A crystal plasticity FE study of macro- and micro-subdivision in aluminium single crystals {001}<110> multi-pass rolled to a high reduction

doi:10.1016/j.jmst.2020.10.020

Abstract

Abstract:

In this study, the substructure formation in a multi-pass rolled aluminium single crystal {001}<110> was investigated by the crystal plasticity finite element model, and the predations were validated by experimental observations at both macro- and micro-scale. A finite element model for multi-pass rolling was developed to follow the real experimental rolling scheme, by which the through-thickness macroscopic subdivision was successfully predicted up to a 90 % reduction. The macro-subdivision was featured by forming matrix bands through the thickness, and the deformation behaviours, in terms of slip activity, shear strain and crystal rotation, alternated between matrix bands. The development of matrix bands, stability of crystal orientations, and correlation between slip activity, shear strain and crystal rotation have been investigated. Another modelling method, Submodel, was used to exceedingly increase the mesh resolution in smaller regions of interest, and the experimentally observed microstructure, i.e., micro-subdivision was explicitly and spatially revealed. Similar predictions were obtained in Submodels with different element sizes, which proves the feasibility of this method in predicting microstructure formation. It was found that the substructure formation by varying slip activity and crystal rotation between domains is energy favourable. The procedure of substructure formation was explained based on the predictions, three types of substructure have been identified, and the substructure formation was discussed.

Key words: Crystal plasticity FE, Single crystal, Multi-pass rolling, Submodel, Subdivision, Substructure

Hui Wang, Cheng Lu, Kiet Tieu, Yu Liu. A crystal plasticity FE study of macro- and micro-subdivision in aluminium single crystals {001}<110> multi-pass rolled to a high reduction[J]. J. Mater. Sci. Technol., 2021, 76: 231-246.

Figures/Tables 18

Fig. 1. Main features of three representative CP models and Submodel.

Table 1 Parameters used in the Bassani-Wu hardening model.

n	$\dot{\gamma}_{0}$(s-1)	h₀ (MPa)	h_s (MPa)	τ₁ (MPa)	τ₀ (MPa)	q
300	0.0001	100	0.01	6.3	6	1

Table 2 Notation of 12 slip systems.

Slip plane	(1 1 1)			$(\overline{1} 11)$			$(1 \overline{1} 1)$			$(\overline{1}\overline{1} 1)$
Slip direction	$[01\overline{1}]$	$[\overline{1}01]$	$[1\overline{1}0]$	$[01\overline{1}]$	$[\overline{1}\overline{1}0]$	[1 0 1]	$[0\overline{1}\overline{1}]$	$[\overline{1}01]$	[1 1 0]	$[0\overline{1}\overline{1}]$	[1 0 1]	$[\overline{1}10]$
Slip system	a1	a2	a3	c1	c3	c2	d1	d2	d3	b1	b2	b3

Fig. 2. (a) Crystal coordinate relative to sample coordinate of rotated-Cube orientation. (b) A {1 1 1} pole figure shows the relation between the three orientations and TD-rotation.

Fig. 3. Schematics of (a) multi-pass rolling FE model (Globalmodel), (b) Submodel1 at the surface, (d) Submodel1 at the centre, and (c) Submodel2 from Submodel1 at the surface.

Fig. 4. {1 1 1} pole figures after reductions of (a) 18 %, (b) 30 %, (c) 50 %, (d) 70 %, (e) 80 %, and (f) 90 % (upper panel: experiment [15], lower panel: simulation). The positions of rotated-Cube and Copper {1 1 2}<1 1 1> are indicated by circle and triangle marks, respectively.

Fig. 5. Distribution of FE meshes and TD-rotation (a) after 1-pass, (b) before 2-pass, (c) after 3-pass, (d) before 4-pass, and (e) after 5-pass.

Fig. 6. Distribution of TD-rotation and redundant shear strain γXY along the ND (from the lower surface to upper surface) after reductions of (a) 18 % (b) 50 %, (c) 70 %, (left panel: experiment [15], right panel: simulation).

Fig. 7. Distribution of simulated slip trace after (a) 1-pass, and (b) 2-pass. (c) Imbalance ratio of shear strain on slip systems, which was calculated according to (γa1-γb1)/max?(γa1,γb1). (d) Distribution of TD-rotation and slip trace in the rolling bite of 1-pass.

