A new way to include the grain shape in texture simulations with the Taylor model
The use of the Hall-Petch relation in texture simulations with the Taylor-Bishop-Hill model is proposed as a mean to take into account grain shape effect. The results are compared with those obtained with the usual and relaxed constraint Taylor model for a simple texture and the consequences for the anisotropy coefficient are investigated On propose d'utiliser la relation de Hall-Petch dans les simulations de texture a l'aide du modele de Taylor-Bishop-Hill pour prendre en compte la forme des grains. Comparaison des resultats avec ceux du modele de Taylor classique ou relaxe dans le cas d'une texture simple; consequences pour le coefficient d'anisotropie
Some applications of the Taylor theory of polycrystal plasticity
The Taylor theory of polycrystal plasticity was applied to three-axial deformation accomplished by glide on (111) [110] or (110) [111] glide systems. The orientation dependence of the Taylor factor was used to calculate the angular dependence of the relative strength of a textured material. The angular dependence of the strain ratio R — calculated from the minimum value of the Taylor factor — was compared with the measured strain ratio. The orientation changes of the crystallites of a polycrystalline aggregate after 1% plastic deformation were calculated and compared with experimental values. The orientations which are deformed without orientation changes were calculated and compared with those of maximum orientation density found by a three-dimensional texture analysis of cold rolled copper and iron. The dependence of the rotationless orientations on the axis ratio of the deformation tensor was calculated. This allows suggestions to be made on the dependence of the rolling textures on the lateral broadening of the sheet during rolling. 
 
 
 
Die Taylor-Theorie der Vielkristallplastizitat wurde auf dreiachsige Verformungszustande und Gleitung auf (111) [110]- oder (110) [111]-Gleitsystemen angewandt. Aus der Orientierungsabhangigkeit des Taylor-Faktors wurde die Winkelabhangigkeit der relativen Festigkeit eines Texturmaterials berechnet. Die Winkelabhangigkeit des R-Wertes der plastischen Verformung — berechnet aus dem Minimalwert des Taylor-Faktors — wurde mit den gemessenen R-Werten verglichen. Die Orientierungsanderungen der Kristallite eines vielkristallinen Aggregates nach 1% plastischer Verformung wurden berechnet und mit experimentellen Werten verglichen. Diejenigen Orientierungen, die sich ohne Orientierungsanderung verformen, wurden berechnet und mit den Orientierungen maximaler Orientierungsdichte verglichen, die sich aus der dreidimensionalen Texturanalyse kaltgewalzter Kupfer- und Eisenbleche ergaben. Die Abhangigkeit der drehungsfreien Orientierungen vom Achsenverhaltnis des Deformationstensors wurde berechnet. Daraus ergeben sich Schlusfolgerungen uber die Abhangigkeit der Walztexturen von der relativen Breitung des Bleches wahrend der Walzung.
Crystal Rotations under Conditions of Imposed Strain and the Influence of Twinning and Cross-Slip
Abstract Slip rotations in cubic crystals under conditions of imposed strain are not, in general, uniquely determined, since several equivalent sets of slip systems are available to produce the particular shape change. However, it is shown that for certain crystal orientations undergoing deformation by rolling only four systems are required to operate and in these cases the slip rotations are determined unambiguously. Two orientation ranges, those having 〈110〉 and 〈111〉 transverse directions, are considered and the rate of crystal rotation determined as a function of orientation. It is shown that orientations of the types {1110}〈112〉, {110}〈001〉, and near-{4,4,11}〈11,11,8〉 are stable for f.c.c. crystals and {112}〈110〉, {001}〈110〉, and near-{11,11,8}〈4,4,11〉 for b.c.c. crystals. The predictions of this limited analysis allow the various mechanistic theories of rolling texture formation in f.c.c. metals to be assessed. It is concluded that both twinning and cross-slip are required to account for the full ra...