materials Article
Comparisons of Different Models on Dynamic Recrystallization of Plate during Asymmetrical Shear Rolling Tao Zhang 1, *, Lei Li 1 , Shi-Hong Lu 1 , Hai Gong 2 and Yun-Xin Wu 2 1 2
*
College of Mechanic and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China;
[email protected] (L.L.);
[email protected] (S.-H.L.) State Key Laboratory of High Performance Complex Manufacturing, Central South University, Changsha 410083, China;
[email protected] (H.G.);
[email protected] (Y.-X.W.) Correspondence:
[email protected]; Tel.: +86-152-5099-7258
Received: 30 November 2017; Accepted: 8 January 2018; Published: 17 January 2018
Abstract: Asymmetrical shear rolling with velocity asymmetry and geometry asymmetry is beneficial to enlarge deformation and refine grain size at the center of the thick plate compared to conventional symmetrical rolling. Dynamic recrystallization (DRX) plays a vital role in grain refinement during hot deformation. Finite element models (FEM) coupled with microstructure evolution models and cellular automata models (CA) are established to study the microstructure evolution of plate during asymmetrical shear rolling. The results show that a larger DRX fraction and a smaller average grain size can be obtained at the lower layer of the plate. The DRX fraction at the lower part increases with the ascending speed ratio, while that at upper part decreases. With the increase of the offset distance, the DRX fraction slightly decreases for the whole thickness of the plate. The differences in the DRX fraction and average grain size between the upper and lower surfaces increase with the ascending speed ratio; however, it varies little with the change of the speed ratio. Experiments are conducted and the CA models have a higher accuracy than FEM models as the grain morphology, DRX nuclei, and grain growth are taken into consideration in CA models, which are more similar to the actual DRX process during hot deformation. Keywords: asymmetrical shear rolling; microstructure evolution models; cellular automata; DRX behavior; grain refinement
1. Introduction Aluminum alloy thick plates with light weight, high strength, good corrosion resistance, and formability, as a key material for integrated-structure parts, are widely used in the aerospace field [1]. Hot rolling is the key process of preparation for thick plates; however, the conventional symmetrical rolling process causes insufficient deformation and large grain at the center of the thick plate, resulting in poor mechanical properties at the center of the plate, which has become a barrier to the development of aerospace technologies. A new technique of asymmetrical shear rolling was adopted to solve uneven deformation [2]. Dynamic recrystallization (DRX) plays a vital role in grain refinement during hot rolling [3]. THe kinetic behavior of the DRX process under hot deformation for different materials had been studied by many researchers and each parameter in Avrami equation was fitted by experimental flow curves [4,5]. The modeling [6] and mechanism [7] of DRX behavior had been conducted by microstructure models and experiment. Maire et al. [8] established a full field modeling of dynamic and post-dynamic recrystallization and simulated topological evolutions by linking boundaries velocity and thermodynamic driving forces. Aashranth et al. [9] used an irreversible thermodynamics
Materials 2018, 11, 151; doi:10.3390/ma11010151
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approach to identify stabilization stress and found that grain growth is the dominant microstructural phenomenon of DRX in the hot working process. Lin et al. [10] studied the effects of strain rate and deformation temperature on the microstructure evolution by integrating thermo-mechanical FEM with microstructure evolution models. In addition to the effects of strain rate and temperature, Wen et al. [11] analyzed the influences of the initial δ phase on DRX behavior and constructed DRX kinetics models by considering the synthetical influences of the initial δ phase. Microstructure variations due to the dynamic recrystallization (DRX) process have been analyzed by cellular automata (CA) methods by many researchers [12–15]. Lee et al. [16] and Seyed et al. [17] established a cellular automata model to analyze the microstructure variation of DRX during non-isothermal hot compression. Zheng et al. [18] established CA models