11:30 AM - 11:45 AM
[SMP24-09] Strain hardening due to deformation twinning: Insight from some interface theories
Keywords:deformation twin, strain hardening, surface dislocation theory, Hall-Petch relation
Deformation twin is known to influence the deformation and strengthening mechanisms of materials. For example, deformation experiments of calcite have shown that as differential stress increases, the deformation twin density also increases [1-2]. Nonetheless, the theoretical background has not been well understood. Hence, this study attempts to explain the relation between the density of deformation twins and stress using surface dislocation theory.
Surface dislocation theory is a theory proposed by Bullough and Bilby [3], stating that a crystal lattice of two different orientations is bounded by a surface dislocation. Since these surface dislocations must be oriented in various directions within the object, they can be regarded macroscopically as general dislocations. In other words, the density of surface dislocations can be expressed as general dislocation density. Hence, applying this to the stress-dislocation relation (Hall-Petch type equation), a relationship between the deformation twin density tensor and stress can be derived from the correspondence between dislocation density and twin density. This is consistent with the correlation between deformation twin density and differential stress obtained from experimental results on calcite [2].
Furthermore, the surface dislocation theory is equivalent to the 0-lattice theory that describes the geometry of the interface structure, and the rank-1 connection and Hadamard jump conditions for maintaining continuity of deformation at the interface. Therefore, it can be applied to the formation of kink and martensite transformations that form interfaces. These interfaces have been indicated to cause strain hardening by hindering the movement of dislocations and show a Hall-Petch relationship [4-5]. Therefore, it is suggested that the surface dislocation theory can comprehensively explain strain hardening due to interface formation.
References
[1] Rowe and Rutter, 1990, J. Struct. Geol. 105, 80-87.
[2] Rybacki et al., 2013, J. Struct. Geol. 601, 20-36.
[3] Bullough and Bilby, 1956, Proc. Phys. Soc. B 69, 1276.
[4] Tadano, 2023, Mater. Trans. 64, 1002-1010.
[5] Morito et al., 2006, Mater. Sci. Eng. A 438-440, 237-240.
Surface dislocation theory is a theory proposed by Bullough and Bilby [3], stating that a crystal lattice of two different orientations is bounded by a surface dislocation. Since these surface dislocations must be oriented in various directions within the object, they can be regarded macroscopically as general dislocations. In other words, the density of surface dislocations can be expressed as general dislocation density. Hence, applying this to the stress-dislocation relation (Hall-Petch type equation), a relationship between the deformation twin density tensor and stress can be derived from the correspondence between dislocation density and twin density. This is consistent with the correlation between deformation twin density and differential stress obtained from experimental results on calcite [2].
Furthermore, the surface dislocation theory is equivalent to the 0-lattice theory that describes the geometry of the interface structure, and the rank-1 connection and Hadamard jump conditions for maintaining continuity of deformation at the interface. Therefore, it can be applied to the formation of kink and martensite transformations that form interfaces. These interfaces have been indicated to cause strain hardening by hindering the movement of dislocations and show a Hall-Petch relationship [4-5]. Therefore, it is suggested that the surface dislocation theory can comprehensively explain strain hardening due to interface formation.
References
[1] Rowe and Rutter, 1990, J. Struct. Geol. 105, 80-87.
[2] Rybacki et al., 2013, J. Struct. Geol. 601, 20-36.
[3] Bullough and Bilby, 1956, Proc. Phys. Soc. B 69, 1276.
[4] Tadano, 2023, Mater. Trans. 64, 1002-1010.
[5] Morito et al., 2006, Mater. Sci. Eng. A 438-440, 237-240.