Mathematical Model for Super Plastic Flow in Advanced Structural Materials

2007 ◽  
Vol 551-552 ◽  
pp. 67-72
Author(s):  
Juan Daniel Muñoz-Andrade
Keyword(s):  
Activation Energy ◽  
Mathematical Model ◽  
Plastic Flow ◽  
Planck Scale ◽  
Mathematical Expression ◽  
Frequency Factor ◽  
Structural Materials ◽  
Strong Temperature Dependence ◽  
Super Plastic ◽  
The Universe

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].

On the Phenomenology and Mechanics of Super Plastic Flow in Advanced Structural Materials

2007 ◽  
Vol 551-552 ◽  
pp. 147-152 ◽  
Author(s):  
Juan Daniel Muñoz-Andrade
Keyword(s):  
Plastic Flow ◽  
Structural Materials ◽  
Planck Length ◽  
Burgers Vector ◽  
Accelerated Motion ◽  
Spatially Extended ◽  
Super Plastic ◽  
Newtonian Constant ◽  
The Universe ◽  
Recession Velocity

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].

scholarly journals CO2 Gasification Kinetics of Shenhua Bituminous Coal by Isothermal Thermo-Gravimetric Analysis

2020 ◽  
Author(s):  
Jinzhi Zhang ◽  
Zhiqi Wang ◽  
Ruidong Zhao ◽  
Jinhu Wu
Keyword(s):  
Activation Energy ◽  
Bituminous Coal ◽  
Thermo Gravimetric Analysis ◽  
Correlation Coefficients ◽  
Mathematical Expression ◽  
Frequency Factor ◽  
Gravimetric Analysis ◽  
Thermo Gravimetric ◽  
Kinetics Of ◽  
Compensation Relationship

Abstract This research performed the gasification kinetics of three Shenhua coal under CO2 atmosphere using isothermal thermogravimetry. Results showed that isothermal gasification curves for three different coal samples revealed different gasification behaviour. Among the eleven kinetic models, A2 was the most suitable one to describe the gasification kinetics of three coal samples, because it can reproduce the experimental data very well with reasonable correlation coefficients. The activation energy for sample A, B and C were 95.9, 79.1, and 69.4 kJ mol-1, respectively. The activation energy decreased with the increase of the particle size. The compensation relationship was observed between activation energy and frequency factor, and the mathematical expression was lnA=0.1041 E+0.54028 with the correlation coefficients of 0.999.

scholarly journals Asymptotic Approximations to the Isothermal Pyrolysis of Deodara Leaves using Gamma Distribution

2017 ◽  
Vol 22 (3) ◽  
pp. 263 ◽  
Author(s):  
Alok Dhaundiyal ◽  
Suraj Singh
Keyword(s):  
Activation Energy ◽  
Mathematical Model ◽  
Gamma Distribution ◽  
Numerical Solutions ◽  
Reaction Order ◽  
Frequency Factor ◽  
Asymptotic Approximations ◽  
Distributed Activation Energy Model ◽  
Upper Limit ◽  
The Mathematical Model

The main aim of th is paper pivote d ar ound th e influence of some parameters relev ant to biomass pyrolys is on the numerical solutions of the nth order distributed activation energy model (DAEM) using the Gamma distribution. The upper limit of ‘dE’ integral, frequency factor, reaction order, and the shape and rate parameters of the Gamma distribution are investigated. Analys is of the mathematical model is done with the help of asymptotic expansion.

Influence of Grain Size and Thermo-Mechanical Conditions on the Activation Energy for Super Plastic Flow in Ti-6Al-4V Alloy

2018 ◽  
Vol 941 ◽  
pp. 1210-1215
Author(s):  
Juan Daniel Muñoz-Andrade
Keyword(s):  
Activation Energy ◽  
Grain Size ◽  
Grain Boundary ◽  
Plastic Flow ◽  
Power Dissipation ◽  
Direct Determination ◽  
Grain Boundary Sliding ◽  
Advanced Materials ◽  
Super Plastic ◽  
Boundary Sliding

