Mathematical Model for Super Plastic Flow in Advanced Structural Materials

Author(s):  
Juan Daniel Muñoz-Andrade
2007 ◽  
Vol 551-552 ◽  
pp. 67-72
Author(s):  
Juan Daniel Muñoz-Andrade

Everything in the universe is a result of their own evolution, in consequence all advanced structural materials are physical objects spatially extended in a permanently cosmic connection with the advanced structural universe. In this context, the nature expansion rate of the universe (ξ u) was obtained in a similar way of super plastic flow in terms of the rate reaction theory, with the strong temperature dependence of strain rate as follow: exp 70( / sec)/ 2.26854593 . 18 1 0 − − = =         −         = = km Mpc s kT c Q H P P P u λ ξ Where, QP = the Planck activation energy of the system at the Planck scale (QP = 1.221x1028eV), λP = Planck length (λP = 1.62x10-35m), c = the speed of light (c = 299 792 458 m/s), (c/λP) = the overall frequency factor, k = the Boltzmann constant (k = 8.617x10-5eV/K), TP = the Planck temperature (TP = 1.010285625x1030K) and H0 = the Hubble constant. On the basis of this mathematical expression and their combination with the Orowan equation, it was obtained the mathematical model to predict the activation energy (Q) that is necessary to the glide cellular dislocations during deformation of the super plastic advanced structural materials. Consequently, in this work the application of this mathematical model for super plastic flow in advanced structural materials and the concept of cellular dislocation are reviewed in order to integrate in a general form the unified interpretation of Hubble flow, plastic flow and super plastic flow [1-3].


2007 ◽  
Vol 551-552 ◽  
pp. 147-152 ◽  
Author(s):  
Juan Daniel Muñoz-Andrade

In connection with ancient and recent view on cosmology, it is interesting to note that our universe could be a spherical crystal and it moves as a crystal in a relative position with others spherical universes, where the Burgers vector for cellular dislocations dynamics is the Hubble length: λH=1.32x1026m. The expansion process of this polycrystalline spatially extended system obey the hyperbolic granular flow, which it is due to an accelerated motion manifested during the deformation process of super plastic advanced structural universes in a similar behaviour of super plastic advanced structural materials. Consequently, in this work the phenomenology and mechanics of super plastic flow are analyzed in the context of the unified interpretation of Hubble flow, plastic flow and super plastic flow, where the combination of fundamentals constants with the natural Planck length, allows obtain in a closed agreement with the Orowan equation the magnitude of the nature Burgers vector of dislocation in the cosmic structure for the universe as follow: 1.62 10 . 35 3 0 x m c H G b P − ⊥ ⊥ ⊥ = = = = h λ ρ ν Where, b⊥ = magnitude of the nature Burgers vector for the universe (b⊥ = 1.62x10-35m), λP = Planck length (λP = 1.62x10-35m), H0 = the Hubble parameter (H0=70 (km/sec)/Mpc = 2.26854593 x10-18s-1), ρ⊥ = dislocation density (ρ⊥ = 1.273x1011 dislocations/m2) in the universe. ν⊥ = the recession velocity of galaxies related with dislocations dynamics in the cosmic structure (ν⊥ = 1100x103 m/s, it is the recession velocity of the Virgo super cluster at 16 Mpc distance). h = h / 2π . Here h = the Planck constant (h = 6.6262x10-34 Joule-s), G = the Newtonian constant (G = 6.67259x10-11 m3/kg s2) and c = the speed of light (c = 299 792 458 m/s) [1-3].


2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kejian Song ◽  
Yuan Long ◽  
Chong Ji ◽  
Fuyin Gao

When subjected to the dynamic load, the behavior of the structures is complex and makes it difficult to describe the process of the deformation. In the paper, an analytical model is presented to analyze the plastic deformation of the steel circular tubes. The aim of the research is to calculate the deflection and the deformation angle of the tubes. A series of assumptions are made to achieve the objective. During the research, we build a mathematical model for simply supported thin-walled metal tubes with finite length. At a specified distance above the tube, a TNT charge explodes and generates a plastic shock wave. The wave can be seen as uniformly distributed over the upper semicircle of the cross-section. The simplified Tresca yield domain can be used to describe the plastic flow of the circular tube. The yield domain together with the plastic flow law and other assumptions can finally lead to the solving of the deflection. In the end, tubes with different dimensions subjected to blast wave induced by the TNT charge are observed in experiments. Comparison shows that the numerical results agree well with experiment observations.


2019 ◽  
pp. 190-199
Author(s):  
A. V. Ryabtsov ◽  
O. Yu Vilensky

One of main operability criteria for fuel subassemblies (FSAs) in fast sodium reactor cores, i.e. the criterion of tolerable shape change in hexagonal wrapper tube is formulated. The equations which enable one to inquire into kinetics of the stress-strained state of a three-dimensional body are adapted to FSAs operating conditions. A mathematical model of radiation-induced shape change in ferritic-martensitic steel of grade EP-450 is proposed. With regard to the proposed model and data on the radiation-induced shape change in other current and prospective structural materials of BN reactor cores, blocks for recording of radiation-induced swelling and radiation-induced creep are developed for ANSYS software package, which made it possible to utilize its potentials within this area of focus. The performed test case with proposed models of the radiation-induced swelling and radiation-induced creep demonstrates that the developed blocks sufficiently describe the radiation-induced shape change in the examined structural materials exposed to radiation. A calculation of the radiation-induced shape change in the FSA hexagonal wrapper tube with various speeds of the radiation-induced swelling and the radiation-induced creep moduli is performed. The calculations results and the results of FSAs post-irradiation dimension inspection are compared. Recommendations for use of the proposed models aimed at performing calculations, as well as estimating the radiation-induced shape change and defining the stress-strained state of FSAs are made.


Sign in / Sign up

Export Citation Format

Share Document