Transformation Toughness: The Field-Theoretical Perspective
摘要
This chapter applies the field-theoretical approach to analyze a transformation toughness in a crystal with a motionless crack. The loaded crack engenders a process zone at its tip. As elaborated earlier, due to the surface tension of the zone’s interface, an interval close to the crack tip exists where the crack surface borders the process zone. It leads to the mechanical shielding of the crack tip, thereby giving rise to transformation toughness. The field-theoretical method empowers us to establish its correlation with the solid’s position on its phase diagram. Based on the outcomes of our simulations described earlier in the book, we have derived an expression for effective fracture toughness using two distinct approaches: (i) leveraging the elastic Green’s function and (ii) utilizing weight functions. Building upon these findings, we have formulated an accurate analytical approximation that characterizes transformation toughness, expressing it in terms of experimentally attainable parameters related to the phase diagram, including the hysteresis width, the slope of the binodal line, and the transformation strain (Boulbitch and Korzhenevskii, 2021).