Generalized Stacking Fault Energy, Twinning And Dislocations Of Materials At FiniteTemperature

Dislocation and twinning are two important modes of plastic deformation in a material. The generalized stacking fault(GSF) energy plays a critical role in describing the dislocation properties and deformation twinning. It can not be obtained from experiment, we can only get it from the theoretical calculations. The first principles method is effective and correct to calculate the GSF energy. Recently, there have been many theoretical studies focused on the qualitative dependence of the dislocation properties and the mechanical twinning tendency on the GSF energy obtained from the first principles method in various materials. The GSF energy mainly includes stable stacking fault energy(SFE), unstable SFE and unstable twin SFE which are used to describe the plastic deformation. The stable SFE has traditionally been used as a rough predictor of twinnability in FCC metals. The smaller the stable SFE, the higher the twinnability. However, Al does not exhibit deformation twinning on a macroscopic scale at any stress despite having a stable SFE lower than Ir which does exhibit deformation twinning. In order to solve the contradiction, Tadmor and Bernstein presented a new criterion for twinnability. The criterion demonstrates that while twinnability does depend on the stable SFE as traditionally assumed, it is equally affected by the unstable SFE and the unstable twin SFE. It can be used to correctly predict the twinnability of FCC metals at 0 K. However, it is lack of the theoretical prediction for the twinnability at different temperature, which makes various experimental results failed to obtain good understanding. For example, experiment observation revealed a few deformation twins in Cu deformed at room temperature, however, Cu showed extensive deformation twins at liquid nitrogen temperature. In order to understand the experimental result, it is necessary to expand the twinnability at 0 K to finite temperature. Besides, the determination of the dislocation core structure is limited at 0 K. We also investigate the dislocation core structure at finite temperature to recognize the influence of the temperature on the nature of materials. Generally, the service temperature of a material is different under different environment. So it has important practical significance to investigate the mechanical properties of materials at different temperature, which can provide crucial reference for the design and the development of the high performance materials. The main contents are as follows:① The GSF energies of Mg and Mg alloys with one Mg atom in the different layers replaced by C, B, N, O and vacancy at 0 K have been calculated by using the first principles method. It is found that the predominant reducing effect of the alloying atoms and vacancy on the GSF energies is resulted from the position of them in the 1st layer near the slip plane. The GSF energies are nearly the same as the pure Mg while the alloying atoms and vacancy are in the plane away from the slip plane. Then we use the first principles method combined with the quasiharmonic approximation to investigate the influence of the temperature and the rare earth elements Er, Ho, Dy, Tb and Gd located on the slip plane at different temperature on the GSF energy and the twinning ability of Mg. Our results show that the twinnability of Mg decreases with increasing temperature. The reason is that the unstable SFE is seriously decreased relative to the unstable twin SFE with increasing temperature. Besides, the rare earth elements incorporation can enhance the twinnability of Mg.② The 1/6<112>{111} GSF energy curves at different temperature have been researched for Al, Ni and Cu. Based on the temperature dependent GSF energy curves the twinnabilities for crack tip twinning, grain boundary twinning and inherent twinning of Al, Ni and Cu are examined. Ni and Cu have the twinnabilities for perfect crystals besides the crystals with grain boundary and crack tip at different temperature. However, Al does not exhibit the inherent twinnability except for Al with grain boundary or crack tip. The twinnabilities of FCC metals decrease with increasing temperature. Cu exhibits the strongest tendency to display twinning modes whereas Al has the lowest twinnability at different temperature. The main reason is that the unstable SFE and the unstable twin SFE are slightly higher than those of Cu, however, the SFE of Al is almost three times larger than that of Cu at the same temperature. Besides, we have investigated the effects of the rare earth elements Sc, Y, Dy, Tb and Nd on the twinnability at a crack tip of Al at different temperature. Our results show that the rare earth elements can make crack tip twinning more easily.③ 1/2<110>{110} slip system is the primary slip system in Na Cl structure crystals Mg O and Ca O. Firstly, we have calculated the elastic constants and GSF energies of Mg O and Ca O at three different temperature of 0 K, 500 K and 1000 K, respectively. The comparisons between our calculated results and the available experimental data for Mg O and Ca O provide good agreements. Based on the temperature dependent elastic constants and GSF energies, the core structure of 1/2<110>{110} edge dislocation, screw dislocation and mixed dislocation has been investigated within the improved Peierls-Nabarro(P-N) dislocation equation using the Foreman’s method. It is found that the core width of dislocation increases with increasing temperature.④ The elastic constants, GSF energies and surface energies of B2 structure Ni Al and Fe Al have been calculated in the temperature range of 0-1200 K. Our results show that all the values decrease with increasing temperature except for the surface energy of Ni Al. The ductlities of Ni Al and Fe Al have been discussed by using the Pugh ratio, the Cauchy pressure and the Rice criterion, respectively. The ductilities of Ni Al and Fe Al increase with increasing temperature. Based on the Pugh ratio and the Cauchy pressure Ni Al has more ductility than Fe Al in the temperature range of 0-1200 K, however, Ni Al has less ductility than Fe Al based on the Rice criterion. The contradiction may be resulted from that the Rice criterion can be employed to roughly estimate the ductility behavior of a material. Finally, the core structure of <111>{110} superdislocation has been investigated within the improved P-N theory containing the lattice discrete effect. The core width of Ni Al is always larger than that of Fe Al at different temperature. It also demonstrates that the ductility of Ni Al is slightly better than that of Fe Al.⑤ The elastic constants and the GSF energies of L12 structure Ni3 Al in the temperature range of 0-900 K have been calculated. The antiphase boundary energy, complex stacking fault energy, superlattice intrinsic stacking fault energy and twinning energy decrease with increasing temperature. The temperature effect on the anomalous yield stress of Ni3 Al has been investigated based on the energy-based criterion p proposed by Yoo et al.. Our results show that all the values of p is bigger than 3 in the temperature range of 0-900 K and p increases obviously with increasing temperature. It demonstrates that the yield stress of Ni3 Al intermetallic compound increases with increasing temperature which is in agreement with the experimental results obtained by Kruml et al.. Besides, the twinnability of Ni3 Al decreases with increasing temperature.