Earing in the cup drawing of sheet metals is calculated quantitatively using a crystallographical theory with measured texture data. In the analysis a polycrystalline sheet is simplified to be an aggregate of many single crystals with various orientations, and a crystallite orientation distribution function which is calculated from the measured texture is used as a volume fraction of a certain oriented crystal. The circumferential distribution of radial strain in a flange of a blank being drawn is calculated by considering a restricted glide in a crystal, and then cup height at each
peripheral position of a drawn cup is calculated from this distribution of radial strain. For an aluminium, a copper and two steel sheets the calculated cup profiles are compared with experimental ones under various drawing conditions of dimension of a punch, a die and a blank. The result shows that earing in the drawn cup can be
predicted satisfactorily by the present calculation for a wide range of drawing conditions and materials.

Naoyuki Kanetake

Yasuhisa Tozawa

Crystallographical Calculation of Earing in Deep Drawing under Various Conditions

From a classification of crystal symmetries involved in texture analysis we define a set of (low) crystal symmetries that can be similarly managed in the same computer program, using the harmonic method. A way of calculating the texture from incomplete pole figures is then proposed. Results are reported for two examples with
hexagonal and trigonal crystal symmetry, respectively, and advantages and limitations of such texture analyses are discussed.

F. Wagner

M. Humbert

Texture Analysis From Incomplete Pole Figures in Low Symmetry Cases

This article describes the development of an X-ray texture analyzer that can be used for continuous on-line inspection of cold rolled steel.

Hermann-Josef Kopineck

Heiner Otten

Texture Analyzer for On-Line <svg style="vertical-align:-3.3907pt" height="11.9625" version="1.1" viewBox="0 0 17.3125 11.9625" width="17.3125" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,7.675)"><path id="x1D45F" d="M393 379q-9 -16 -28 -29q-15 -10 -23 -2q-19 19 -36 19q-21 0 -52 -38q-57 -72 -82 -126l-40 -197q-23 -3 -75 -18l-7 7q49 196 74 335q7 43 -2 43q-7 0 -30 -14.5t-47 -37.5l-16 23q37 42 82 73t67 31q41 0 15 -113l-11 -50h4q41 71 85 117t77 46q29 0 45 -26&#xA;q13 -21 0 -43z" /></g><g transform="matrix(.012,-0,0,-.012,7.238,11.762)"><path id="x1D45A" d="M766 88q-40 -45 -83.5 -72.5t-63.5 -27.5q-39 0 -16 103l49 224q15 68 -10 68q-36 0 -112.5 -78.5t-105.5 -133.5q-27 -101 -38 -165q-35 -4 -77 -18l-6 6q42 153 70 288q12 55 10 78t-19 23q-38 0 -114 -80.5t-101 -131.5q-24 -68 -41 -165q-36 -3 -76 -18l-8 6&#xA;q56 202 87 347q7 33 -3 33q-8 0 -31.5 -17.5t-41.5 -35.5l-12 28q42 45 84 72t63 27q44 0 10 -124l-20 -75h2q92 121 193 178q36 21 64 21q62 0 28 -159l-8 -37h2q50 67 103.5 112t94.5 65q39 19 62 19q60 0 23 -156l-45 -189q-9 -39 2 -39q17 0 71 49z" /></g></svg>-Value Estimation

Peter R. Morris

Book Review

Charts are presented showing the cubic unit cell and tetrahedron for various simple orientations relative to the rolling plane and direction.

J. C. Casato

W. G. Fricke

Orientations of the Cubic Unit Cell and Tetrahedron

A new specimen holder is described which allows true area scanning of circular texture specimens. For large grain sized materials and geological samples this method can lead to a significant increase in the number of grains sampled and thus to more reliable texture measurements. The principle of operation is explained and a prototype apparatus described.

P. I. Welch

H. A. D. M. Cronj&#xE4;ger

H. J. Bunge

A New Translational Sample Holder for Reflection Polefigure Measurements

Several authors have proposed methods which use the Taylor&#x2013;Bishop&#x2013;Hill theory in order to calculate the yield surface of textured samples of which the O.D.F. is known.The purpose of this paper is to show how these methods can be generalized while keeping the computational effort within reasonable limits. It must be emphasized that the new method produces &#x201C;true&#x201D; plane sections of the yield locus instead of so-called &#x201C;principle strain yield loci.&#x201D;A theorem that permits the exploitation of the sample symmetry is demonstrated. After a general description of the method, it is explained how the theorem can be used in order to restrict the number of deformation modes that must be considered.The next section discusses how a data bank of Taylor factors can be constructed. The full-constraint Taylor theory as well as the relaxed Taylor theory are considered.In the next section, it is explained how the plane sections through the multidimensional yield locus are generated. A few applications are finally discussed, including a study of the elongation of a torsion sample of which the O.D.F. has been measured.

P. Van Houtte

Calculation of the Yield Locus of Textured Polycrystals Using the Taylor and the Relaxed Taylor Theory

The effect of differential carbon contents on recrystallisation and texture development has been studied using samples designed to have a known concentration profile. Dissolved carbon can play an active role both at the deformation and annealing stages. Textural changes are associated principally with enhancement of the nucleation rate for recrystallisation with increasing carbon contents. The {111} components become weaker and are replaced by widely scattered orientations. Interstitial carbon present during rolling gives rise to shear banding, causing a
further increase in nucleation rate during recrystallisation and an associated development of the Goss texture.

