A New Approach to Model Heterogonous Recrystallization Kinetics Based on the Natural Inhomogeneity of Deformation

2007 ◽  
Vol 558-559 ◽  
pp. 1139-1144 ◽  
Author(s):  
Hai Wen Luo ◽  
Lian Zi An ◽  
Hong Wei Ni
Keyword(s):  
Standard Deviation ◽  
Normal Distribution ◽  
Strain Distribution ◽  
Distribution Density ◽  
Local Strain ◽  
Avrami Exponent ◽  
Recrystallization Process ◽  
Rate Parameter ◽  
New Approach ◽  
Modified Equation

The classical JMAK equation was modified by combination with distribution density of the rate parameter k, which was deduced from a normal distribution of local strain. The modified equation is able to calculate the JMAK plots and the average Avrami exponent to characterize the entire heterogeneous recrystallization process. This new extension can successfully describe the relevant experimental observations, such as a smaller exponent than the basic JMAK theory predicts, and a decreasing slope of JMAK plots with the proceeding recrystallization. Moreover, it reveals that the Avrami exponent observed experimentally should significantly decrease with the increasing standard deviation of local strain distribution. In addition, it has a great potential to explain why most of experimentally observed values of Avrami exponents are less than 2 and why the Avrami exponent is insensitive to temperature and deformation conditions when the real standard deviation of local strain distribution in deformed metals is known.

scholarly journals Strain distribution due to surface domains: a self-consistent approach with respect to surface elasticity

2015 ◽  
Vol 6 ◽  
pp. 321-326 ◽  
Author(s):  
Javier Fuhr ◽  
Pierre Müller
Keyword(s):  
Integral Equation ◽  
Strain Field ◽  
Strain Distribution ◽  
Surface Elasticity ◽  
Local Strain ◽  
New Approach ◽  
Self Consistent ◽  
Point Forces ◽  
Surface Domains ◽  
Consistent Approach

Elastically mediated interactions between surface domains are classically described in terms of point forces. Such point forces lead to local strain divergences that are usually avoided by introducing a poorly defined cut-off length. In this work, we develop a self-consistent approach in which the strain field induced by the surface domains is expressed as the solution of an integral equation that contains surface elastic constants, S ij . For surfaces with positive S ij the new approach avoids the introduction of a cut-off length. The classical and the new approaches are compared in case of 1-D periodic ribbons.

scholarly journals Local Strain Distribution in ZnO Microstructures Visualized with Scanning Nano X‐Ray Diffraction and Impact on Electrical Properties

2021 ◽  
pp. 2100201
Author(s):  
Philipp Jordt ◽  
Stjepan B. Hrkac ◽  
Jorit Gröttrup ◽  
Anton Davydok ◽  
Christina Krywka ◽  
...  
Keyword(s):  
Electrical Properties ◽  
Strain Distribution ◽  
Local Strain ◽  
X Ray Diffraction ◽  
X Ray

scholarly journals Design of a New Synthetic Acceptance Sampling Plan

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 653 ◽  
Author(s):  
Saeed Dobbah ◽  
Muhammad Aslam ◽  
Khushnoor Khan
Keyword(s):  
Standard Deviation ◽  
Normal Distribution ◽  
Operating Characteristic ◽  
Linear Optimization ◽  
Sampling Plan ◽  
Quality Characteristic ◽  
Acceptance Sampling ◽  
Acceptance Sampling Plan ◽  
Non Linear

In this paper, we propose a new synthetic sampling plan assuming that the quality characteristic follows the normal distribution with known and unknown standard deviation. The proposed plan is given and the operating characteristic (OC) function is derived to measure the performance of the proposed sampling plan for some fixed parameters. The parameters of the proposed sampling plan are determined using non-linear optimization solution. A real example is added to explain the use of the proposed plan by industry.

Interpretation of the Standard Error of Measurement when True Scores and Error Scores on Mental Tests are Not Independent

1966 ◽  
Vol 19 (2) ◽  
pp. 611-617 ◽  
Author(s):  
Donald W. Zimmerman ◽  
Richard H. Williams
Keyword(s):  
Standard Deviation ◽  
Standard Error ◽  
Test Score ◽  
Test Reliability ◽  
True Score ◽  
Observed Score ◽  
Standard Error Of Measurement ◽  
True Scores ◽  
Modified Equation ◽  
Error Of Measurement

