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Acta Metall Sin  2016, Vol. 52 Issue (1): 120-128    DOI: 10.11900/0412.1961.2015.00264
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CRYSTAL PLASTICITY FINITE ELEMENT SIMULA- TION OF SLIP AND DEFORMATION IN ULTRA- THIN COPPER STRIP ROLLING
Shoudong CHEN1,Xianghua LIU1(),Lizhong LIU2,Meng SONG1
1 State Key Laboratory of Rolling and Automation, Northeastern University, Shenyang 110819, China
2 School of Materials and Metallurgy, Northeastern University, Shenyang 110819, China
Cite this article: 

Shoudong CHEN,Xianghua LIU,Lizhong LIU,Meng SONG. CRYSTAL PLASTICITY FINITE ELEMENT SIMULA- TION OF SLIP AND DEFORMATION IN ULTRA- THIN COPPER STRIP ROLLING. Acta Metall Sin, 2016, 52(1): 120-128.

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Abstract  

When the part size is scaled down to micro-scale, the material consists of only a few grains and the material properties and deformation behaviors are quite different from the conventional ones in macro-scale. In micro-scaled plastic deformation process such as ultra-thin strip rolling, material thickness effect is difficult to reveal and investigate using conventional material models. The distributions of the stress, strain and active slip systems, and the slip and deformation behavior in rolled pure ultra-thin copper strip with the same reduction were simulated by the crystal plasticity finite element method (CPFEM) and Voronoi polycrystalline model with respect to specimen dimension, grain size, grain orientation and its distribution to evaluate quantitatively the influence of grain orientation and structure on inhomogeneous deformation behavior of ultra-thin strip rolling on a mesoscale. A polycrystalline aggregate model is generated and a crystal plasticity based an implicit finite element model is developed for each grain and the specimen as a whole. The crystal plasticity model itself is rate dependent and accounts for local dissipative hardening effects and the original orientation of each grain was generated based on the orientation distribution function (ODF). Voronoi tessellation has been applied to describe the polycrystalline aggregation. The accuracy of the developed CPFEM model is verified by the fact that the simulated stress-strain curves agree well with the experimental results. The deformation behaviors, including inhomogeneous material flow, and slip system activity with the increase of thickness size for the constant size of grain, are studied. It is revealed that when the ultra-thin strips are composed of only a few grains through thickness direction, the grains with different size, shapes and orientations are unevenly distributed in the ultra-thin strip and each grain plays a significant role in micro-scale plastic deformation, slip system activity and leads to inhomogeneous deformation. The simulation result reveals that the deformation behavior in the polycrystalline aggregates is inhomogeneous not only in intracrystalline but also in intergranule regions by simulation of deformation behavior of pure ultra-thin copper strip rolling with 40% rolling reduction. This can be attributed to the different initial grain orientations and structures, the misorientation of neighboring grains, and the different properties of active slip systems and lattice rotation. Activation often initially occurs at free surface and near the boundary adjacent to grains, and then the slip develops in interior grain. The results from the proposed modeling methodologies provide a basic for understanding and further exploring of micro-scaled plastic deformation behavior in ultra-thin strip rolling process.

Key words:  ultra-thin strip rolling      crystal plasticity finite element      grain heterogeneity      slip system activation     
Received:  17 May 2015     
Fund: Supported by National Natural Science Foundation of China (Nos.51374069 and U1460107)

URL: 

https://www.ams.org.cn/EN/10.11900/0412.1961.2015.00264     OR     https://www.ams.org.cn/EN/Y2016/V52/I1/120

