Elsevier

Materials Science and Engineering: A

Volume 560, 10 January 2013, Pages 273-277
Materials Science and Engineering: A

Quantification of local and global elastic anisotropy in ultrafine grained gradient microstructures, produced by linear flow splitting

https://doi.org/10.1016/j.msea.2012.09.067Get rights and content

Abstract

Severely deformed materials often show strong plastic strain gradients, which can lead to a variety of gradients in microstructure and texture. Since the elastic behavior of a material is in most cases linked to its crystallographic texture, gradients in the elastic properties are also possible. Consequently, the macroscopic elastic behavior results from the local elastic properties within the gradient. In the present investigation profiles produced by the linear flow splitting process were examined with respect to local and global elastic anisotropy, which develops during the complex forming process. The local grain orientations determined by EBSD measurements were used to calculate the elastic tensors at several positions along the strain gradient. Based on the geometric mean, the calculated local elastic constants were transferred into global ones by appropriate weighting. Ultrasonic measurements were carried out to determine the macroscopic stiffness tensor of the severely deformed parts, showing a good agreement with the global stiffness tensor calculated from orientation data.

Introduction

The steadily increasing expenses for energy and raw material led to several developments in product and material design during the last few decades. Components are expected to show an increased strength and stiffness, while simultaneously being produced with less material usage and less production costs. An elegant way to increase the stiffness, while reducing the material usage and thus reducing the weight, is to use bifurcations. Linear flow splitting (LFS) offers the possibility to produce bifurcated structures integrally with low production costs, even while using high strength materials. Linear flow split profiles are well suitable as stiffening elements or, owing to the low surface roughness of the produced flanges, as linear guides [1]. Linear flow splitting induces severe plastic deformation at the edge of a sheet, using obtuse angled splitting rolls [2]. The edge is being broadened so that a bifurcation is produced after several steps (see Fig. 1a). As depicted in Fig. 1b, the material flow is perpendicular to the feed direction, thus the direction from the splitting center to the flange tip can be identified as the rolling direction (RD) (see Fig. 1c). Consequently the feed direction corresponds to the transverse direction (TD) and the direction from the flange top to the bottom surface is the normal direction (ND). Unlike established severe plastic deformation (SPD) processes like equal channel angular pressing (ECAP), high pressure torsion (HPT) or accumulative roll bonding (ARB), which are characterized by inducing severe strains while almost maintaining the initial dimensions of the work piece [3], [4], linear flow splitting leads to significant changes in the geometry. Thus, strictly speaking LFS cannot be categorized as a SPD process in the narrower sense. Nevertheless it imposes severe strains and produces an ultrafine grained (UFG) microstructure in a surface layer [5]. The process zone is less defined than in the previously mentioned SPD processes and exhibits steep strain gradients [6], leading to strong microstructure and yield strength gradients in the flange thickness direction [7]. Earlier investigations using electron backscattering diffraction (EBSD) have shown that the crystallographic texture also varies along with the other gradients [8]. Due to the severe plastic deformation and the distinct property gradients, it is reasonable to assume, that the Young's modulus exhibits an anisotropic and heterogeneous character as well. Consequently, elastic material properties obtained by conventional experimental methods (for example tensile tests) could deviate significantly from the local elastic properties within the microstructure gradient, since the measured values would only be averages over the flange thickness. However, for special applications it is important to determine the microscopic elastic properties more precisely. Additional roll forming or the application of the profiles as linear guides requires the previous evaluation of the process layout and the rolling contact fatigue using FEM simulations. In order to obtain most accurate simulation results, it is essential to have an exact knowledge of the local elastic properties and the potential gradient within the flanges. The calculation of the elastic parameters using orientation data obtained by EBSD can be carried out with the well-established methods proposed by Voigt and Reussin [9]. Voigt used the assumption of spatially constant strains within the material, while Reuss proposed constant stresses. The results of these calculations are upper and lower bounds, within which the actual values have to lie. The grain orientations at every discrete measurement point obtained by EBSD can be used to determine rotation matrices (T), which rotate the single crystal stiffness (C) and compliance (S) tensors for all points (N) of the measurement grid. The polycrystal stiffness and compliance tensors after Voigt (CV) and Reuss (SR) can then be calculated as follows [10]:CV=1NiN[Ti]T[C][Ti]SR=1NiN[TiT]1[C]1[Ti]1=1NiN[TiT]1[S][Ti]1

