Hot Deformation Behaviors and Intrinsic Hot Workability Map of Ti-12Mo-4Zr-5Sn Alloy Based on Physical Model and Polar Reciprocity Model

The hot compression tests of Ti-12Mo-4Zr-5Sn alloy were tested on the thermo-mechanical simulator of Gleeble-3500 under isothermal and constant strain rate. We studied this alloy’s behavior during thermal deformation at the conditions of T = 670~820 °C, ε ˙ = 0.001~10 s−1, and deformation degree 70%. The rheological stress curves of the alloy were modified, the characteristics of the rheological stress curves were analyzed, and the activation energy map of hot deformation was established. A physical constitutive model of the alloy based on strain compensation was established, which has taken the relationship between Young’s modulus and self-diffusion coefficient and temperature into account. Moreover, the intrinsic hot workability ξ map of the alloy was established based on the polar reciprocity model. The results show that this alloy’s rheological stress will descend when the temperature of deformation rises and grow when the strain rate increases, and has negative sensitivity of temperature and positive sensitivity of strain rate. According to the error calculation, the physical constitutive model’s correlation coefficient is 0.9910 and the average relative error is 3.97%, which has good accuracy. Through the analysis of the microstructures of the instability zone and the stability zone, it was found that the instability mode of the instability zone was dominated by the local flow, and the deformation mechanism of the stability zone was dominated by the dynamic recrystallization. The optimum processing parameters of the alloy known from ξ map and metallographic structure are the following: T = 790~820 °C and ε ˙ = 0.001~0.01 s−1.

TO ESTIMATE THE NON-RIGIDITY OF BEARING SUPPORTS OVER THE WIDTH OF THE UNSTABLE ZONE OF A NONLINEAR SYSTEM

In this paper, questions are investigated the influence of non-ideal elasticity and non-rigidity of support bearings on the dynamic response of an object under external vibration excitation is investigated. A method based on the sensitivity of the instability zone width of a nonlinear system in relation to the elastic characteristic of supports is proposed to estimate the non-rigidity of bearings. For this range of specific problems, we consider an operational method for estimating the width of the insta-bility zone by linearization of nonlinear equations based on energy equivalence. The main purpose of this work is to investigate the influence of non-ideal elasticity and non-elastic support bearings on the dynamic response of the object under external vibration excitation, to determine the evaluation of non-ideal bearings. for this purpose, a sufficiently effective method based on the sensitivity of the instability zone width of a nonlinear system in relation to the elastic characteristics of the supports is proposed, for this range of specific problems, we consider an operational method for estimating the width of the instability zone by lineariza-tion of nonlinear equations based on energy equivalence. Conclusions and suggestions. Thus, these dependences allow us to assess the degree of non-linearity of the elastic characteristic and, as a result, the non-rigidity of the bearing supports based on the results of vibration studies. In field tests, the width of the instability zone can be determined by an automatic forward and reverse fre-quency scanning system at a fixed overload level. Keywords: construction, dynamic response, dynamic parameters, vibrational excitation, structural model, in-stability zone, frequency and amplitude of vibrations, nonlinear system, elastic characteristic, non-uniformity, sensitivity of dynamic parameters, operational method, energy equalization.

Influence of initial fines content on fabric of soils subjected to internal erosion

Seepage-induced internal erosion often happens in earth structures. This paper presents experimental investigations on the influence of initial fines content on fabric of soils subjected to internal erosion. The tested materials were the binary mixtures of silica No. 3 and silica No. 8, which correspond to the coarse and fine fractions, respectively. One group of specimens was prepared with initial fines contents of 0, 15%, 25%, and 35% by weight. The undrained monotonic compression tests were performed on this group to examine the influence of fines content on the undrained behavior. The other group was prepared with initial fines contents of 15%, 25%, and 35% by weight, on which the seepage tests and subsequent undrained compression tests were carried out to demonstrate the mechanical influence of the internal erosion. The undrained behavior of the first group of specimens reveals that the presence of fines would decrease the peak and residual strengths. A comparison between the undrained behavior of soils with erosion and that of soils without erosion shows that the soils become less contractive after the internal erosion. When the axial strain is less than 0.4%, the undrained secant stiffness of soils with erosion is larger than that without erosion at the same axial strain. Meanwhile, the undrained peak strength and residual strength are larger for soils with erosion than that for soils without erosion. The less amount of excess pore-water pressure is generated during the undrained compression for the eroded soils comparing to those of the uneroded soils. Furthermore, the eroded soils show a wider instability zone than that of the uneroded soils, which suggests that the instability zone be enlarged by the internal erosion. Besides, one-dimensional upward seepage tests were performed to investigate the change of fabric of the mixed sand with 15%, 25%, and 35% fines contents due to internal erosion. The recorded microscopic images of soils before and after erosion reveal that the fabric is altered by the internal erosion.

Numerical study of the structure of thermal plume in a vertical channel: Effect of the height of canal

In this paper we propose to study numerically, by means of a software Named Calculation FDS, a thermal plume evolve from a source at the entrance to of a vertical channel. In the literature, there are researchers who interested in the interaction of plume with his the confinement medium. These studies are based on the determination of the global structure of plume confined. They found that this plume consists of three distinct zones. A first zone near source (instability zone) followed by a second zone, such as the development of plume, and a third zone which is the zone of turbulence, Comparing the overall structure of the plume confined to that of the free plume, we can identify the presence of a third zone (zone of instability). The aim is firstly to determine the height of the instability zone located above of source, and secondly, to make a spectral study frequencies exhaust. Thus, effects of the geometrical parameters on frequencies of these escapements and the height an instability zone. The final aim is to establish correlations between the dimensionless numbers of Strouhal and Grashof.

Viscous fingering and deformation of a miscible circular blob in a rectilinear displacement in porous media

The deformation of an initially circular miscible blob in a rectilinear displacement is investigated numerically for porous media when the blob is more viscous than the displacing fluid. We find in the parameter space spanned by the Péclet number and log-mobility ratio the existence of a new lump-shaped instability zone between two distinct regimes of comet and viscous fingering (VF) deformations. The more viscous circular blob is destabilized by VF only over a finite window of log-mobility ratio, contrary to the displacement of a more viscous finite slice with planar interfaces. This difference is attributed to the initial curvature of the miscible blob.

Boundaries of instability zones for symplectic twist maps

Very few things are known about the curves that are at the boundary of the instability zones of symplectic twist maps. It is known that in general they have an irrational rotation number and that they cannot be KAM curves. We address the following questions. Can they be very smooth? Can they be non-${C}^{1} $?Can they have a Diophantine or a Liouville rotation number? We give a partial answer for${C}^{1} $and${C}^{2} $twist maps.In Theorem 1, we construct a${C}^{2} $symplectic twist map$f$of the annulus that has an essential invariant curve$\Gamma $such that$\bullet $ $\Gamma $is not differentiable;$\bullet $the dynamics of${f}_{\vert \Gamma } $is conjugated to the one of a Denjoy counter-example;$\bullet $ $\Gamma $is at the boundary of an instability zone for$f$.Using the Hayashi connecting lemma, we prove in Theroem 2 that any symplectic twist map restricted to an essential invariant curve can be embedded as the dynamics along a boundary of an instability zone for some${C}^{1} $symplectic twist map.