Downloaded from orbit.dtu.dk on: Dec 19, 2017 Computer programs for texture simulation Leffers, Torben Publication date: 1973 Document Version Publisher's PDF, also known as Version of record Link back to DTU Orbit Citation (APA): Leffers, T. (1973). Computer programs for texture simulation. (Denmark. Forskningscenter Risoe. Risoe-R; No. 283). 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Gjellerup, 87, Sølvgade, DK-1307 Copenhagen K, Denmark Available on exchange from: Library, Danish Atomic Energy Commission, Risø, DK-4000 Roskilde, Denmark We regret that some of the pages in the microfiche copy of this report may not be up to the proper legibility standards, even though the best possible copy WPS used for preparing the master fiche. UPC 6*1.3.06 : »9.374:621.771 March t 973 Risø Report No. 283 Computer Programs for Texture Simulation by Torben Leffers Danish Atomic Energy Commission Research Establishment Risø Metallurgy Department Abstract A description is given of three computer programs (ROL.TEX 2, ROL - TEX 1, and HORS dOEUVRE) for the simulation of the plastic deformation in face-centred cubic poiycrystals and the derived development of rolling texture. The description includes a variety of test examples demonstrating that the programs work correctly. The report does not deal with the actual results produced by the programs and the physical interpretation of these results. i ISBN 87 550 0)89 0 - 3 - CONTENTS Page 1. Introduction 5 2. The Computer Programs 5 2.1. Mode of Operation 5 2.2. The Program ROLTEX 2 6 2. 3. The Program ROLTEX 1 18 2.4. The Program HORS dOEUVRE 20 3. The Testing of the Programs 21 3.1. Lattice Rotations 22 3.2. Additional Stresses 25 3.3. Random Stresses 28 3.4. Random Orientation Distributions 30 3.5. Miscellaneous 32 4. Concluding Remarks 33 Acknowledgements 33 References 33 Tables and Figures 34 Appendices - 5 - 1. INTRODUCTION The computer programs ROLTEX 1 and ROLTEX 2 are used for simu­ lating the plastic deformation during rolling of face-centred cubic poly- crystals and the derived texture development. HORS dOEUVRE is an auxil­ iary program to the ROLTEX programs. The results obtained with the programs and the discussion of the physi­ cal significance of these results are published elsewhere ~ \ This report will provide a detailed description of the organization of the programs, of the mathematical formulation of the problems, and of the testing procedure applied to ensure that the programs actually do perform the desired calcu­ lations. Listings of the programs are included as appendices. ROLTEX 1 was written first, but before it came into real use, it was realized that so many alterations and so much rationalization were needed that it would be the easiest to write a new program, ROLTEX 2. All the results referred to in refs. 1 -6 have been obtained with ROLTEX 2, and therefore only ROLTEX 2 will be described in detail. The only reason for including ROLTEX 1 is that some of the tests referred to can only be per­ formed with this program. The parts of the auxiliary and test program HORS dOEUVRE that are different from ROLTEX 2 will also be described. 2. THE COMPUTER PROGRAMS 2.1. Mode of Operation A predetermined number of crystals are treated one by one. The starting orientation of the crystals may be fed into the computer, or the computer may generate random orientations. In the individual crystals the program selects the {ill} (110) slip system with the highest resolved shear stress. The resolved stress is calculated from the following external stresses: (i) the basic stress system which is a tensile stress in the rolling direction combined with a compress­ ive stress in the normal direction, the two stress components being of equal size numerically, (ii) if wanted, additional stresses restricting the changes in shape that the crystals can undergo, and (iii) if wanted, random stresses (the physical significance of these stresses are given in refs. 2,3,6). When the most heavily loaded slip system has been found, a certain amount of slip takes place on this system, and the crystal lattice is rotated - 6 - correspondingly. The lattice rotatum Likes place such as to fulfil the fol­ lowing two requirements: (a) a string of material lying in the rolling direc­ tion before slip must retain this orientation after deformation and lattice rotation, and (b) a plate of material lying parallel to the rolling plane be­ fore slip must also retain its orientation after deformation and rotation (see refs. 1, 2, 3, 6). The change in shape caused by the slip is registered; it is used for calculating the total deformation and, if the stresses (ii) men­ tioned above are applied, for calculating the new shape-restoring stresses. Then a new slip event with rotation takes place like the one already de­ scribed, and so on until the predetermined degree of deformation is reached. When the deformation of a crystal is finished, its {ill} and {100} poles are either plotted directly in stereographic projection or stored in the drum for later plotting (the plotting of the poles is only accomplished in ROLTEX 1 and ROLTEX 2, not in HORS dOEUVRE). 2. 2. The Program ROLTEX 2 The program was written in GIER ALGOL, and the structure of the program is such as to minimize the running time on a G1ER computer (minimum number of array calls, drum storing of the plotter data for plotting when all calculations are finished). Later the program has been translated into ILLINOIS ALGOL for use on the IBM 7094. The version listed in this report (Appendix A) is the GIER ALGOL version. The present description will concentrate on showing how the physical problems of deformation and texture development are translated into com­ puter language. Less attention will be paid to computer-administration problems (such as the problem of plotting the poles in the order that will minimize the computer-time consumption). 2. 2.1. Meaning of the General Variables The underlined variables are input variables, the others are only used inside the computer. indicator An integer that governs the program; it can be given values from -2 to 3. The different values correspond to the following operation modes; -1: orientations are given ) to the computer ) no deformation, 0: random orientations ) "J"?!*11*« are generated j Pitting of the poles 1: random orientations ) are generated ) - 7 - -2: orientations are given) to the computer ) deformation 2 and 3: random orienta- ) bff?5e tions are generated ) PtottuW indicator * Q: plotdng in four quadrants indicator ) 0: plotting in first quadrant only indicator * 3: apart from plotting, the orientations of the crystals are printed out. The number of crystals. RANDOM The maximum number of steps for which the same random stress is allowed to operate. STOP The maximum number of steps for each crystal. randomparameter An integer that governs the generation of random stresses. crystalparameter An integer that governs the generation of random orientations. counter An integer used for counting the number of steps. K P. «t r, s. t, rr, ø, Integers used for different purposes P. 0. PP, 00. PQ throughout the program. K. Kfi12, KS13. Ks23 Proportionality factors for the shape- restoring stresses; when they are all given the value zero, there is no shape restoration. K is used for tensile and compressive stresses, the others for shear components. L A real used for the calculation of the maximum value for the random stresses. SHOOT A real used when overshooting is included. When SHOOT < -0.5, the part of the program that takes care of the overshooting is omitted. R The final reduction in per cent. step The amount of shear in each slip event. sq, u Reals used for various purposes. red The actual reduction of a crystal during "deformation". length T> e actual length of the crystal considered. thickness The actual thickness of the crystal. trans dim The actual transverse dimension (width) of the crystal. - 8 - SA lised for finding the slip system with the highest resolved shear stress. fault Used for calculating the deviation from orthogonality in the crystal lattice after deformation. A11, A12, A1 3, A21 When starting with a new crystal Apq is the ..., A33 q-co-ordinate of the crystallographic p-axis in the "geometric" co-ordinate system having the transverse, the rolling, and the normal direction as axes (it should be noted that the numbering of the geometric axes in the program is different from the numbering in refs. 2, 3,6). When dealing with the lattice rotation corresponding to a slip event, Apq is the q-co-ordinate of the "old" geometric p-axis (the p-axis before rotation) in the "new" geometric co-ordinate system. In routine use of the program the Apq's are not input variables, and therefore they are not underlined.