Since the Voigt and Reuss approximations can be considered as upper and lower bounds, an additional approach is needed, which describes the actual elastic properties more precisely. Hill proposed a simple arithmetic mean of the approximations calculated after Voigt and Reuss, namely the Voigt–Reuss–Hill average (VRH) [11]. This approach is often sufficient for the description of the elastic properties. Nevertheless it has some detrimental characteristics. The tensor inversion of CV leads to a tensor which differs from SR and vice versa. So there are four ways of calculating an arithmetic mean, with slight differences from each other. In contrast, the concept of the geometric mean offers the possibility of calculating stiffness and compliance tensors, which lie within the Voigt and Reuss bounds [12] and can be transferred into each other via proper tensor inversion. In most cases the geometric mean provides similarly accurate approximations of the actual elastic properties as self-consistent approaches, but with substantially less calculation effort [13]. The calculation routines are analog to Voigt and Reuss, except for the additional calculation of the natural logarithm of the stiffness and compliance tensors before averaging [14]:Cgeom=exp(1NiNln([Ti]T[C][Ti]))=[exp(1NiNln([TiT]1[S][Ti]1))]1

Section snippets

Experimental

All investigations were carried out on a high strength low alloy steel (H480LA) with the following chemical composition (wt%): 0.07 C, 0.688 Mn, 0.039 Nb, 0.033 Al, 0.029 Si, 0.012 P, 0.003 S. The thickness of the initial sheet was 2 mm. The microstructure of the as received material consists of ferrite grains and small Fe3C particles (1 vol%) located at the grain boundaries. Linear flow splitting was carried out continuously in 10 stages and led to flanges with lengths of 12 mm and a thickness of

Results and discussion

Due to the fact that the strains at the split surface are much larger than at the center or the lower side of the flanges, a strong microstructural gradient develops in flange thickness direction, as shown in Fig. 2 exemplarily for 25 μm and 600 μm underneath the split surface. In association with a significant decrease in grain aspect ratio, the grain dimensions in flange thickness direction increase from less than 0.1 μm in the near surface UFG regions to approximately 1 μm at the lower surface

Summary and conclusion

The bifurcated structures produced by linear flow splitting exhibit strong property gradients within the flanges due to the complex forming process. A significant texture gradient develops within the flanges, which however has only a minor effect on the elastic properties. With respect to the anisotropic character of Young's modulus the disappearing of the rolling texture in conjunction with the loss of the α- and γ-fiber is nearly completely compensated by the appearance of the Goss

Acknowledgments

The authors thank the German Research Foundation (DFG) for founding the present work, which has been carried out within the Collaborative Research Centre 666 “Integral sheet metal design with higher order bifurcations—Development, Production, Evaluation”.

References (17)

  • P. Groche et al.

    J. Mater. Process. Technol.

    (2007)
  • M. Kamaya

    Int. J. Solids Struct.

    (2009)
  • P. Groche et al.

    Key Eng. Mater.

    (2007)
  • M. Nemoto et al.

    Met. Mater. Int.

    (1998)
  • Y. Saito et al.

    Acta Mater.

    (1998)
  • T. Bohn et al.

    J. Mater. Sci.

    (2008)
  • C. Müller et al.

    Materwiss Werksttech

    (2007)
  • E. Bruder et al.

    Mater. Sci. Forum

    (2008)
There are more references available in the full text version of this article.

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