The Mathematical Model of the Relation among the Resistance, the Distortion Temperature and the Rate of the Steel in the Plastic Deformation

2012 ◽  
Vol 502 ◽  
pp. 184-188
Author(s):  
Hong Li ◽  
Xiao Lin You
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Tensile Strength ◽  
Basic Theory ◽  
Deformation Resistance ◽  
Deformation Degree ◽  
Plastic Processing ◽  
Hardening Curve ◽  
Fundamental Equations ◽  
The Mathematical Model

the hardening curve of the steel in the plastic deformation only considers the influence of the deformation degree on the resistance. This paper, according to the basic theory of plastic processing, proposes out the respective relation between the deformation resistance and the deformation degree, the temperature, as well as the rate. This paper gets the curves of these relations by experiments, summarizes the fundamental equations by simulation and finally deduces the plastic conditional equations relating to the material performance----the tensile strength.

Mathematical Model of Hot Deformation Resistance of X120 Pipeline Steel

2012 ◽  
Vol 538-541 ◽  
pp. 1724-1731
Author(s):  
Hong Wei Zheng ◽  
Di Tang ◽  
Hui Bin Wu ◽  
Liu Yang
Keyword(s):  
Mathematical Model ◽  
Deformation Rate ◽  
Deformation Temperature ◽  
Pipeline Steel ◽  
Deformation Resistance ◽  
Effect Of Temperature ◽  
Temperature Deformation ◽  
Test Machine ◽  
Deformation Degree ◽  
The Mathematical Model

The high-temperature deformation resistance of X120 pipeline steel was studied under different deformation temperature and different deformation rate through the hot compression test on the Gleeble-3500 thermal/mechanics simulation test machine. The influence of deformation degree, deformation temperature and deformation rate on deformation resistance was thoroughly investigated. The deformation resistance of X120 pipeline steel increased slowly when deformation degree was higher than 0.2. With the increase of deformation temperature, the work-hardening effect was weakened, so the deformation resistance decreased. And the deformation rate had dual influences on the deformation resistance, including the effect of temperature and time. Based on the experiment data, the parameters in the mathematical model were regressed by using SPSS (Statistic Package for Social Science), and the mathematical model of the deformation resistance of X120 pipeline steel was established finally. Through the regression analysis, the model had been proved to have great matching precision.

Mathematical Model and Program Development for the Efficient Process Conditions Determination during FeC0.15Cr12Ni2 Steel Diamond Smoothing

2016 ◽  
Vol 684 ◽  
pp. 477-482 ◽  
Author(s):  
Aleksei Nicolaevich Shvetcov ◽  
Dmitrii Leonidovich Skuratov
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Surface Layer ◽  
Program Development ◽  
Synthetic Diamond ◽  
Process Conditions ◽  
Deformation Degree ◽  
Efficient Process ◽  
The Mathematical Model

In this paper the mathematical model and the program based on this model for efficient process conditions during a diamond smoothing is introduced. The mathematical model has been tested with heatproof martensite category steel FeC0.15Cr12Ni2 by the synthetic diamond DSB-1 using as a smoothing tool. The mathematical model takes into account plastic deformation degree which could have both smoothing and reinforcing nature. Through the smoothing conditions the surface has a microroughnesses crumpling but reinforcing conditions involve also surface layer microhardness increasing.

scholarly journals Mathematical Modeling of the Fracture Toughness of Phenol Formaldehyde Composites Reinforced with E-Spheres

2009 ◽  
Vol 79-82 ◽  
pp. 1165-1168
Author(s):  
H. Ku ◽  
W. Xiang ◽  
N. Pattarachaiyakoop
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Fracture Toughness ◽  
Tensile Strength ◽  
Polynomial Interpolation ◽  
Phenol Formaldehyde ◽  
Simple Mathematical Model ◽  
The Mathematical Model ◽  
Conventional Oven ◽  
Lagrange’S Method

The fracture toughness of SLG filled phenolic composites have been determined by short bar tests. It is expensive to prepare the samples for the tests. Therefore, it is necessary to develop a mathematical model that will predict the fracture toughness of particulate filled phenolic composites. Mathematical models for tensile strength, Young’s modulus are available but not for impact strength and fracture toughness. There is no sign that it can be built up from simple mathematical model; polynomial interpolation using Lagrange’s method was therefore employed to generate the fracture toughness model using the data obtained from experiments. From experiments, it was found that the trend of the fracture toughness of the samples cured conventionally was similar to that cured in microwaves; it is therefore possible to predict the fracture toughness of the samples cured in microwaves from shifting the mathematical model generated for fracture toughness of samples post-cured in conventional oven. The shifted model represented the fracture toughness of the samples cured in microwaves vey well.

Chaotic Phenomena Induced by the Fast Plastic Deformation of Metals During Cutting

2005 ◽  
Vol 73 (2) ◽  
pp. 240-245 ◽  
Author(s):  
Zoltan Palmai
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Shear Stress ◽  
General Structure ◽  
Equation System ◽  
Qualitative Description ◽  
Balance Equations ◽  
Different Types ◽  
Energy Equations ◽  
The Mathematical Model

In the present study the examination of chip formation is focused on the primary shear zone, which is divided into two layers, and the variation of shear stress and temperature in time are given by two mechanical balance equations and three energy equations. All the five evolution differential equations are autonomous and nonlinear. The material characteristics are determined by an exponential constitutive equation. The mathematical model is suitable for the qualitative description of different types of chips, such as continuous chips and periodic or aperiodic shear localized chips, which is demonstrated by the general structure and typical solutions of the equation system.