to predict the microstructure variation of different recrystallization processes during multi-pass symmetrical rolling. Li et al. [19] and Jiang et al. [20] studied the relationship between microstructure and mechanical properties during asymmetrical rolling. Asymmetrical shear rolling is a rolling method with velocity asymmetry and geometry asymmetry, which is beneficial to deformation permeation and grain refinement, especially at the center point of an ultra-thick plate. Many previous studies have focused on the effect of parameters of symmetrical rolling or different speed rolling on DRX fraction and grain size by microstructure evolution models or experiments. However, the effects of the speed ratio and offset distance on grain refinement or microstructure distribution of the plate in asymmetrical rolling are rarely published. Microstructure evolution models are empirical models and they are in relation to the variation of macro parameters in the rolling process, such as strain, strain rate, and temperature, in which the DRX process can be calculated very quickly. The nucleation and grain growth in the DRX process are considered in CA models and the topology of the microstructure can be obtained; however, the computing efficiency is relatively lower. Metallographic experiments can be conducted after rolling or just at given passes, but they are not able to track the microstructure variation during multi-pass rolling processes. Meanwhile, these experiments tend to damage the plate and cause material loss as well as decrease production efficiency. Therefore, the microstructure evolution in asymmetrical shear rolling as well as the effects of the speed ratio and offset distance on grain size variation need to be studied further in order to regulate and control the microstructure variation. However, the difference between these two methods is rarely studied and the accuracy of them needs to be compared in order to obtain the microstructure evolution efficiently. In this study, coupled FEM-microstructure evolution models and CA models are established to study the DRX behavior and variation of grain size for aluminum alloy plate during asymmetrical shear rolling, especially for the cross shear zone. The effects of the speed ratio and offset distance on the DRX fraction and average grain size are analyzed. Finally, experiments are conducted to compare the accuracy of these two kinds of models. 2. Asymmetrical Shear Rolling Asymmetrical shear rolling is a rolling method with velocity asymmetry and geometry asymmetry. The lower roll has a larger velocity than the upper roll and there is also a horizontal offset distance (S) of the slow roll in outlet direction, as shown in Figure 1. As the lower work roll has a larger velocity, the neutral points of the upper and lower surfaces are not in the same vertical line. As a result, the deformation zone of the plate is divided into three zones: Backward slip zone, cross shear zone, and forward slip zone. The plate is subjected to strong shear strain in the cross shear zone, which is the prominent distinction to symmetrical rolling. The velocity asymmetry is beneficial for a large cross shear zone and strong shear strain at the center of thick plate, which contributes to deformation permeation into center part of the plate during the rolling process [21,22]. Due to velocity asymmetry, the plate will bend upwards for faster flow velocity of at the lower layer of the plate. The offset distance is adopted to apply a moment in the opposite direction of bending upwards to the plate during asymmetrical shear rolling. Through a good combination of speed ratio, offset distance, pass reduction, and initial thickness, quasi smooth plate can be obtained in asymmetrical
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shear rolling [23]. As a result, the plate can be subjected to strong shear strain with a small curvature, in asymmetrical shear rolling [23]. As rolling a result,deformation. the plate can be subjected to strong shear strain with a thus guaranteeing smooth multi-pass small curvature, thus guaranteeing smooth multi-pass rolling deformation.
Figure 1. Schematic diagram of asymmetrical shear Velocity of shear rolling rolling (V (V11: Velocity of upper upper roll; roll; V V22 : Velocity lower roll; S: Offset distance; αα11:Neutral :Neutral angle of upper roll; αα22:Neutral :Neutral angle angle of of lower lower roll). roll).