It is shown that for the case of non-independence of true scores and error scores interpretation of the standard error of measurement is modified in two ways. First, the standard deviation of the distribution of error scores is given by a modified equation. Second, the confidence interval for true score varies with the individual's observed score. It is shown that the equation, so=√[(N−O/a]+[so2(roō−roo)/roō]̄, where N is the number of items, O is the individual's observed score, a is the number of choices per item, so2 is observed variance, roo is test reliability as empirically determined, and roō is reliability for the case where only non-independent error is present, provides a more accurate interpretation of the test score of an individual.

scholarly journals Verification of normal distribution of welding distortions

2019 ◽  
Vol 91 (3) ◽  
Author(s):  
Damian Grzesiak ◽  
Jarosław Plichta
Keyword(s):  
Statistical Analysis ◽  
Standard Deviation ◽  
Normal Distribution ◽  
Sheet Metal ◽  
Welding Process ◽  
Experiment Planning ◽  
Geometrical Parameters ◽  
Butt Welds ◽  
Planning Methods ◽  
Smirnov Test

The aim of this paper is to answer the question of the distribution of welding distortions. The MIG method was used to make 31 butt welds of 0H18N9 sheet metal, of 6 mm thickness and dimensions 150x350 mm. All joints are made with constant parameters of the welding process. Statistical analysis of the distribution and Kolomogorov-Smirnov test were used in this paper. On the grounds of the analysis it was proved that the distribution of welding deformations is a normal distribution. This justifies the use of experiment planning methods and the use of average values. The relatively high value of the standard deviation makes it necessary to take into account the geometrical parameters of the joint.

scholarly journals Multiple Linear Regressions by Maximizing the Likelihood under Assumption of Generalized Gauss-Laplace Distribution of the Error

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Lorentz Jäntschi ◽  
Donatella Bálint ◽  
Sorana D. Bolboacă
Keyword(s):  
Normal Distribution ◽  
Linear Models ◽  
Linear Regression Analysis ◽  
Likelihood Estimation ◽  
Real Data ◽  
Multiple Linear Regression Analysis ◽  
Laplace Distribution ◽  
New Approach ◽  
Feature Information ◽  
Linear Regressions

Multiple linear regression analysis is widely used to link an outcome with predictors for better understanding of the behaviour of the outcome of interest. Usually, under the assumption that the errors follow a normal distribution, the coefficients of the model are estimated by minimizing the sum of squared deviations. A new approach based on maximum likelihood estimation is proposed for finding the coefficients on linear models with two predictors without any constrictive assumptions on the distribution of the errors. The algorithm was developed, implemented, and tested as proof-of-concept using fourteen sets of compounds by investigating the link between activity/property (as outcome) and structural feature information incorporated by molecular descriptors (as predictors). The results on real data demonstrated that in all investigated cases the power of the error is significantly different by the convenient value of two when the Gauss-Laplace distribution was used to relax the constrictive assumption of the normal distribution of the error. Therefore, the Gauss-Laplace distribution of the error could not be rejected while the hypothesis that the power of the error from Gauss-Laplace distribution is normal distributed also failed to be rejected.

A Simple Method for Estimating the Parameters of the Beta Distribution Applied to Modeling Uncertainty in Gas Turbine Inlet Temperature

2002 ◽  
Author(s):  
Frederic A. Holland
Keyword(s):  
Standard Deviation ◽  
Conventional Method ◽  
Beta Distribution ◽  
Conventional Approach ◽  
Algebraic Solution ◽  
Inlet Temperature ◽  
Shape Parameters ◽  
Simple Method ◽  
New Approach ◽  
A Value

The beta distribution is a particularly convenient model for random variables when only the minimum, maximum and most likely values are available. It is also very useful for estimating the mean and standard deviation given this information. In this paper a simple method is proposed to estimate the beta parameters from these three values. The proposed method has advantages over the conventional approach. In the conventional approach, the four parameters of the beta distribution are determined from only three values by assuming a standard deviation that is one-sixth the range. In contrast, the new method assumes a value for one of the beta shape parameters based on an analogy with the normal distribution. This new approach allows for a very simple algebraic solution of the beta shape parameters in contrast to the simultaneous solution required by the conventional method. The results of the proposed method are very similar to the conventional method. However, the proposed method generally gives a slightly higher (more conservative) estimate of the standard deviation when the distribution is skewed. In addition, the new approach allows the standard deviation to vary as the shape or skew of the distribution varies. Both methods were applied to modeling the probability distribution of temperature.

Characterization of Local Strain Distribution in Zircaloy-4 and M5® Alloys

2009 ◽  
pp. 181-181-12
Author(s):  
Kamal Elbachiri ◽  
Pascal Doumalin ◽  
Jéro^me Crépin ◽  
Michel Bornert ◽  
Pierre Barberis ◽  
...  
Keyword(s):  
Strain Distribution ◽  
Local Strain
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