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A B S T R A C T Dislocation group dynamics theory is used to deduce a power type expression for fatigue crack growth. In general, the results reflect only a single rate process, and thus one activation energy which is small compared to those in usual rate processes. The frequency dependence for this power function type fatigue crack growth rate was also obtained, and yield reasonable agreement with experimental results from the literaturel

Previously, one of the authors developed a noninvasive measurement method of acceleration and deceleration during the expansion process of the blood vessel wall under pulsatile pressure flow by measuring the strain rate of the blood vessel wall using a supersonic Doppler effect sensor aided by computer analysis (DPC method). In this paper, on the basis of the analysis of chaos theory, that is, the complexity of science, the unstable behavior of the blood vessel wall with an aneurysm was investigated by identifying the characteristic DPC wave forms induced by the onset and progression of aneurysm. These results showed that unstable dynamic behavior of the blood vessel wall occurs due to the progression of the aneurysm. Furthermore, using the theoretical analysis of chaos, this unstable behavior of the blood vessel wall was quantified and the fundamental principle of a noninvasive diagnostic method of the progressive degree of aneurysm was proposed. IntroductionThe supersonic Doppler effect sensor has been used to measure blood flow velocity as a non-invasive method 1, 2) and some researches into its clinical application have been conducted [3][4][5] . However, whether the output from the Doppler effect sensor really detects blood flow velocity remains a problem.Theoretically, when the Doppler effect sensor is set perpendicular to the blood flow direction, that is, perpendicular to the blood vessel, the output will correspond to the expansion velocity of the blood vessel wall, because it detects the frequency of Doppler-shifted supersonic scattered from the blood vessel wall.One of the authors developed a noninvasive measurement method of acceleration and deceleration of the blood vessel wall during its expansion process under pulsatile pressure flow by measuring the strain rate of the blood vessel wall using a supersonic Doppler effect sensor 6) . On the basis of this method, a noninvasive quantitative diagnostic method of the progressive degree of atherosclerosis has been developed by obtaining accelerating and decelerating responses of the blood vessel wall under pulsatile pressure flow (DPC method) 7,8) . Furthermore, if noninvasive diagnosis of the onset and the progressive degree of the aneurysm becomes possible, the progressive degree of aneurysm can be shown quantitatively together with that of atherosclerosis and it will be useful in clinical application from the viewpoint of predicting the rupture time of the aneurysm, because not only the aneurysm itself Until now, researches into aneurysms, the clarification of blood flow behavior around an aneurysm have focused on treatment using fluid dynamics [9][10][11][12] . On the other hand, under pulsatile conditions, since the analysis of the deformation behavior of the blood vessel wall with an aneurysm is not feasible, there is little research into the dynamic behavior of the blood vessel wall with an aneurysm which is useful for clinical matters.Therefore, in this paper, on the basis of an chaos theory analysis 13) , that is, the complexity of science, the...

In situ observations of crack growth and damage progression were conducted under creep conditions for P92 and titanium aluminides inter-metallic compound. A proposed analysis of stress induced particle diffusion was applied to stress induced vacancy diffusion. Results obtained from this analysis were successfully correlated with the experimental behaviour of macroscopic damage progression and a theoretical characteristic of creep deformation was derived. It was found to be in good agreement with experimental characteristics of creep deformation. Furthermore, the experimental characteristics of creep damage progression which concern voids and micro crack formations at grain boundary were found to be well correlated with those of deformation. From these results, correlation between vacancy diffusion in nano-scale, creep damage in mezzo-scale and creep deformation in macro-scale were successfully realized.