A New Analytical Approach for the Velocity Field in Rolling Processes and Its Application in Through-Thickness Texture P
- PDF / 1,331,870 Bytes
- 14 Pages / 593.972 x 792 pts Page_size
- 90 Downloads / 136 Views
UCTION
ON single crystal level, plastic deformation occurs on slip systems, which consist of a slip plane and a slip direction.[1] When a large plastic deformation occurs in a polycrystalline aggregate, each particular crystal rotates in order to maintain compatibility with its surrounding and as a result a specific crystallographic orientation distribution arises called texture.[1] As the single crystal’s plastic behavior is highly anisotropic, a textured material has in general an anisotropic plastic behavior. Knowledge of the texture and anisotropy is important since it influences the macroscopic deformation behavior such as formability. A more sophisticated material law could be used as an input in various numerical and analytical approaches such as the finite element (FE) based simulations,[2] the slab method,[3] the slip-line method[4] and the upper bound method,[5–7] to calculate various technological outputs of the rolling process. In order to predict the plastic behavior of a polycrystalline material, several models have been developed. These models could be subdivided into two types, namely the computationally costly crystal plasticity finite element models (CPFEM)[8,9] and statistical mes-
KOEN DECROOS, Post-doctoral Researcher, and MARC SEEFELDT, Professor, are with the Department of Metallurgy and Materials Engineering, Faculty of Engineering, Catholic University of Leuven, Heverlee, 3001 Leuven, Belgium. Contact e-mail: koen.Decroos@ gmail.com, [email protected] JURIJ SIDOR, Research Assistant, is with the Department of Materials Science and Engineering, Faculty of Engineering and Architecture, Ghent University, Zwijnaarde, 9052 Gent, Belgium. Manuscript submitted January 10, 2013. Article published online November 7, 2013 948—VOLUME 45A, FEBRUARY 2014
oscopic polycrystal plasticity models. In polycrystal plasticity models, the macroscopic velocity gradient tensor is imposed whereas the stresses and strains in the grains, as well as the macroscopic stress, are obtained based on specific assumptions. Particular examples are the Taylor[10] model, the visco-plastic self consistent model,[11] the Alamel model,[12] and the GIA model.[13] An overview of these models is given by Qie et al.[14] Numerous literature sources report on the calculation of the velocity gradient tensor coupled with polycrystal plasticity models.[15–18] Choi et al.[15] used the FE method to calculate the local strain evolution. Van Houtte et al. used an incremental texture updating procedure in a FE model of a cup drawing process.[16] Segurado et al.[17] reported on a multiscale model to embed the VPSC model in an implicit FE model of sheet rolling. Engler et al.[18] imposed a sine-shaped 31 and 13 shear (where 1 represents the rolling direction, and 3 the sheet’s normal direction) in the top layers to implement the shear between the rolls and the plate’s surface. Alternatively, the deformation flow across the thickness in rolled materials is described by analytical flow functions. Both two and three dimensional functions we
Data Loading...
