As all factors governing the process of the development of texture are strongly dependent on stacking fault energy, a marked influence ofSFE on the wire texture and rolling texture characteristics should be expected. This relationship has been established for wires by English and Chin. Using their own experimental data, as well as those from literature, they plotted the amount of (100) wire texture component against v/Gb, being SFE, G the shear modulus, and b the Burgers vector, as shown in Figure 1. The most important conclusion drawn by the authors from this relationship is that the general trend toward larger proportions of (100) with reduced SFE is reversed for the lowest values of v/Gb. At the same time they come to the con
{"title":"On the Rolling Texture Reversal in Fcc Metals","authors":"W. Truszkowski","doi":"10.1155/TSM.1.141","DOIUrl":"https://doi.org/10.1155/TSM.1.141","url":null,"abstract":"As all factors governing the process of the development of texture are strongly dependent on stacking fault energy, a marked influence ofSFE on the wire texture and rolling texture characteristics should be expected. This relationship has been established for wires by English and Chin. Using their own experimental data, as well as those from literature, they plotted the amount of (100) wire texture component against v/Gb, being SFE, G the shear modulus, and b the Burgers vector, as shown in Figure 1. The most important conclusion drawn by the authors from this relationship is that the general trend toward larger proportions of (100) with reduced SFE is reversed for the lowest values of v/Gb. At the same time they come to the con","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"53 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121099261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The textures that develop during rolling are among the most important factors affecting the properties of rolled sheets, as well as their behaviour in subsequent forming processes. For FCC polycrystals, the main ideal orientations of rolling textures are cube, Goss, brass, copper, Taylor and S. The behaviour of these ideal orientations during rolling are investigated in this paper. Analytical and numerical results for the stress states, slip distributions, lattice rotation fields and orientation developments are obtained using a rate-sensitive crystal plasticity model. The rate-sensitive results are compared with those obtained from the classical rate-independent Bishop and Hill theory. Comparisons are also made with the experimental observations reported by Hirsch and Lucke.
{"title":"On The Ideal Orientations of Rolling Textures for FCC Polycrystals","authors":"Y. Zhou, K. Neale, L. Toth","doi":"10.1155/TSM.14-18.1055","DOIUrl":"https://doi.org/10.1155/TSM.14-18.1055","url":null,"abstract":"The textures that develop during rolling are among the most important \u0000factors affecting the properties of rolled sheets, as well as their behaviour in subsequent \u0000forming processes. For FCC polycrystals, the main ideal orientations of \u0000rolling textures are cube, Goss, brass, copper, Taylor and S. The behaviour of \u0000these ideal orientations during rolling are investigated in this paper. Analytical \u0000and numerical results for the stress states, slip distributions, lattice rotation fields \u0000and orientation developments are obtained using a rate-sensitive crystal plasticity \u0000model. The rate-sensitive results are compared with those obtained from the classical \u0000rate-independent Bishop and Hill theory. Comparisons are also made with \u0000the experimental observations reported by Hirsch and Lucke.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"54 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121106378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Modellisations of the deformation texture development in a Ti20V alloy (20 volumic % Vanadium) during rolling have been carried out using the viscoplastic self consistent model of Molinari and Toth (1994). The model parameters and the slip and twinning systems were identified from experimental data. The experimental texture evolution is well reproduced with only a small contribution of the twinning activity.
{"title":"Modelling of Texture Development and Deformation Mechanisms in a Ti20V Alloy Using a Self Consistent Polycrystal Approach","authors":"S. Mercier, L. Toth, A. Molinari","doi":"10.1155/TSM.25.45","DOIUrl":"https://doi.org/10.1155/TSM.25.45","url":null,"abstract":"Modellisations of the deformation texture development in a Ti20V alloy (20 volumic % Vanadium) during rolling have been carried out using the viscoplastic self consistent model of Molinari and Toth (1994). The model parameters and the slip and twinning systems were identified from experimental data. The experimental texture evolution is well reproduced with only a small contribution of the twinning activity.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116543087","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In order to simulate adequately the formability of sheet, it is necessary to generate a yield criterion that takes into account the anisotropy of the crystallographic texture. This yield function must be in a form that can be used easily in finite element analysis. In addition, the formulation should allow the possibility to update the yield surface during simulation to take into account the texture evolution. This work investigates the use of a sixth-order strain rate potential that, when differentiated with respect to the strain rate, gives the components of stress. A method is given to solve the non-convexity problems that can arise when the proposed analytical sixth-order function is used. Examples are given for one cold rolled and one annealed aluminium sheet.
