scholarly journals Calculation of Yield Surfaces and Determination of Forming Limit Diagrams of Aluminium Alloys

1993 ◽  
Vol 21 (2-3) ◽  
pp. 93-108 ◽  
Author(s):  
J. J. Fundenberger ◽  
M. J. Philippe ◽  
C. Esling ◽  
P. Lequeu ◽  
B. Chenal
Keyword(s):  
Aluminium Alloys ◽  
Expansion Method ◽  
Strain Ratio ◽  
Orientation Distribution ◽  
Forming Limit ◽  
Deformation Model ◽  
Plastic Strain Ratio ◽  
Yield Loci ◽  
Series Expansion Method

In order to point out the influence of the crystallographic texture on the formability of 2 aluminium alloys, the orientation distribution function (ODF) will be carried out using the series expansion method. Combining the ODF with a Taylor plastic deformation model we are able to calculate the yield loci and to predict the plastic strain ratio which is of high interest in the formability.

scholarly journals A Positivity Method for the Determination of Complete Orientation Distribution Functions

1988 ◽  
Vol 10 (1) ◽  
pp. 21-35 ◽  
Author(s):  
M. Dahms ◽  
H. J. Bunge
Keyword(s):  
Expansion Method ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Positivity Condition ◽  
Odd Order ◽  
Pole Figures ◽  
Zero Range ◽  
Even Order ◽  
Series Expansion Method

A refinement of the zero-range method, a procedure to calculate the odd order coefficients in the series expansion method of texture analysis, is presented. The only assumption in this procedure is the positivity condition. In this respect, it is comparable to the quadratic method. Contrary to this method, however, the even order coefficients are not changed. No zero range in the pole figures and no shape of the existing texture is to be assumed.

scholarly journals Approximation of the Orientation Distribution of Grains in Polycrystalline Samples by Means of Gaussians

1992 ◽  
Vol 19 (1-2) ◽  
pp. 9-27 ◽  
Author(s):  
D. I. Nikolayev ◽  
T. I. Savyolova ◽  
K. Feldmann
Keyword(s):  
Rolling Texture ◽  
Expansion Method ◽  
Operating Mode ◽  
Orientation Distribution ◽  
New Method ◽  
Gaussian Distributions ◽  
Positivity Condition ◽  
The Central Limit Theorem ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) obtained by classical spherical harmonics analysis may be falsified by ghost influences as well as series truncation effects. The ghosts are a consequence of the inversion symmetry of experimental pole figures which leads to the loss of information on the “odd” part of ODF.In the present paper a new method for ODF reproduction is proposed. It is based on the superposition of Gaussian distributions satisfying the central limit theorem in the SO(3)-space as well as the ODF positivity condition. The kind of ODF determination offered here is restricted to the fit of Gaussian parameters and weights with respect to the experimental pole figures. The operating mode of the new method is demonstrated for a rolling texture of copper. The results are compared with the corresponding ones obtained by the series expansion method.

Formability and Correlation between Formability Indices of Al-0.9Mg-1.0Si-0.7Cu-0.6Mn Alloy for Automotive Body Sheets

2010 ◽  
Vol 638-642 ◽  
pp. 356-361 ◽  
Author(s):  
Ni Tian ◽  
Gang Zhao ◽  
Liang Zuo ◽  
Chun Ming Liu
Keyword(s):  
Solid Solution ◽  
Uniform Elongation ◽  
Annealing Treatment ◽  
Aging Treatment ◽  
Strain Ratio ◽  
Orientation Distribution ◽  
Distribution Functions ◽  
Strain Hardening Exponent ◽  
Plastic Strain Ratio ◽  
Automotive Body

The texture, the formability and the correlation between formability indices of Al-0.9Mg- 1.0Si-0.7Cu-0.6Mn alloy for automotive body sheets subjected to solid solution, T4, annealing treatment and artificial aging at 443k for different time were investigated by orientation distribution functions(ODF) analysis, tensile and cupping test, FLD measurement and regression analysis method. The results showed that the textures of cold rolled alloy sheets consist mainly of copper and brass orientations, which are transformed into the texture mainly containing {001}<310> orientation after recrystallization, and aging treatment has little influence on the recrystallization texture. The formability of alloy sheets subjected to solid solution, T4 and annealing treatment is similar, however, the formability was observably deteriorated after aging at 443k. The correlation between uniform elongation δu and FLD0 is the most remarkable in all the given formability indices, the correlation between strain-hardening exponent n and the FLD0 take second place, while there is no correlation between plastic strain ratio r and FLD0. The correlation between reduction of area ψ and cupping value IE is distinct, while ψ and IE have little correlation with FLD0.