3. Models Establishment 3.1. Microstructure Evolution Model The microstructure evolution model is a kind of empirical model to calculate the DRX fraction, fraction, dynamic recrystallized recrystallized grain grainsize, size,and andaverage averagegrain grain size during deformation, which is related to size during deformation, which is related to the the strain, strain temperature. Therefore, an model is necessary to obtain the deformation strain, strain rate,rate, andand temperature. Therefore, an model is necessary to obtain the deformation and and temperature distributions in the rolling process. this study,single singlepass passrolling rolling models models are temperature distributions in the hothot rolling process. In In this study, established and rolling parameters are shown in Table 1. The material of the plate is 7055 aluminum alloy, and its constitutive constitutive equation equation [24] [24] isis shown shownin inEquation Equation(1). (1).The Theinitial initial rolling temperature rolling temperature is ◦ C and the inlet thickness is 250 mm. The heat transfer coefficient [25] to the environment is is 410 410 °C and the inlet thickness is 250 mm. The heat transfer coefficient [25] to the environment is 5 −1 and the contact heat transfer coefficient to the work roll and emulsion is 30,000 W·2m2−1·K−1 . 5W·m W·2m ·K2−1·Kand the contact heat transfer coefficient to the work roll and emulsion is 30,000 W·m ·K . . −1.36382 × 105 5 ε = 6.1192 × 109 9 [sin h(0.0147σ )]5.2212 exp − × 1.36382 10 RT ε =6.1192 × 10 [sinh(0.0147σ )]5.2212 exp
.
RT
(1) (1)
where ε is strain rate, σ is flow stress, and T is temperature.
where
ε
is strain rate, σ is flow stress, and T is temperature.
Table 1. Single rolling parameters.
Table 1. Single rolling parameters. Parameter Value
Parameter Work roll radius, R/mm Shear friction m Work rollcoefficient, radius, R/mm Velocity of lower roll, V 2 /(m/s) Shear friction coefficient, m Velocity of upper roll, V 1 /(m/s) Velocity of lower roll, V2/(m/s) Pass reduction, ∆h/mm Velocity of upper Speed ratio, i = V 2roll, /V 1 V1/(m/s) Offset S/mm Passdistance, reduction, Δh/mm
Value 500 0.4 500 1~1.3 0.4 1 1~1.3 30, 50 1 1.00~1.3 0~70 30, 50 Speed ratio, i = V2/V1 1.00~1.3 Offset distance, S/mm 0~70critical strain. In terms of micro The DRX process begins when the strain of the material exceeds perspective, the dislocation density is in relation to the strain and the DRX nuclei appear when reaching The DRX process density. begins when thestrain strainisof the material critical In terms of micro the critical dislocation Critical connected withexceeds peak strain andstrain. they are both functions perspective, thestrain, dislocation density is the in relation to the strain and the appear when of temperature, and strain rate in models proposed by Sellars andDRX Yadanuclei [26,27], as shown in reaching the critical dislocation density. Critical strain is connected with peak strain and they are Equations (2) and (3). both functions of temperature, strain, and strain in the models .rate 42448 proposed by Sellars and Yada 0.15975 ε p = 1.697 × 10−5 ε exp( ) (2) [26,27], as shown in Equations (2) and (3). RT
ε p = 1.697 ×10-5 ε 0.15975 exp(
42448 ) RT
(2)
where εp is peak strain, εc is critical strain. The DRX process mainly depends on two parameters: The DRX fraction Xd and recrystallized grain size Dd. In general, the value of the recrystallized grain size is much smaller than the initial grain size. Therefore, the initial grain can be intensively refined through sufficient DRX processing. Materials 2018, 11, 151 4 of 13 The DRX fraction, recrystallized grain size, and average grain size can be calculated by Equations (4)–(7). ε c = 0.8ε p (3)
ε −ε
c 1.065 where εp is peak strain, εc is critical X d =strain. 1 − exp −3.4 × 10 −2 ( ) (4) The DRX process mainly depends on two The DRX fraction Xd and recrystallized parameters:ε 0.5 grain size Dd . In general, the value of the recrystallized grain size is much smaller than the initial grain size. Therefore, the initial grain can be intensively refined through sufficient DRX processing. The DRX 25707 4 0.09349 fraction, recrystallized grain size, average canbe calculated by Equations (4)–(7). (5) = 7.57 ×10−grain ε and ε sizeexp
0.5
Xd = 1 − exp −3.4 × 10−2 (
RT 1.065
ε − εc ) ε 0.5
−21542 Dd = 1.0473 ×103 ε 0.129 exp( ) 25707 RT −4 . 0.09349 exp ε = 7.57 × 10 ε 0.5
RT
D = X D +. 0.129 (1− X d )−D21542 0
Dd = 1.0473 ×d 10d3 ε
exp(
)
(4)
(6) (5)
(7) (6)
