pages 171-202 Macrocrack Microcrack Interaction in Piezoelectric Materials....Pages 203-233 Conservation Laws for Microcrack Damage in Piezoelectric Materials....Pages 235-259 Some other Developments of the Conservation Laws and Energy Release Rates....Pages 261-296 Back Matter....Pages 297-298