Symmetric and Asymmetric Rolling Pure Copper Foil: Crystal Plasticity Finite Element Simulation and Experiments

doi:10.1007/s40195-015-0290-0

Abstract

Abstract:

A systematic study has been conducted aiming to attain an insight into the influence of coefficient of roll speed asymmetry, crystal orientation and structure on the deformation behavior, and crystallographic orientation development during foil rolling. Simulations were successfully carried out by using crystal plasticity finite element method (CPFEM), and a novel computational framework is presented for the representation of virtual polycrystalline grain structures. It has been found that asymmetric rolling (ASR) is more efficient in producing plastic deformation since it develops additional shear strain and activity of slip system compared with symmetric rolling (SR). For ASR, increase in the length of the shear zone, and decrease in the amount of the pressure and roll force would lead to further reduction. The shear strain path in SR and ASR is strictly influenced by the misorientation of neighbor grains, and corresponding {1 1 1} pole figures offer direct evidence of the spread of crystallographic orientation around the normal direction. The activity of slip systems was examined in detail and found that the predicted results are consistent with the surface layer model. The accuracy of the developed CPFEM model is verified by the fact that the simulated results of roll force coincide well with the experimental results.

Key words: Foil rolling, Shear deformation, Polycrystals model, Finite element analysis

Shou-Dong Chen, Xiang-Hua Liu, Li-Zhong Liu. Symmetric and Asymmetric Rolling Pure Copper Foil: Crystal Plasticity Finite Element Simulation and Experiments[J]. Acta Metallurgica Sinica (English Letters), 2015, 28(8): 1024-1033.

Figures/Tables 14

Table 1 Definition of slip system in present study

Slip system	Slip plane	Slip direction
a ₁		[0 -1 1]
a ₂	(1 1 1)	[1 0 -1]
a ₃		[-1 1 0]
b ₁		[1 0 1]
b ₂	(-1 1 1)	[1 1 0]
b ₃		[0 -1 1]
c ₁		[0 1 1]
c ₂	(1 -1 1)	[1 1 0]
c ₃		[1 0 -1]
d ₁		[0 1 1]
d ₂	(1 1 -1)	[1 0 1]
d ₃		[-1 1 0]

Table 2 Parameters used in the constitutive model

n	γ ˙ 0 (1/s)	h ₀ (MPa)	h _s (MPa)	τ (MPa)	τ ₀ (MPa)	γ ₀	a ₁	a ₂	a ₃	a ₄	a ₅
20	0.0001	90	1.5	1.3	1	0.001	8	8	8	15	20

Fig. 1 Schematic diagram of the rolling progress and coordinate system

Fig. 2 a Partial input geometry used for CPFE simulation (Gn represents the nth grain, and different colors mean different grain orientations); b {1 1 1} pole figure of initial crystallographic orientation

Table 3 Initial cold foil rolling conditions for CPFE simulation

Rolling type	H (mm)	Length (mm)	Upper roll rotational speed (rad/s)	Lower roll rotational speed (rad/s)	Reduction (%)	Friction coefficient	Asymmetric speed coefficient (S _r)
SR	0.1	5	1.04	1.04	20	0.1	1
ASR	0.1	5	1.04	1.144	20	0.1	1.1

Fig. 3 Grain shape and mesh in the rolling deformation zone under asymmetric speed coefficients of S r = 1 a, S r = 1.1 b

Fig. 4 Distribution of LE maximum principal strain in the rolling deformation zone under asymmetric speed coefficients of S r=1 (a),S r= 1.1 (b)

Fig. 5 Distributions of the contact pressure and frictional stress in the deformation zone under different asymmetric speed coefficients of S r=1(a, b), Sr =1.1 (c, d)

Fig. 6 Distributions of Mises stress and shear strain through thickness direction under different asymmetric speed coefficients in different paths: a path-1, stress; b path-2, stress; c path-3, stress; d path-1, shear strain; e path-2, shear strain; f path-3, shear strain

Fig. 7 {1 1 1} pole figures of the grains G26, G27, and G28: a-c initial crystallographic orientation; d-f S r = 1; g-i S r = 1.1

Fig. 8 Illustration of (1 1 1) slip plane for the initial cube orientation

Fig. 9 Comparisons of shear strain rate of slip system a 3 (a-d) and slip system c 2 (e-h) under asymmetric speed coefficients of S r = 1 (a, c, e, g), S r = 1.1 (b, d, f, h) at the moments of 1.5, 1.75, 1.9 and 2.0 s, respectively

Fig. 10 Microstructure of the annealed pure copper foil

Table 4 Comparison between the simulative and experimental roll forces per unit width of roll

Rolling type	Experiment (N/mm)	Simulation (N/mm)
SR	826.5	820.71
ASR	734	730.15

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