RT where Xd is the DRX fraction, ε0.5 is the strain corresponding to 50% DRX fraction, Dd is the D = Xd Dd + (1 − Xd ) D0 (7) recrystallized grain size, D0 is the initial grain size, and D is the average grain size after where Xd is the DRX fraction, ε0.5 is the strain corresponding to 50% DRX fraction, Dd is the deformation. grain size, D is the initial grain size, and D is the average grain size after deformation. recrystallized 0
3.2. Cellular 3.2. Cellular Automata Automata Model Model During the thehothot rolling process, hardening and dynamic recovery common During rolling process, work work hardening and dynamic recovery are commonare phenomena; phenomena; takethe place when the dislocation reaches thewhich criticalhas value, which has DRX will takeDRX placewill when dislocation density reachesdensity the critical value, a significant rolea significant role in grain refinement. In this study, probabilistic CA models are adopted to predict the in grain refinement. In this study, probabilistic CA models are adopted to predict the variation of the variation of the microstructure and grain size during hot rolling. In the CA model, the complex microstructure and grain size during hot rolling. In the CA model, the complex object is divided into objectdiscrete is divided intoand cells discrete in time and spaceby and cell is density, definedcrystal by its orientation, dislocation cells in time space and each cell is defined its each dislocation density, crystal orientation, temperature, and strain rate, in which cells with the same crystal temperature, and strain rate, in which cells with the same crystal orientation belong to a specific orientation belong to a specific grain. The status values of each cell are updated at each CA time step grain. The status values of each cell are updated at each CA time step according to the transition rules accordingthetocell theand transition rules between andthe itstemperature, neighborhood. In strain the CA model, the between its neighborhood. In thethe CA cell model, strain, rate, and flow temperature, strain, strain rate, and flow stress are derived from FEM results. stress are derived from FEM results. To acquire acquire equiaxed equiaxed grain grain and and decrease decrease microsegregation microsegregation from from casting, casting, the the homogenization homogenization To treatment is conducted before hot rolling. The nucleation points are spread uniformly into the the treatment is conducted before hot rolling. The nucleation points are spread uniformly into simulation zone and they grow into equiaxed grains in all directions with the same probability. simulation zone and they grow into equiaxed grains in all directions with the same probability. Figure 22 shows shows the the initial initialmicrostructure microstructurefor forthe thegrain grainsize sizeofof100 100µm, μm, which corresponds a point Figure which corresponds to to a point at at the macro level in a finite element model. the macro level in a finite element model.
Figure 2. Initial microstructure of 7055 aluminum alloy (v represents rolling direction; A, B and C represent point at upper surface, center and lower point of the plate).
7055 aluminum alloy is a kind of material with high stacking fault energy, which plays a vital role in its softening mechanism in hot deformation. The softening mechanism during hot rolling consists of two processes: Dnamic recovery and DRX. The flow stress decreases in the macro level and the dislocation density reduces in the micro level. The stacking fault energy of the material significantly affects the variation of dislocation density and thus influences the softening mechanism.
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The dislocation density in a material provides the relationship between flow stress at the macro level and microstructure characteristics at the micro level, as shown in Equation (8). Therefore, the variation of dislocation density can be obtained by true stress-strain curves [21]. A Kocks–Mecking (KM) model is used to describe the variation of dislocation density under different conditions [28], as shown in Equation (9). p σ = αµb ρ (8)
√ dρ = k1 ρ − k2 ρ dε
(9)
where ρ is the average dislocation density, ρ is the dislocation density, k1 and k2 are work hardening and dynamic softening coefficients, respectively; α is the dislocation interaction term, µ is the shear modulus, and b is the modulus of Burger’s vector. Newly dynamically recrystallized nuclei start to appear when the dislocation density exceeds . critical value. The nucleation rate (n) can be calculated by models from Ding and Guo [29,30], as shown in Equation (10). The recrystallized nuclei start to grow into recrystallized grain after nucleation during the deformation process. The grain growth velocity (v) [31] is related to pressure (p) and the grain boundary (GB) mobility (M), as shown in Equation (11). .