The essential objective of this work is to establish the influence of grain size and thermo-mechanical conditions on the activation energy for super plastic flow (QSPF) in Ti-6Al-4V alloy by applying the quantum mechanics and relativistic model (QM-RM) proposed by Muñoz-Andrade, in the framework of the unified physics. The QM-RM allows the direct determination of the QSPF in advanced materials at instantaneous thermo-mechanical material working conditions. By applying, the QM-RM on the experimental results reported previously by some authors, it is shown for grain size of 6.1μm, that the calculated QSPF for grain boundary sliding is about 193 and 178 kJ/mol, at 850°C with an efficiency of power dissipation, η=0.65. These results are in closed agreement with the values of 204 and 174 kJ/mol reported previously for grain boundary self-diffusion energy of α-Ti. Nevertheless, for grain size of 0.6μm the calculated QSPF is 142 kJ/mol at 650°C, with an efficiency of power dissipation, η=0.61. As well, in order to understand the phenomenology and mechanics of SPF in Ti-6Al-4V alloy, the variation of the activation energy with the temperature; stress and strain rate is analyzed in association with coupled mechanisms during SPF, such as grain boundary sliding, cooperative grain boundary sliding and self-accommodation process related to the microstructure. In summary, the results of QSPF obtained in this work, by the QM-RM are in closed agreement with results reported previously by using the theoretical and conventional methodology set up by Mohamed and Langdon.

Super Plastic Flow and Cosmic Micromechanics

2007 ◽  
Vol 345-346 ◽  
pp. 577-580 ◽  
Author(s):  
Juan Daniel Muñoz-Andrade
Keyword(s):  
Dark Matter ◽  
Dark Energy ◽  
Plastic Flow ◽  
Volume Fraction ◽  
Relativistic Cosmology ◽  
Clusters Of Galaxies ◽  
Spatially Extended ◽  
Super Plastic ◽  
New Interpretation ◽  
The Universe

A unified interpretation of super plastic flow (SPF) and cosmic micromechanics in spatially extended single and polycrystalline systems (SESPS) allows determined that the nature of the hyperbolic granular flow in SESPS is assisted by the movement of dislocations as the pattern of the inner dimension flow. Consequently in this work a mathematical model related with relativistic cosmology and quantum mechanics is used in order to obtain the activation energy for super plastic flow in SESPS. This correspondence law between SPF and cosmic micromechanics is important in the light of recent cosmological theories of the existence of dark matter and dark energy in the cosmic structure, because in this new interpretation of the universe the planets, stars, galaxies, clusters of galaxies, etc., are considered as precipitates on dislocations in the cosmic structure, which is formed in a nature way by the dark matter and dark energy, in a similar form of precipitates on dislocations in a SESPS of metals. Physically in this context the expansion process of the universe is highly dependent upon the volume fraction, size and distribution of precipitates on dislocations in the cosmic structure. Therefore, in this work the main results obtained in cosmic micromechanics and cosmic macromechanics are related with the Max Planck’s scale (MPE) and Edwin Hubble’s scale (EHS) respectively.

Unification of Physics during Super Plastic Flow in Advanced Materials

2016 ◽  
Vol 838-839 ◽  
pp. 78-83 ◽  
Author(s):  
Juan Daniel Muñoz-Andrade
Keyword(s):  
Activation Energy ◽  
Grain Boundary ◽  
Plastic Flow ◽  
Grain Boundary Sliding ◽  
Dislocation Dynamics ◽  
Advanced Materials ◽  
Direct Evaluation ◽  
Super Plastic ◽  
Boundary Sliding ◽  
Material Forming

In the framework connected with the unification of physics, the activation energy for super plastic flow in advanced materials has been obtained by applying the new quantum mechanics and relativistic model proposed by Muñoz-Andrade. This new model allows the direct evaluation of the activation energy for super plastic flow at instantaneous thermo-mechanical material forming conditions. Also, in order to establish the phenomenology and mechanics of super plastic flow, the dependence on strain rate and phase velocity de Broglie is obtained, for the reason that the nature wavelength of the cellular dislocations is essential in the association with coupled mechanisms during super plastic flow, such as grain boundary sliding, cooperative grain boundary sliding and self-accommodation process. In conclusion, cellular dislocation dynamics is a nature mechanism during super plastic flow in advanced materials. The results obtained in this work are in a closed agreement with results reported previously.

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