Fig. 8. Distribution of TD-rotation in the Submodel1 of the central region (a) after 1-pass, (e) before 2-pass, (f) after 2-pass, (g) after 3-pass, and (h) after 4-pass. (i) Distribution of TD-rotation and slip trace of an enlarged region after 2-pass. Distribution of TD-rotation after 1-pass in the Submodel1 with element sizes of (b) 60 μm × 60 μm in the Globalmodel and 2 μm × 2 μm in the Submodel1, (c) 30 μm × 30 μm in the Globalmodel and 2 μm × 2 μm in the Submodel1, and (d) 30 μm × 30 μm in the Globalmodel and 1 μm × 1 μm in the Submodel1. (j) A TEM image of the central region after 2-pass [15]. (k) Through-thickness EBSD maps after 2- and 3-pass in the experiment [15], where the maps are shown in grey scale, and pure white and black represent the most positive and negative TD-rotation, respectively. The region of Submodel1 in the corresponding experimental sample is marked in (k).

Fig. 9. (a) Distribution of TD-rotation in the Submodel1 at the surface. (b) A schematic drawing of substructure in Fig. 8(a). Distribution of TD-rotation in the Submodel1 and Submodel2 of region A (c, d) and region B (f, g). (e) Distribution of TD-rotation in the Globalmodel having the element size as small as that in the Submodel1. (h) Comparison of average TD-rotation through the thickness between Submodel1 and Globalmodel.

Table 3 Summary of deformation at different elements, where all values are those evolved in a single pass, not the cumulative ones.

	Increase of shear strain on slip systems			Ω_TD^P	Ω_TD^*	Redundant γXY	(Ω_TD)	Relation
element	a1, a2	b1, b2	c3, d3	Direction	Value	Value	Direction	Ω_TD^P+Ω_TD^*=Ω_TD
A, 1-pass	0.0974	0.146	0	+TD	-3.8°	-0.015	-TD	(+)+(-)=(-), \|Ω_TD^P\| < \|Ω_TD^*\|
A, 2-pass	0.0647	0.131	0	+TD	-2.9°	0.02	+TD	(+)+(-)=(+), \|Ω_TD^P\| > \|Ω_TD^*\|
B, 1-pass	0.156	0.0863	0	-TD	4.13°	0.0157	+TD	(-)+(+)=(+), \|Ω_TD^P\| < \|Ω_TD^*\|
B, 5-pass	0.463	0	0.242	-TD	2.14°	-0.212	-TD	(-)+(+)=(-), \|Ω_TD^P\| > \|Ω_TD^*\|
C, 1-pass	0.134	0.126	0	-TD	0.31°	0.0032	+TD	(-)+(+)=(+), \|Ω_TD^P\| < \|Ω_TD^*\|
D, 1-pass	0.00583	0.216	0	+TD	-11.3°	-0.0447	-TD	(+)+(-)=(-), \|Ω_TD^P\| < \|Ω_TD^*\|
E, 1-pass	0.281	0.00135	0	-TD	15.3°	0.02	+TD	(-)+(+)=(+), \|Ω_TD^P\| < \|Ω_TD^*\|

Fig. 10. TD-rotation and imbalance ratio along (a) Line1, and (b) Line2 in Fig. 9(a).

Fig. 11. Evolution of (a) material spin rate about TD, (b) shear strain rates on slip systems, (c) TD-rotation, and (d) stress, as a function of rolling time at element A in the Globalmodel.

Fig. 12. Ratios between increase of crystal rotation to increase of shear strain in each pass of the Globalmodel.

Fig. 13. (a) Evolution of cumulative shear strain at element A in the Globalmodel. Distribution of (b) strength (τc) on slip systems, (c) shear strain rate on a1 and b1, (d) TD-rotation, and (e) cumulative shear strain on a1 and b1 at different rolling time in the Submodel2 of region A.

Fig. 14. (a) Evolution of plastic work as a function of rolling time in the Submodel1 and Submodel2 of region A and C.

Fig. 15. A schematic shows substructure formation. (a) Only one set of slip systems activated in stage1, (b) the activation of the other set of slip systems in stage2 leads to the formation of a cell-block structure (in matrix bands), (c) the two equally activated sets of slip systems in stage2 result in an equi-axised structure (in transition bands), and (d) the high activation of one set of slip systems in different regions gives rise to the sharp change of crystal rotation between domains (band III in the centre region). Shear strain on a1 and b1 at (e) element A, and (g) element C in the Globalmodel during 1-pass. Distribution of TD-rotation in Submodel2 of (f) region A, and (h) region C after 1-pass. (i) Shear strain at point D and E marked in (j). (j) Distribution of TD-rotation at the central region of Submodel1 after 1-pass.

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