.m
n = C ε exp(
− Q act ) RT
v = Mp
(10) (11)
where C is the material constant, m is the sensitivity coefficient of strain rate, and Qact is active energy. 4. Results and Discussion 4.1. DRX Fraction and Grain Size In the hot rolling process, DRX plays an important role in grain refinement. With velocity asymmetry and geometry asymmetry in asymmetrical shear rolling, the distributions of the DRX fraction and average grain size are asymmetrical, as shown in Figure 3. The DRX fraction at the lower layer of the plate is larger than that at the upper layer; as a result, finer grains appear at the lower layer. Due to the larger velocity of the lower work roll, the metal flow is faster and the equivalent strain is much larger than that at the upper layer; meanwhile, the temperature is higher than that at the upper layer because the contact time and heat exchange with the work roll are obviously reduced with a faster work velocity. However, the maximum DRX fraction and minimum average grain size are located subsurface of the plate (about 25 mm from surface). Due to direct contact with the work rolls, the metal flow at the surface is hindered by contact friction force and the equivalent strain is smaller than that at the subsurface. Therefore, large deformation and high temperature contribute to a more sufficient DRX process and intense grain refinement. Figure 4 shows variations of the DRX fraction and average grain size at different positions of the plate. The DRX fraction is 19.2% at the lower surface; it is 26% larger than that at the upper surface. For a given pass reduction, large deformation at the lower layer will result in small strain at the upper layer because the average deformation is constant. As a result, smaller grain size (84.5 µm) can be obtained at a lower surface compared to that (87.5 µm) at the upper surface.
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DRX fraction is 19.2% at the lower surface; is 26% larger than at the upper surface. a given DRX fraction is 19.2% at the lower surface; it isit26% larger than thatthat at the upper surface. ForFor a given pass reduction, large deformation at the lower layer will result in small strain at the upper layer pass reduction, large deformation at the lower layer will result in small strain at the upper layer because average deformation is constant. a result, smaller grain (84.5 can be because thethe average deformation is constant. As As a result, smaller grain sizesize (84.5 μm)μm) can Materials 2018, 11, 151 6 ofbe 13 obtained at a lower surface compared to that (87.5 μm) at the upper surface. obtained at a lower surface compared to that (87.5 μm) at the upper surface.
FigureDistribution 3. Distribution(a) of (a) Dynamic recrystallization (DRX) fraction and (b) average grain size of Figure Figure 3. 3. Distributionof of (a)Dynamic Dynamicrecrystallization recrystallization(DRX) (DRX)fraction fractionand and(b) (b)average averagegrain grainsize sizeof of plate during asymmetrical shear rolling. plate plateduring duringasymmetrical asymmetrical shear shear rolling. rolling.
(a) (a) 0.20
(b) 102 (b) 102 100
0.20
0.05 0.00
0.15 Upper surface Upper surface Center Center Lower surface Lower surface
0.10 0.05
R=500mm,m=0.4,i=1.1, R=500mm,m=0.4,i=1.1, S=40mm,V1=1m/s,Δh=30mm S=40mm,V1=1m/s,Δh=30mm
0.00 0.0
0.0
0.5
0.5
1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 Time /s Time /s
Average grain size /μm
0.10
98
Average grain size /μm
DRX fraction
DRX fraction
0.15
100
96 94 92 90 88 86 84
Upper surface Upper surface Center Center Lower surface Lower surface
98 96
R=500mm,m=0.4,i=1.1, R=500mm,m=0.4,i=1.1, S=40mm,V1=1m/s,Δh=30mm S=40mm,V1=1m/s,Δh=30mm
94 92 90 88 86 84 0.0
0.0
0.5
0.5
1.0 1.5 2.0 2.5 1.0 1.5 2.0 2.5 Time /s Time /s
Figure 4. Variation of (a) DRX fraction and (b) average grain size at different positions of plate. Figure 4. Variation of DRX (a) DRX fraction (b) average grain at different positions of plate. Figure 4. Variation of (a) fraction andand (b) average grain sizesize at different positions of plate.
