Mathematical model for the plastic flow of a polycrystalline material medium

2011 ◽  
Vol 65 (12) ◽  
pp. 1053-1056 ◽  
Author(s):  
Miguel Lagos ◽  
Víctor Conte
Keyword(s):  
Mathematical Model ◽  
Plastic Flow ◽  
Polycrystalline Material ◽  
Material Medium

scholarly journals Plastic Deformation of Metal Tubes Subjected to Lateral Blast Loads

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Kejian Song ◽  
Yuan Long ◽  
Chong Ji ◽  
Fuyin Gao
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Plastic Flow ◽  
Cross Section ◽  
Circular Tube ◽  
Circular Tubes ◽  
Simply Supported ◽  
Different Dimensions ◽  
Thin Walled ◽  
Wave Induced

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.

scholarly journals Three-dimensional birefringence imaging with a microscope tilting stage. II. Biaxial crystals

2006 ◽  
Vol 39 (6) ◽  
pp. 856-870 ◽  
Author(s):  
L. A. Pajdzik ◽  
A. M. Glazer
Keyword(s):  
Mathematical Model ◽  
Polycrystalline Material ◽  
Three Dimensional ◽  
Crystalline Material ◽  
Optical Orientation ◽  
Specific Group ◽  
Crystalline Materials ◽  
Comprehensive Information ◽  
Stage System ◽  
Biaxial Materials

The technique enables precise three-dimensional birefringence information of optically biaxial materials to be obtained. Equations derived here describe a mathematical model of the tilting-stage system for such crystals in any general orientation. This leads to precise values of the three principal birefringences and the optical orientation. The method is also able to obtain information on preferred orientation in a biaxial polycrystalline material, providing comprehensive information on both optical orientation of crystallites and spatial resolution. In addition, an unknown crystalline material may be identified, or at least classified within a specific group of crystalline materials.

A mathematical model for generating microplastic hysteresis loops

1968 ◽  
Vol 3 (1) ◽  
pp. 50-56 ◽  
Author(s):  
A Esin ◽  
W J D Jones
Keyword(s):  
Mathematical Model ◽  
Cyclic Loading ◽  
Total Energy ◽  
Yield Point ◽  
Plastic Flow ◽  
Elastic Limit ◽  
Hysteresis Loops ◽  
Elastic Region ◽  
Proportional Limit ◽  
Cycles To Failure

A method is suggested for defining the extent of the microplasticity which can exist in a material at stresses between the ‘true elastic limit’ and the nominal yield point or proportional limit. The suggested mathematical model makes it possible to extrapolate the macroscopic plastic equation into the elastic region in order to take account of the localized nature of the plastic flow. This analysis can be used to calculate the microplastic hysteresis energy absorbed per cycle by a material under cyclic loading and with a knowledge of the total energy to fracture can be used to predict the number of fatigue cycles to failure; an example is given.

Research on Model of Plastic Flow Heat Transfer during Linear Friction Welding for Low Melting Point Metal

2013 ◽  
Vol 395-396 ◽  
pp. 1082-1086
Author(s):  
Yong Zhang ◽  
Tao Zhang ◽  
Guo Dong Wen ◽  
Tie Jun Ma
Keyword(s):  
Heat Transfer ◽  
Mathematical Model ◽  
Melting Point ◽  
Plastic Zone ◽  
Plastic Flow ◽  
Friction Welding ◽  
Linear Friction Welding ◽  
Linear Friction ◽  
Lead Metal ◽  
Flow Heat

With the self-developed physical simulation equipment of linear friction welding, the plastic flow heat transfer simulation experiment of low melting point Lead metal was implemented. A physical model of plastic flow heat transfer of linear friction welding low melting point metal was established based on the process of the Lead metal plastic flow recorded by high speed digital camera and the Lead metal temperature variation recorded by infrared thermal imager. Introducing the plastic flow element into one-dimensional unsteady heat transfer differential equation, heat transfer mathematical model of plastic zone, perpendicular to the direction of vibration, was proposed. Using finite difference method to solve this mathematical model, calculated value of this model and measured temperature was compared. The results show that the two values correspond basically, which indicates that the proposed model could be used to characterize the process of heat transfer of plastic zone during linear friction welding low melting point metal.