{"title":"A Sixth Order Inverse PotentialFunction for Incorporation ofCrystallographic Texture IntoPredictions of Properties ofAluminium Sheet","authors":"J. Savoie, S. Macewen","doi":"10.1155/TSM.26-27.495","DOIUrl":"https://doi.org/10.1155/TSM.26-27.495","url":null,"abstract":"In order to simulate adequately the formability of sheet, it is necessary to generate a yield criterion \u0000that takes into account the anisotropy of the crystallographic texture. This yield function must be in \u0000a form that can be used easily in finite element analysis. In addition, the formulation should allow the \u0000possibility to update the yield surface during simulation to take into account the texture evolution. This \u0000work investigates the use of a sixth-order strain rate potential that, when differentiated with respect \u0000to the strain rate, gives the components of stress. A method is given to solve the non-convexity problems \u0000that can arise when the proposed analytical sixth-order function is used. Examples are given for one \u0000cold rolled and one annealed aluminium sheet.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131409106","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The use of incomplete pole figure data for defining the orientation distribution function (ODF) in a polycrystalline material is of great practical importance, because it enables the use of experimental data from a simplified measurement. The present paper provides the source text of a computer program for calculating the coefficients of ODF series expansion, Clμυ. The data for computations are in the incomplete pole figures of rhombic symmetry as determined by the back reflection or transmission technique for crystalline solids of the cubic system. Also described is the numerical method of determining the coefficients Clμυ, and the results so obtained are discussed.
{"title":"THE DETERMINATION OF ORIENTATION DISTRIBUTION FUNCTION FROM INCOMPLETE POLE FIGURES AN EXAMPLE OF A COMPUTER PROGRAM","authors":"J. Jura, J. Pośpiech","doi":"10.1155/TSM.3.1","DOIUrl":"https://doi.org/10.1155/TSM.3.1","url":null,"abstract":"The use of incomplete pole figure data for \u0000defining the orientation distribution function (ODF) in \u0000a polycrystalline material is of great practical importance, \u0000because it enables the use of experimental data \u0000from a simplified measurement. The present paper provides \u0000the source text of a computer program for calculating \u0000the coefficients of ODF series expansion, Clμυ. The data for computations are in the incomplete pole figures of rhombic symmetry as determined by the \u0000back reflection or transmission technique for crystalline \u0000solids of the cubic system. Also described is the \u0000numerical method of determining the coefficients Clμυ, \u0000and the results so obtained are discussed.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"191 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131448891","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Using a rate-sensitive crystal plasticity model together with the full constraint Taylor theory, the formation of textures during biaxial stretching of FCC sheet metals is investigated in detail. Three-dimensional lattice rotation fields, orientation evolution and polycrystalline texture development are simulated for the entire range of biaxial strain ratio. The investigation discloses the paths of orientation development and respective stable end orientations, as well as the relation between the evolution paths and the biaxial strain ratio. Our results show that the formation of textures depends mainly on the behaviour of the α- and βρ fibres in biaxial stretching. The strain ratio affects the composition of the βρ-fibre, as well as the flow direction and velocity of orientations towards and along α and βρ, and thus results in different biaxial-stretching textures. The predictions of FCC biaxial-stretching textures are compared with experimental observations reported in literature. Finally, we discuss the influence of complex strain paths on texture formation.