In the the author’s previous studiesstudies [21], the[21], speed ratio and offset distance were found towere significantly author’s previous speed ratio offset distance found In In the author’s previous studies [21], thethe speed ratio andand offset distance were found to to affect distributions of equivalent strain, shear strain,strain, and temperature. According to Equations (4)–(7), to significantly affect distributions of equivalent shear strain, and temperature. According significantly affect distributions of equivalent strain, shear strain, and temperature. According to theEquations DRX fraction and average grain and size average are functions withare strain, strainwith rate,strain, and temperature. (4)–(7), DRX fraction grain functions strain rate, Equations (4)–(7), thethe DRX fraction and average grain sizesize are functions with strain, strain rate, andand Therefore, the effects of the speed ratio and offset distance on the DRX process and grain size are temperature. Therefore, effects of the speed ratio offset distance DRX process temperature. Therefore, thethe effects of the speed ratio andand offset distance on on thethe DRX process andand necessarily analyzed to gain a analyzed better understanding of microstructure variation in asymmetrical rolling. in grain necessarily to gain a better understanding of microstructure variation grain sizesize are are necessarily analyzed to gain a better understanding of microstructure variation in Figure 5 shows the effect of speed ratio on distributions of the DRX fraction and average grain size asymmetrical rolling. asymmetrical rolling. in asymmetrical Theeffect DRX fractions at the lower surface andofsubsurface increaseand withaverage ascending Figure 5 rolling. shows of speed ratio distributions DRX fraction grain Figure 5 shows thethe effect of speed ratio on on distributions of thethe DRX fraction and average grain speed ratio; meanwhile, rolling. the average grain sizes at these positions decrease. However, a smaller DRX size in asymmetrical The DRX fractions at the lower surface and subsurface increase with size in asymmetrical rolling. The DRX fractions at the lower surface and subsurface increase with fraction and larger average grain size appear at the upper surface and subsurface with the increase ascending speed ratio; meanwhile, average grain sizes at these positions decrease. However, ascending speed ratio; meanwhile, thethe average grain sizes at these positions decrease. However, a a of smaller the speed ratio. As the speed ratio increases, the total strain andupper temperature are both enlarged DRX fraction and larger average grain size appear at the surface and subsurface with smaller DRX fraction and larger average grain size appear at the upper surface and subsurface with at lower part of the plate. Firstly, a speed large work roll velocity is beneficial to reduce the contact increase of the speed ratio. ratio increases, total strain temperature both thethe increase of the speed ratio. As As thethe speed ratio increases, thethe total strain andand temperature are are both time and decrease the temperature drop, which results inwork higher temperature. Furthermore, higherthe enlarged at the lower of the plate. Firstly, a large velocity is beneficial to reduce enlarged at the lower partpart of the plate. Firstly, a large work rollroll velocity is beneficial to reduce the temperature willand reduce the flow stress of the plate, which has a positive effect on strain enlargement, contact time decrease the temperature drop, which results in higher temperature. Furthermore, contact time and decrease the temperature drop, which results in higher temperature. Furthermore, and large temperature deformation energy may the in turn increase thethe temperature. With the increaseeffect of the speed higher reduce flow stress of plate, which a positive strain higher temperature willwill reduce the flow stress of the plate, which hashas a positive effect on on strain ratio, the minimum DRX fraction movesenergy to a position toincrease the upper part instead ofWith locating at the enlargement, large deformation may innear turn temperature. increase enlargement, andand large deformation energy may in turn increase thethe temperature. With thethe increase center point of the plate, which illustrates that a large speed ratio is beneficial toupper strain part permeation of the speed ratio, the minimum DRX fraction moves to a position near to the instead of the speed ratio, the minimum DRX fraction moves to a position near to the upper part instead of of from the lower surface into upper part. The DRX fractionthat varies fromspeed 24.9%ratio to 32.1% at the lower locating at the center point of the plate, which illustrates a large is beneficial to strain locating at the center point of the plate, which illustrates that a large speed ratio is beneficial to strain surface and thefrom increase rate issurface 28.9%. into upper part. The DRX fraction varies from 24.9% to 32.1% at permeation the lower permeation from the lower surface into upper part. The DRX fraction varies from 24.9% to 32.1% at lower surface increase is 28.9%. thethe lower surface andand thethe increase raterate is 28.9%.
