Stress-Induced Local Phase Transformations Near Cracks and Dislocations

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.

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.