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].

A Mathematical Model for the Mixed Lubrication of Non-Conformable Contacts With Asperity Friction, Plastic Deformation, Flash Temperature, and Tribo-Chemistry

2014 ◽  
Vol 136 (2) ◽  
Author(s):  
L. Chang ◽  
Yeau-Ren Jeng
Keyword(s):  
Mathematical Model ◽  
Plastic Flow ◽  
Fluid Pressure ◽  
Elastohydrodynamic Lubrication ◽  
Mixed Lubrication ◽  
Flash Temperature ◽  
Power Intensity ◽  
Mixed Regime ◽  
Asperity Contacts ◽  
Mixed Lubrication Regime

A mathematical model is presented in this paper for rolling-sliding contacts operating in a mixed regime of elastohydrodynamic lubrication and boundary lubrication. The model is based on the framework of Johnson et al. (1972, “A Simple Theory of Asperity Contacts in Elastohydrodynamic Lubrication,” Wear, 19, pp. 91–108). It incorporates into this framework a number of important asperity-level variables including asperity friction, friction-induced plastic flow, flash temperature, and boundary-film tribo-chemistry. The model yields a number of variables useful for the assessment of the state of the mixed lubrication. They include the load sharing between fluid and asperities, area of asperity contacts, and fraction area of asperity contacts undergoing plastic flow along with experimentally measurable variables such as the traction coefficient, friction power intensity, and temperature of the overall contact. The model is limited to mixed-lubrication problems in which the load is mainly carried by the fluid pressure and the total area of asperity contacts is a small percentage of the Hertz area. Further development is possible to formulate a model into a wider mixed-lubrication regime using some modeling concepts developed in this paper in conjunction with other modeling techniques.

Atomic orientation effects in proton stopping at low velocity

1983 ◽  
Vol 41 ◽  
pp. 708-709
Author(s):  
Kin Lam
Keyword(s):  
Polycrystalline Material ◽  
Charged Particles ◽  
Target Material ◽  
Stopping Power ◽  
Low Velocity ◽  
Electronic Density ◽  
Interatomic Distances ◽  
Frame Work ◽  
Image Position ◽  
Atomic Orientation

The energy of moving ions in solid is dependent on the electronic density as well as the atomic structural properties of the target material. These factors contribute to the observable effects in polycrystalline material using the scanning ion microscope. Here we outline a method to investigate the dependence of low velocity proton stopping on interatomic distances and orientations.The interaction of charged particles with atoms in the frame work of the Fermi gas model was proposed by Lindhard. For a system of atoms, the electronic Lindhard stopping power can be generalized to the formwhere the stopping power function is defined as

Determination of creep mechanisms in various silicon carbides via TEM

1986 ◽  
Vol 44 ◽  
pp. 484-487
Author(s):  
C. H. Carter ◽  
J. E. Lane ◽  
J. Bentley ◽  
R. F. Davis
Keyword(s):  
Heat Exchangers ◽  
Sintered Material ◽  
Polycrystalline Material ◽  
Chemical Vapor ◽  
Graphite Substrate ◽  
Second Phase ◽  
Reaction Bonding ◽  
Creep Mechanisms ◽  
Porous Sic

Silicon carbide (SiC) is the generic name for a material which is produced and fabricated by a number of processing routes. One of the three SiC materials investigated at NCSU is Norton Company's NC-430, which is produced by reaction-bonding of Si vapor with a porous SiC host which also contains free C. The Si combines with the free C to form additional SiC and a second phase of free Si. Chemical vapor deposition (CVD) of CH3SiCI3 onto a graphite substrate was employed to produce the second SiC investigated. This process yielded a theoretically dense polycrystalline material with highly oriented grains. The third SiC was a pressureless sintered material (SOHIO Hexoloy) which contains B and excess C as sintering additives. These materials are candidates for applications such as components for gas turbine, adiabatic diesel and sterling engines, recouperators and heat exchangers.

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