reduction is smaller than the given pass reduction. As a result, the deformation over the whole thickness of the plate will be decreased. The offset distance has little effect on temperature variation as the contact time of the upper surface and lower surface is almost the same. The DRX fraction at the center point decreases by only 1.1% when the offset distance varies from 0 to 70 mm, which Materials 2018, 11, 151 7 of 13 indicates the offset distance has slight effect on the DRX fraction and grain size. Materials 2018, that 11, 151 7 of 13
DRX fraction
Average grain size /μm
The effect of the speed ratio on distributions of the DRX fraction and average grain size is depicted in Figure 6. Increase of the offset distance will decrease the DRX fraction and increase the 86 0.38 i=1.0 average grain size almost across Although the arm of force between 84 i=1.0 the whole thickness of the plate. i=1.05 0.36 i=1.0 5 i=1.1 the two work rolls increases with the offset distance, the force value will decrease because the actual 82 0.34 i=1.1 i=1.2 i=1.2 given pass reduction. As a result, i=1.3 reduction0.32is smaller than the the deformation over the whole 80 i=1.3 78 little effect on temperature variation thickness0.30 of the plate will be decreased. The offset distance has 0.28 76almost the same. The DRX fraction at as the contact time of the upper surface and lower surface is 0.26 74 0.24 the center point decreases by only 1.1% when the offset distance varies from 0 to 70 mm, which R=500mm,m=0.4,S=0 0.22 72 R=500mm,m=0.4,S=0 V =1m/s,Δh=50mm indicates that the offset distance has slight effect on the DRX fraction and grain size. 0.20 0.18
1
V1=1m/s,Δh=50mm
0
50
100
150
70
200
0
Distance from upper surface/mm 0.38
(a)
DRX fraction
0.32 0.30
Average grain size /μm
0.34
100
150
84
i=1.0 i=1.05 i=1.1 i=1.2 i=1.3
0.36
50
200
Distance from upper surface/mm
86
82
(b)
80
i=1.0 i=1.05 i=1.1 i=1.2 i=1.3
Figure Effect speed ratio distributions fraction and average grain 78DRX Figure 5. 5. Effect of of speed ratio onon distributions of of (a)(a) DRX fraction and (b)(b) average grain sizesize in in asymmetrical shear rolling. 76 asymmetrical shear rolling. 0.26 0.28 0.24 0.22
R=500mm,m=0.4,S=0 speed ratio on distributions V1=1m/s,Δh=50mm
74 R=500mm,m=0.4,S=0
72
=1m/s,Δh=50mm effect of the of the DRX fraction Vand average grain size is depicted 0.32 84 70 0.18 in Figure 6. Increase of the offset distance will decrease the DRX fraction S=0mm and increase the average 0 50 100 150 S=0mm 200 0 83 50 100 150 200 S=30mm 0.30 S=30mm grain size almost across thesurface/mm whole thickness of the plate. Although theS=50mm arm of surface/mm force between the two Distance from upper Distance from upper 82 S=50mm S=70mm 0.28 S=70mm work rolls increases with the offset distance, the force value will81decrease because the actual reduction 80 is smaller than the given pass reduction. As a result, the deformation over the whole thickness of the 0.26 (a) (b) 79 plate will be0.24 decreased. The offset distance has little effect on temperature variation as the contact 78 Effectsurface of speed ratio on distributions of (a) the DRXsame. fraction (b)fraction average at grain size in point timeFigure of the5.upper and lower surface is almost Theand DRX the center 0.22 77 asymmetrical R=500mm,m=0.4,i=1.0 decreases by onlyshear 1.1%rolling. when the offset distance varies from 0 to 70 mm, which indicates that the offset R=500mm,m=0.4,i=1.0 76 V =1m/s,Δh=50mm V =1m/s,Δh=50mm 0.20 distance has slight effect on the DRX fraction and grain size. 75 1
DRX fracrion
Average grain size /μm
The 0.20
1
1
0.32 0.30
DRX fracrion
0.28
50
100
150
0
200
Distance from upper surface /mm S=0mm S=30mm S=50mm (a) S=70mm
84 83
Average grain size /μm
0
82 81
50
100
150
200
Distance from upper surface /mm S=0mm S=30mm S=50mm S=70mm
(b)
