Read more
This book introduces a powerful new framework for describing the states and dynamics of heterophase solids subjected to inhomogeneous stress fields. It serves both as an accessible introduction to the underlying theory and as a specialized monograph that deepens understanding of crack and dislocation behavior related to phase transformation. It addresses the interaction between such transformations and defects—primarily cracks and dislocations—though the approach is applicable to other, as yet unstudied, defect types. It further examines the effects of the stress-induced transitions on the mesoscopic properties of the material such as the peculiarities of the crack or dislocation motion, configuration of dislocations and elements of the dislocation ensemble. Finally, it studies variations of some macroscopic solid’s properties, such as the transformation toughness, shift of the elastic point, anomalous plasticity. All these aspects the book analyzes in relation to the solid’s position in the phase diagram. The authors’ analysis combines computer simulations with analytical methods. The presentation is clear and self-contained, with all necessary derivations included, making it unnecessary for the reader to consult additional literature. The material is accessible to readers with a mathematical background equivalent to that of a third-year university student or higher.
The book is intended for experimentalists, theorists, and students across disciplines interested in solid-state transformations and defect mechanics.
List of contents
Cracks and Dislocations.- Bifurcation Theory.- Landauís Theory with a One-Component Order Parameter.- Inhomogeneous Case:Elimination of Elastic Degrees of Freedom.- Rescaling of Equations Describing the Process Zone.- Formation of the Second-Order Process Zone.- Second-Order Mother-Phase Process Zones.- Universal Characteristics of First Order Process Zones.- Crack Tip Zone: Equation of Motion and Properties.- The Second-Order Process Zone at the Crack Tip.- Numerical Study of the Second Order Process Zone at the Crack Tip.- First Order Zone at the Crack Tip.- Morphological Transformation of the First-Order Process Zone.- Key Geometrical Parameters of the Crack Tip Zone.- Observations of the Wake and Zone at the Crack Tip.- The Complete Phase Diagram of the Process Zone.- Transformation Toughness: The Field Theoretical Perspective.- Crack Velocity Jumps.- Wedging-Induced SticknSlip Crack Propagation.- General Remarks on the Dislocations Process Zone.- In Search for the Bifurcation Point.- Motionless Dislocation Studied by Simulations: The Phase Diagram.- Manifested First-Order Zone at the Dislocation.- Process Zone at the Propagating Dislocation.- A Low Angle Grain Boundary.- Formation of Plastic Instability.- Numerical Estimates of the Zoneis Key Parameters.- Elastic Limit of a Crystal Close to a First Order Transition345.- Segment of a Dislocation Subjected to Stress Field.- Climbing Instability.- Thermoauctuation Motion of Dressed Dislocations.- Experiments Reporting Dressed Dislocations.- Concluding Remarks.-Annex1: Parameters Typical for Inorganic Solid.- Annex2: Simulations of Formation of a Soft Process Zone.- Annex3: Numerical Justification of Free Energy of the Mother-Phase Zone.- Annex 4: Simulation of the crack velocity jumps.- Annex 5: Relaxation Method for the First-Order Zone.
About the author
Alexei Boulbitch (born 19 January 1958) graduated from Rostov State University, USSR (now Southern Federal University, Russia), in 1980 and earned his PhD in Solid State Physics there in 1988. He completed his habilitation in Theoretical Biophysics at the Technical University of Munich (Germany) in 2001. Starting his career at the Institute for Physics in Rostov-on-Don (USSR), he developed a field-theoretical approach to stress-induced phase transitions and worked on liquid crystals, domain walls, and hydrogen in metals. From 1990 to 1992, he was a visiting scientist in Amiens, France, focusing on liquid crystals. In 1995, he joined the Technical University of Munich, working on biophysics. He published about 60 scientific papers. In 2005, he moved to industry, joining R&D at IEE S.A. (Luxembourg), specializing in sensorics. There he filed seven patent families. From 2014 to 2017, he also lectured on polymers and soft matter at the University of Luxembourg. He retired in 2023, still working on stress-induced phase transformations.
Alexander L. Korzhenevskii (born 30 April 1951) graduated from Leningrad State University (now St. Petersburg State University, Russia) in 1974. He earned his Ph.D. in Solid State Physics in 1979 and his Habilitation in Physico-mathematical sciences in 1992, both at the Ioffe Institute. From 1974 to 1994, he worked at the Electrotechnical Engineering Institute (St. Petersburg), where he developed a field-theoretical approach to stress-induced phase transitions at dislocations, focusing on their impact on the thermodynamic and optical properties of crystals. In 1994, he joined the Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (St. Petersburg), where he continues to work. From 1993 to 2015, he was a visiting scientist at the University of Munich, Ruhr University Bochum, and the University of Düsseldorf in Germany. He is currently active in applying field-theoretical methods to dislocations and interfaces in solids, as well as in the theory of solidification in dilute alloys.
Summary
This book introduces a powerful new framework for describing the states and dynamics of heterophase solids subjected to inhomogeneous stress fields. It serves both as an accessible introduction to the underlying theory and as a specialized monograph that deepens understanding of crack and dislocation behavior related to phase transformation. It addresses the interaction between such transformations and defects—primarily cracks and dislocations—though the approach is applicable to other, as yet unstudied, defect types. It further examines the effects of the stress-induced transitions on the mesoscopic properties of the material such as the peculiarities of the crack or dislocation motion, configuration of dislocations and elements of the dislocation ensemble. Finally, it studies variations of some macroscopic solid’s properties, such as the transformation toughness, shift of the elastic point, anomalous plasticity. All these aspects the book analyzes in relation to the solid’s position in the phase diagram. The authors’ analysis combines computer simulations with analytical methods. The presentation is clear and self-contained, with all necessary derivations included, making it unnecessary for the reader to consult additional literature. The material is accessible to readers with a mathematical background equivalent to that of a third-year university student or higher.
The book is intended for experimentalists, theorists, and students across disciplines interested in solid-state transformations and defect mechanics.