An Application for Analysis of Temperature during Cold Rolling

2013 ◽  
Vol 199 ◽  
pp. 131-136
Author(s):  
Olena Yevtushenko
Keyword(s):  
Mathematical Model ◽  
Plastic Deformation ◽  
Temperature Field ◽  
Numerical Analysis ◽  
Cold Rolling ◽  
Partition Ratio ◽  
Transient Temperature ◽  
Heat Partition ◽  
Transient Temperature Field ◽  
The Mathematical Model

The problem of software creation for the analysis of transient temperature field in cold rolling of metals is under consideration. Firstly, the mathematical model of the process of heating the strip and rolls at cold rolling it is proposed. This model assumes that the generation of heat during the rolling takes place due to friction on the contact surface of the rolls and the strip as well as plastic deformation of the strip material. Next, some fragments of created application for the purpose of an overall numerical analysis of heat partition ratio between the rolls and a strip as well as the temperature in any point of these elements are presented.

scholarly journals Mathematical modeling of plastic deformation of a tube from dispersion-hardened aluminum alloy

2018 ◽  
Vol 243 ◽  
pp. 00008 ◽  
Author(s):  
Oleg Matvienko ◽  
Olga Daneyko ◽  
Tatyana Kovalevskaya
Keyword(s):  
Mathematical Modeling ◽  
Mathematical Model ◽  
Plastic Deformation ◽  
External Pressure ◽  
Dislocation Loops ◽  
Balance Equations ◽  
Deformable Solid ◽  
Deformation Defects ◽  
Resistance Decrease ◽  
The Mathematical Model

The influence of the internal and external pressure subjected to the tube from dispersion-hardened aluminium alloy was investigated. The approach which combines methods of crystal plasticity and mechanics of deformable solid was used to explore the limits of elastic and plastic resistance. The mathematical model of plastic deformation includes balance equations for deformation defects with regard to the generation and annihilation of shear dislocations, vacancy and interstitial prismatic dislocation loops, and dislocations in dipole configurations of vacancy and interstitial types and also equilibrium equation, geometrical and physical relations between the deformations, displacements and stresses. It has been established that as the temperature increases, the limits of the elastic and plastic resistance decrease. Results of investigation demonstrate that the hardening the alloy by nanoparticles significantly improves the strength characteristics of the material.

Establishment of Flow Stress Model of EW75 Alloy

2013 ◽  
Vol 423-426 ◽  
pp. 241-246
Author(s):  
Ming Long Ma ◽  
Kui Zhang
Keyword(s):  
Mathematical Model ◽  
Flow Stress ◽  
Magnesium Alloy ◽  
Strain Rate ◽  
Strain Rate Range ◽  
Strain Rates ◽  
Stress Strain ◽  
Deformation Degree ◽  
Maximum Deformation ◽  
The Mathematical Model

The behavior evolvement of Mg-7.22Gd-4.84Y-1.26Nd-0.58Zr (EW75) magnesium alloy during the hot deformation process was discussed. The flow stress behavior of magnesium alloy over the strain rate range 0.002s-1to 2s-1and the temperature range 623K to 773K had been researched on Gleeble-1500D hot simulator under the maximum deformation degree 60%. A mathematical model was established to predict the stress-strain curves of this alloy during deformation. The experimental results showed that the stress-strain curves were obviously affected by the strain rates and deformation temperatures. The mathematical model could predict the stress-strain curves when the strain rates were under 0.2-1, but there was significant error in some of stress-strain curves when the strain-rate was 2-1by the reason of deformation temperature rising.

Research on the Separation Performance of Deoiling Hydrocyclones

2014 ◽  
Vol 608-609 ◽  
pp. 14-18
Author(s):  
Jun Wang
Keyword(s):  
Mathematical Model ◽  
Optimization Design ◽  
Basic Theory ◽  
Separation Performance ◽  
Separation Mechanism ◽  
Convection Diffusion ◽  
Optimization Principle ◽  
Partition Method ◽  
Coupling Algorithm ◽  
The Mathematical Model

This paper uses FLUENT as the researching tools of 3D numerical simulation of deoiling hydrocyclones, analysis on the geometric structure of deoiling Hydrocyclone, summed up a set of grid partition method based on the basic theory and turbulence simulation of CFD theory, to determine a reasonable mathematical model, boundary conditions, convection diffusion the discrete format and pressure velocity coupling algorithm. This paper establishes the mathematical model, calculation method and the optimization principle for the separation mechanism; it also provides basic theory and experience for studying on deoiling hydrocyclone such as separation mechanism, flow and turbulent scalar field characteristics and structure optimization design.

A New Method of Data Pre-Processing to Two-Way Satellite Time and Frequency Transfer Experiments

2013 ◽  
Vol 718-720 ◽  
pp. 1316-1323
Author(s):  
Chang He Wang ◽  
Wei Chao Li ◽  
Ji Kun Ou ◽  
Xu Hai Yang
Keyword(s):  
Mathematical Model ◽  
Simulated Data ◽  
Measured Data ◽  
Basic Theory ◽  
New Method ◽  
Accurate Detection ◽  
Frequency Transfer ◽  
The Mathematical Model

Based on the basic theory of two-way satellite time and frequency transfer (TWSTFT), the mathematical model on real errors of observations is established in this paper. However, the model is rank-deficient. In order to solve this problem effectively, the paper introduces the algorithm of combining parameters, and applies Quasi-Accurate Detection of Gross Errors (QUAD) proposed in reference [ to data pre-processing. The method programs opportune algorithms and resolves the problem of detecting gross errors. In the end, the method has been verified to be successful by calculating and analysing simulated data and practical measured data.

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