Manual and Automatic Determination of the Plastic Strain Ratio

2013 ◽  
Vol 55 (6) ◽  
pp. 483-486
Author(s):  
András Bocz ◽  
Dénes Márkus ◽  
Zsolt Narancsik
Keyword(s):  
Plastic Strain ◽  
Strain Ratio ◽  
Automatic Determination ◽  
Plastic Strain Ratio

The Anisotropic Yield, Flow and Creep Behaviour of Pre-Strained En24 Steel

1975 ◽  
Vol 17 (2) ◽  
pp. 93-104 ◽  
Author(s):  
S. N. Shahabi ◽  
A. Shelton
Keyword(s):  
Internal Pressure ◽  
Creep Behaviour ◽  
Strain Ratio ◽  
Stress Axis ◽  
Cross Effect ◽  
Plastic Strain Ratio ◽  
Strain Components ◽  
Yield Behaviour ◽  
Yield Loci ◽  
The Cross

Tests under combinations of tension, torsion and internal pressure have been performed at constant stress ratio on En24 steel, previously annealed, and then subjected to a pre-stress in either axial or circumferential tension or torsion. Post-yield behaviour showed marked room-temperature creep by all strain components in the logarithmic form ε = a In t + c. The initial direction of the incremental plastic strain-ratio vector was markedly different from isotropic behaviour and remained constant in direction with time. Increased loading resulted in a progressive rotation towards the isotropic direction. Anisotropic yield loci were established from the normality rule and from the backward extrapolation of curves of creep coefficient versus stress and stress versus ‘long-time’ strain. The yield locus was translated to the pre-stress point and this local work-hardening was accompanied by softening in both the transverse and reverse directions, i.e. the cross-effect and Bauschinger effect respectively. Yield loci in planes not containing the pre-stress axis showed softening in all directions and under axial tension-internal pressure the cross-effect caused a rotation of the locus. All yield loci were smooth and continuous. Yield criteria derived from the theories of Edelman and Drucker and also Williams and Svensson were in good agreement with experiment over the whole locus. Hill's theory was thought to be more appropriate to material behaviour following large deformations.

The iterative series-expansion method for quantitative texture analysis. II. Applications

1992 ◽  
Vol 25 (2) ◽  
pp. 259-267 ◽  
Author(s):  
M. Dahms
Keyword(s):  
Distribution Function ◽  
Series Expansion ◽  
Expansion Method ◽  
Orientation Distribution ◽  
Polycrystalline Materials ◽  
Pole Density ◽  
General Outline ◽  
Positivity Condition ◽  
Pole Figures ◽  
Series Expansion Method

The orientation distribution function (ODF) of the crystallites of polycrystalline materials can be calculated from experimentally measured pole density functions (pole figures). This procedure, called pole-figure inversion, can be achieved by the series-expansion method (harmonic method). As a consequence of the (hkl)-({\bar h}{\bar k}{\bar l}) superposition, the solution is mathematically not unique. There is a range of possible solutions (the kernel) that is only limited by the positivity condition of the distribution function. The complete distribution function f(g) can be split into two parts, \tilde {f}(g) and \tildes {f}(q), expressed by even- and odd-order terms of the series expansions. For the calculation of the even part \tilde {f}(g), the positivity condition for all pole figures contributes essentially to an `economic' calculation of this part, whereas, for the odd part, the positivity condition of the ODF is the essential basis. Both of these positivity conditions can be easily incorporated in the series-expansion method by using several iterative cycles. This method proves to be particularly versatile since it makes use of the orthogonality and positivity at the same time. In the previous paper in this series [Dahms & Bunge (1989) J. Appl. Cryst. 22, 439–447] a general outline of the method was given. This, the second part, gives details of the system of programs used as well as typical examples showing the versatility of the method.

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