The process of dislocation multiplication has been described hv chaos theory, trying to reveal the connection between the microstructures on the mesoscopic scale and the mechanical properties of material on the macros...The process of dislocation multiplication has been described hv chaos theory, trying to reveal the connection between the microstructures on the mesoscopic scale and the mechanical properties of material on the macroscopic scale. The relationship between the dislocation velocity exponent and the maximum of strain rate is given. The results obtained from logistic equation with exponent and the dislocation multiplication dynamic equation are compared. A scale law in one-dimension-map model with exponent is shown when the exponents of equations are changed.展开更多
The chaotic behaviour of dislocation multiplication process was investigated. The change of Lyapunov exponent which is used to determine the stability of quasi-periodic and chaotic behavior as well as that of equilib...The chaotic behaviour of dislocation multiplication process was investigated. The change of Lyapunov exponent which is used to determine the stability of quasi-periodic and chaotic behavior as well as that of equilibrium points, and periodic solution was reported by using an iteration model of dislocation multiplication. An unusual behavior of Lyapunov exponent and Feigenbaum exponent which respond to the geometric convergence of orbit from bifurcation to chaos was shown by dislocation velocity exponent m and there is a distinction on the tendency of convergence for the dislocation multiplication model when it was compared with logistic map. It is reasonable for the difference to be analyzed from the materials viewpoint. (Edited author abstract) 9 Refs.展开更多
基金This work was financially supported by the NationalNatural Science FOundation of China (grant No.5987l056 and No.59831020) an
文摘The process of dislocation multiplication has been described hv chaos theory, trying to reveal the connection between the microstructures on the mesoscopic scale and the mechanical properties of material on the macroscopic scale. The relationship between the dislocation velocity exponent and the maximum of strain rate is given. The results obtained from logistic equation with exponent and the dislocation multiplication dynamic equation are compared. A scale law in one-dimension-map model with exponent is shown when the exponents of equations are changed.
文摘The chaotic behaviour of dislocation multiplication process was investigated. The change of Lyapunov exponent which is used to determine the stability of quasi-periodic and chaotic behavior as well as that of equilibrium points, and periodic solution was reported by using an iteration model of dislocation multiplication. An unusual behavior of Lyapunov exponent and Feigenbaum exponent which respond to the geometric convergence of orbit from bifurcation to chaos was shown by dislocation velocity exponent m and there is a distinction on the tendency of convergence for the dislocation multiplication model when it was compared with logistic map. It is reasonable for the difference to be analyzed from the materials viewpoint. (Edited author abstract) 9 Refs.
