A program was undertaken to develop a fully predictive model of the scatter in toughness across a wide range of transition temperatures based on a physical understanding of deformation and fracture behavior. The temperature dependence of the proposed model is taken from previous work in which the local mechanisms of cleavage fracture were used to define the plastic work to fracture. The local to global stress transference is achieved by a dislocation-mechanics based examination of the interaction between the globally applied stresses, a macroscopic crack and a nearby accumulation of dislocations blocked by a second phase particle, i.e. slip band, whose position relative to the macroscopic crack tip is variable. The scatter of toughness values at each temperature is captured through variation of this macro-crack / micro-crack geometry, and of the particle size. Once the local stress field is determined using the dislocation-based transference equations, an energy balance criterion for fracture is applied that incorporates the temperature-dependent fracture work term and the local stresses determined from the transference equations. This paper summarizes this multiscale fracture model, which serves as a foundation for more detailed descriptions of the mathematics of the quantitative model, its temperature dependence and scatter characteristics and coding efforts. These latter topics will be addressed in greater detail in subsequent papers.
A Theoretically-Based Statistical Model of Transition Toughness
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EricksonKirk, MA, & Wagenhofer, M. "A Theoretically-Based Statistical Model of Transition Toughness." Proceedings of the ASME 2007 Pressure Vessels and Piping Conference. Volume 6: Materials and Fabrication. San Antonio, Texas, USA. July 22–26, 2007. pp. 561-568. ASME. https://doi.org/10.1115/PVP2007-26303
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