{"title":"Texture Evolution During the Biaxial Stretching of FCC SheetMetals","authors":"Y. Zhou, K. Neale","doi":"10.1155/TSM.22.87","DOIUrl":"https://doi.org/10.1155/TSM.22.87","url":null,"abstract":"Using a rate-sensitive crystal plasticity model together with the full constraint Taylor theory, the \u0000formation of textures during biaxial stretching of FCC sheet metals is investigated in detail. Three-dimensional \u0000lattice rotation fields, orientation evolution and polycrystalline texture development are \u0000simulated for the entire range of biaxial strain ratio. The investigation discloses the paths of orientation \u0000development and respective stable end orientations, as well as the relation between the evolution paths \u0000and the biaxial strain ratio. Our results show that the formation of textures depends mainly on the \u0000behaviour of the α- and βρ fibres in biaxial stretching. The strain ratio affects the composition of the βρ-fibre, as well as the flow direction and velocity of orientations towards and along α and βρ, and thus results in different biaxial-stretching textures. The predictions of FCC biaxial-stretching textures are compared with experimental observations reported in literature. Finally, we discuss the influence of complex strain paths on texture formation.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"79 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131491957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Bishop and Hill-type isostrain analysis for the deformation of BCC crystals by pencil glide has been re-examined. Expressions have been derived for slip-plane orientations and shears for simultaneous slip along four directions. The expressions for shears, in conjunction with expressions for the stress states previously calculated by Piehler and Backofen, permit comparison of external and internal work, which must be equal for the active stress state. Additional relations are introduced which must be satisfied for simultaneous operation of three slip systems. These relations permit a straightforward computational procedure for determining possible stress states, and insure that external and internal work are equal. If for a possible stress state involving activation of three slip directions, the shear stress on the supposedly inactive system is less than the yield stress, that stress state is active.
{"title":"The Prediction of Plastic Properties of Polycrystalline Aggregates of BCC Metals Deforming by Pencil Glide","authors":"P. R. Morris, S. Semiatin","doi":"10.1155/TSM.3.113","DOIUrl":"https://doi.org/10.1155/TSM.3.113","url":null,"abstract":"The Bishop and Hill-type isostrain analysis for the deformation of BCC crystals by pencil glide has been re-examined. Expressions have been derived for slip-plane orientations and shears for simultaneous slip along four directions. The expressions for shears, in conjunction with expressions for the stress states previously calculated by Piehler and Backofen, permit comparison of external and internal work, which must be equal for the active stress state. Additional relations are introduced which must be satisfied for simultaneous operation of three slip systems. These relations permit a straightforward computational procedure for determining possible stress states, and insure that external and internal work are equal. If for a possible stress state involving activation of three slip directions, the shear stress on the supposedly inactive system is less than the yield stress, that stress state is active.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127577541","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis tends to align along the fiber axis for this polyethylene terephthalate sample.
{"title":"A TEST OF THE REFINEMENT PROCEDURE FOR DETERMINING THE CRYSTALLITE ORIENTATION DISTRIBUTION: POLYETHYLENE TEREPHTHALATE","authors":"W. R. Krigbaum, A. Vasek","doi":"10.1155/TSM.1.9","DOIUrl":"https://doi.org/10.1155/TSM.1.9","url":null,"abstract":"A test of the refinement procedure for improving the crystallite orientation distribution function is presented for a \u0000fiber texture sample of polyethylene terephthalate. This is a particularly difficult example because the triclinic unit \u0000cell offers no simplification due to symmetry, and the pole figures are sharply peaked. The analysis employed 17 \u0000observed pole figures and an additional 29 unobserved pole figures reconstructed from the crystallite orientation \u0000distribution function. After three cycles of refinement, in which the maximum value of the coefficient was increased \u0000from 6 to 16, the standard deviations, σq and σw, of the plane-normal and crystallite orientation distributions were \u0000reduced by about a factor of 3. The refined crystallite orientation distribution function indicates that the c-axis \u0000tends to align along the fiber axis for this polyethylene terephthalate sample.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127612096","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A new algorithm of quantitative texture analysis (QTA), which is called the modified maximum entropy method (MMEM), has been proposed and applied to determination of textures in polycrystalline samples of lower crystal symmetry with overlapping diffraction peaks (Wang and Xu, 1995a). By introducing directly the maximum entropy principle into the least square procedure of pole figure inversion (Bunge, 1969), then both minimizing the differences between experimental and postulated pole figure data, and maximizing entropy may be satisfied simultaneously. Thus, the maximum entropy principle is applied to the entire process of QTA in frame of the harmonic method (HM). The detailed comparisons among the three pole figure inversion methods, i.e. the traditional HM, the primary maximum entropy method (MEM) and the MMEM, are given through a model example of simulated fiber texture. It is shown that the precise and stable solution of inverse pole figure for the polycrystalline samples with smooth or sharp textures will be obtained by the MMEM even using a less number of pole figures. The minimum range of polar angle and the least number of pole figures, which are needed in the QTA for pretended tetragonal materials by the MMEM, are discussed in detail.