K. Ushioda

U. 
                    v. Schlippenbach

W. B. Hutchinson

The Effect of Carbon Content on Recrystallisation and Texture Development in Steel

Crystal plastic models are applied to textured Zircaloy in order to explain the recent experimental results on yield and creep loci by Suzuki <i>et al.</i> Crystallite orientation distribution functions were developed using texture pole figures obtained on cold-worked stress-relieved and recrystallized Zircaloy-4 tubings. The model predictions are in good agreement with experimental loci, and clearly point out the predominance of prism slip contribution for recrystallized material while the contribution of the basal slip increased as the amount of cold work increased.

K. Linga Murty

Ratnaji R. Kola

Sheikh T. Mahmood

Creep and Yield Loci of Zircaloy Cladding at Elevated Temperatures

Integrals of the type indicated can be evaluated using the Fourier-series development of the Jacobi-polynomials. An alternative procedure is given yielding an analytical expression in terms of <i>l, m</i> and <i>n</i>.

C. M. Brakman

Evaluation of the Integral <svg style="vertical-align:-5.78758pt" height="25.9" version="1.1" viewBox="0 0 171.2625 25.9" width="171.2625" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns="http://www.w3.org/2000/svg"><g transform="matrix(.017,-0,0,-.017,.062,18.637)"><path id="x222B" d="M480 853q0 -20 -13.5 -32.5t-34.5 -12.5q-19 0 -34.5 18t-27.5 18q-13 0 -21 -11.5t-13 -50.5t-4 -109l6 -574q6 -488 -183 -488q-28 0 -46.5 16t-18.5 38q0 19 14 32.5t33 13.5t40.5 -19t30.5 -19q14 0 21.5 12.5t11.5 48.5t4 103l-6 654q-1 201 46.5 305t138.5 104&#xA;q24 0 40 -13.5t16 -33.5z" /></g><g transform="matrix(.012,-0,0,-.012,9.75,7.613)"><path id="x2B" d="M535 230h-212v-233h-58v233h-213v50h213v210h58v-210h212v-50z" /></g><g transform="matrix(.012,-0,0,-.012,16.735,7.613)"><path id="x31" d="M384 0h-275v27q67 5 81.5 18.5t14.5 68.5v385q0 38 -7.5 47.5t-40.5 10.5l-48 2v24q85 15 178 52v-521q0 -55 14.5 -68.5t82.5 -18.5v-27z" /></g><g transform="matrix(.012,-0,0,-.012,9.75,25.838)"><path id="x2212" d="M535 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Cubic-orthorhombic texture functions (e.g., of rolling textures) are conventionally
represented by Euler diagrams with a range of 0&#xB0; to 90&#xB0; for <i>&#x3C6;</i><sub>1</sub>, &#x3A6; and <i>&#x3C6;</i><sub>2</sub>. Some drawbacks of this method are discussed. By means of inverse pole figure representations,
it is explained how this range can be subdivided into three completely equivalent &#x201C;unit zones&#x201D;. In order to overcome the drawbacks mentioned above, without adding yet a new type of O.D.F. representation to the list of those that already exist, it is proposed to continue using the same type of representation but to consider only unit zone 3, which is much less distorted than the two other unit zones. It is recommended to show the limits between the unit zones in the Euler diagrams.

On the Representation of Texture Functions of Cubic Metals in Euler Space

The calculation of orientation distribution functions (ODF) from incomplete pole figures can be carried out by an iterative procedure taking into account the positivity condition for all pole figures. This method strongly reduces instabilities which may occasionally occur in other methods.

M. Dahms

ODF Calculation by Series Expansion from Incompletely Measured Pole Figures Using the Positivity Condition Part I&#x2014;Cubic Crystal Symmetry

The textural development and flow stress have been determined in compression and tension of copper (99.999&#x25;). For strains below 1.4 (compression) and 1.0 (tension) the textural development is in qualitative agreement with Taylor-model predictions, i.e. a maximum concentration at the <mml:math id="E1" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>110</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> and <mml:math id="E2" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>111</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> + <mml:math id="E3" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mrow><mml:mo>&#x2329;</mml:mo><mml:mrow><mml:mn>100</mml:mn></mml:mrow><mml:mo>&#x0232A;</mml:mo></mml:mrow></mml:mrow></mml:math> orientations for compression and tension, respectively. The grain size (23 and 125 <i>&#x3BC;</i>m) has only a relatively small effect on the textural development. For large strains 1.4&#x2013;2.9
(compression) the textural development is in broad agreement with relaxed-constraints (RC) model predictions. In the strain range where the Taylor-model is prevalent the textural development has only a small effect on the <i>M</i>-factor, i.e. on the flow stress&#x2013;strain relationship.

H. Naaman

R. Talreja

D. Juul Jensen

N. Hansen

Development of Deformation Textures in Polycrystalline Copper Experiments and Model Predictions

Molybdenum and molybdenum alloys exhibit brittle behavior in the transverse direction of wrought bar stock despite having good ductility in the longitudinal direction. This is believed to be due to the presence of cracked-carbide stringers on adversely oriented grain boundaries. In the present paper, the possible role of
anisotropy in strength, as a result of the presence of a strong fiber texture, is investigated. It is concluded, both theoretically and experimentally, that anistropy in strength between the transverse and longitudinal direction of barstock containing a perfect fibre texture is not a factor promoting brittle behavior.

T. Oyama

J. Wadsworth

Anisotropy of Microstructure and Strength in Fiber Textured Molybdenum Alloys

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Texture, Stress, and Microstructure