Plane Direction Slip system
(111) [011] a1
[101] a2
[110] a3
(111) [101] b1
[110] b2
[011] b3
(111) [011] c1
[110] c2
[101] c3
(111) [011] d1
[101] d2
[110] d3
Table 1  Slip systems of fcc metal
Fig.1  Dimensions of tensile specimen (unit: mm)
Fig.2  Stress-strain curves of ultra-thin Cu strip by experiment and crystal plasticity finite element method
Fig.3  Initial simulation models for ultra-thin Cu strip with thickness t=200 μm (a), t=400 μm (b) and the microstructure after rolling for t=200 μm (c) (ND—normal direction, RD—rolling direction, TD—transverse direction; different grain orientations are indicated by colors)
Fig.4  Shear stress (S12) distributions of ultra-thin Cu strip with t=200 μm (a) and t=400 μm (b) after 40% reduction (Gn1 represents the number n1 grain in the simulation)
Fig.5  lne distributions of ultra-thin Cu strip with t=200 μm (a) and t=400 μm (b) after 40% reduction (lne is the logarithmic strain)
Fig.6  Shear strain rate evolution of active slip systems with time at points D (a), K (b) and L (c) in Figs.4a and 5a
Fig.7  Shear strain rate evolution of active slip systems with time at points G (a), N (b) and P (c) in Figs.4b and 5b
Fig.8  Shear strain rate along active slip systems a1 (a01~a03), b3 (b01~b03) and d3 (c01~c03) for ultra-thin Cu strip with t=200 μm after 40% reduction for rolling times 0.25 s (a01, b01, c01), 0.5 s (a02, b02, c02) and 1.0 s (a03, b03, c03)
Fig.9  Shear strain rate along active slip systems a1 (a01~a03), b3 (b01~b03) and d3 (c01~c03) for ultra-thin Cu strip with t=400 μm after 40% reduction for rolling times 0.25 s (a01, b01, c01), 0.5 s (a02, b02, c02) and 1.0 s (a03, b03, c03)
Fig.10  {111} pole figures of grains G64 (a, c) and G63 (b, d) before (a, b) and after (c, d) 40% reduction for ultra-thin Cu strip with t=200 μm (Orientation scattering of the grains after deformation is indicated by the red areas)
[1] Groeber M, Ghosh S, Uchic M D, Dimiduk D M. JOM, 2007; 59(9): 32
[2] Engel U, Eckstein R. J Mater Process Technol, 2002; 125-126: 35
[3] Pierard O, Lorca J, Segurado J, Doghri I. Int J Plasticity, 2007; 23: 1041
[4] Si L Y, Lu C, Huynh N N, Tieu A K, Liu X H. J Mater Process Technol, 2008; 201(1-3): 79
[5] Taylor G I. J Inst Met, 1938; 62: 307
[6] Parks D M, Ahzi S. J Mech Phys Solids, 1990; 38: 701
[7] Honneff H, Mecking H. Textures Mater, 1978; 1: 265
[8] Molinari A, Canova G R, Ahzi S. Acta Metall, 1987; 35: 2983
[9] Hill R, Rice J R. J Mech Phys Solids, 1972; 20: 401
[10] Deng G Y, Lu C, Su L H, Liu X H, Tieu A K. Mater Sci Eng, 2012; A534: 68
[11] Deng G Y, Tieu A K, Si L Y, Su L H, Lu C, Wang H, Liu M, Zhu H T, Liu X H. Comput Mater Sci, 2014; 81: 2
[12] Tamimi S, Correia P J, Lopes A B, Ahzi S, Barlat F, Gracio J J. Mater Sci Eng, 2014; A603: 150
[13] Klusemann B, Svendsen B, Vehoff H. Comp Mater Sci, 2012; 52: 25
[14] Li L, Shen L M, Proust G, Moy Charles K S, Ranzi G. Mater Sci Eng, 2013; A579: 41
[15] Zhang X, Aifantis K E, Ngan Alfonso H W. Mater Sci Eng, 2014; A591: 38
[16] Liu M, Tieu A K, Lu C, Zhu H T, Deng G Y. Comput Mater Sci, 2014; 81: 30
[17] Turner T J, Shade P A, Schuren J C, Groeber M. Modell Simul Mater Sci Eng, 2013; 21: 015002
[18] Prakash A, Weygand S M, Riedel H. Comput Mater Sci, 2009; 45: 744
[19] Kanjarla A K, Van Houtte P, Delannay L. Int J Plast, 2010; 26: 1220
[20] Keller C, Hug E, Habraken A M, Duchene L. Int J Plast, 2012; 29: 155
[21] Grogan J A, Leen S B, McHugh P E. J Mech Behav Biomed Mater, 2013; 20: 61
[22] Chen Y, Kraft O, Walter M. Acta Mater, 2015; 87: 78
[23] Fleurier G, Hug E, Martinez M, Dubos P A, Keller C. Philos Mag Lett, 2015; 95: 122
[24] Xu Z T, Peng L F, Fu M W, Lai X M. Int J Plast, 2015; 68: 34
[25] Peirce D, Asaro R J, Needleman A. Acta Metall, 1983; 31: 1951
[26] Asaro R J, Needleman A. Acta Metall, 1985; 33: 923
[27] Bassani J L, Wu T Y. Proc Soc Lond, 1991; 435A: 21
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