提出了一种新的定量织构分析(QTA)算法，称为修正最大熵法(MMEM)，并将其应用于衍射峰重叠的低晶对称多晶样品的织构测定(Wang and Xu, 1995a)。通过将最大熵原理直接引入到极点图反演的最小二乘过程中(Bunge, 1969)，可以同时满足实验极点图数据与假设极点图数据之间差异的最小化和熵的最大化。因此，将最大熵原理应用于谐波法框架下QTA的整个过程。以模拟纤维纹理为例，对传统的最大熵法(HM)、最大熵法(MEM)和最大熵法(MMEM)三种极图反演方法进行了详细的比较。结果表明，对于具有光滑或尖锐纹理的多晶样品，即使使用较少的极点图，MMEM也能得到精确而稳定的反极点图解。详细讨论了MMEM对拟四边形材料进行QTA时所需要的最小极角范围和最小极位数。
{"title":"The Modified Maximum Entropy Method (MMEM) in QTA for Lower Symmetry Polycrystalline Aggregates","authors":"Y. D. Wang, J. Z. Xu, Z. Liang","doi":"10.1155/TSM.26-27.103","DOIUrl":"https://doi.org/10.1155/TSM.26-27.103","url":null,"abstract":"A new algorithm of quantitative texture analysis (QTA), which is called the modified maximum entropy method (MMEM), has been proposed and applied to determination of textures in polycrystalline samples of lower crystal symmetry with overlapping diffraction peaks (Wang and Xu, 1995a). By introducing directly the maximum entropy principle into the least square procedure of pole figure inversion (Bunge, 1969), then both minimizing the differences between experimental and postulated pole figure data, and maximizing entropy may be satisfied simultaneously. Thus, the maximum entropy principle is applied to the entire process of QTA in frame of the harmonic method (HM). The detailed comparisons among the three pole figure inversion methods, i.e. the traditional HM, the primary maximum entropy method (MEM) and the MMEM, are given through a model example of simulated fiber texture. It is shown that the precise and stable solution of inverse pole figure for the polycrystalline samples with smooth or sharp textures will be obtained by the MMEM even using a less number of pole figures. The minimum range of polar angle and the least number of pole figures, which are needed in the QTA for pretended tetragonal materials by the MMEM, are discussed in detail.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"32 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127633633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The purpose of this note is to make a few observations on several analyses of lattice rotation by slip and by twinning in deformation.
本笔记的目的是对滑移和变形中孪晶对晶格旋转的几种分析作一些观察。
{"title":"On Orientation Changes Accompanying Slip and Twinning","authors":"W. Hosford","doi":"10.1155/TSM.2.175","DOIUrl":"https://doi.org/10.1155/TSM.2.175","url":null,"abstract":"The purpose of this note is to make a few observations on several analyses of lattice \u0000rotation by slip and by twinning in deformation.","PeriodicalId":413822,"journal":{"name":"Texture, Stress, and Microstructure","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133244377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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