Figure 6. Effect of offset distance on distributions of (a) DRX fraction and (b) average grain size in 80 0.26 79 asymmetrical shear rolling. 0.24 0.22
78
77 As discussed above, the speed ratio and offset distance haveR=500mm,m=0.4,i=1.0 an effect on the asymmetrical R=500mm,m=0.4,i=1.0 V =1m/s,Δh=50mm V =1m/s,Δh=50mm 0.20 distribution of the DRX fraction and average grain size76between the upper and lower surfaces. In 75 0 100 fraction 150 200 0 50 100describe 150 200 asymmetry, a parameter order to quantificationally this of 50 the DRX difference, ΔX, Distance from upper surface /mm Distance from upper surface /mm is defined. Figure 7 shows the effects of speed ratio and offset distance on ΔX, which increases significantly with the ascending speed ratio. A large speed ratio is beneficial to induce strong shear (a) the strain gap between the upper and lower surfaces. (b) strain and will enlarge The offset distance has little effect on the DRX fraction difference. Therefore, a proper speed ratio should be set by Figure distributions inin Figure6.6.Effect Effectofofoffset offsetdistance distanceon distributionsofof(a) (a)DRX DRXfraction fractionand and(b) (b)average averagegrain grainsize comprehensive consideration of aonsufficient DRX fraction at the center point as well assize a small DRX asymmetrical shear rolling. asymmetrical shear rolling. fraction difference between the upper and lower surfaces. 1
1
As discussed above, the speed ratio and offset distance have an effect on the asymmetrical As discussed above, the speed ratio and offset distance have an effect on the asymmetrical distribution of the DRX fraction and average grain size between the upper and lower surfaces. In distribution of the DRX fraction and average grain size between the upper and lower surfaces. In order order to quantificationally describe this asymmetry, a parameter of the DRX fraction difference, ΔX, to quantificationally describe this asymmetry, a parameter of the DRX fraction difference, ∆X, is defined. is defined. Figure 7 shows the effects of speed ratio and offset distance on ΔX, which increases Figure 7 shows the effects of speed ratio and offset distance on ∆X, which increases significantly with significantly with the ascending speed ratio. A large speed ratio is beneficial to induce strong shear the ascending speed ratio. A large speed ratio is beneficial to induce strong shear strain and will strain and will enlarge the strain gap between the upper and lower surfaces. The offset distance has enlarge the strain gap between the upper and lower surfaces. The offset distance has little effect on the little effect on the DRX fraction difference. Therefore, a proper speed ratio should be set by DRX fraction difference. Therefore, a proper speed ratio should be set by comprehensive consideration comprehensive consideration of a sufficient DRX fraction at the center point as well as a small DRX of a sufficient DRX fraction at the center point as well as a small DRX fraction difference between the fraction difference between the upper and lower surfaces. upper and lower surfaces.
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DRX fracrion difference ΔXdΔX DRX fracrion difference d
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i=1.3 i=1.3 i=1.2 i=1.2 i=1.1 i=1.1 i=1.05 i=1.05 i=1.0 i=1.0 0 0
10 10
20
30
40
50
60
20 30 40 S/mm 50 60 Offset distance Offset distance S/mm
70 70
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Figure 7. Effect of offset distance on DRX fraction difference between the upper and lower surfaces Figure 7. Effect of offset offset distance on DRX DRX fraction fraction difference difference between between the the upper upper and and lower lower surfaces surfaces Figure Effect of distance on during7. asymmetrical shear rolling. during rolling. during asymmetrical asymmetrical shear shear rolling.
4.2. Microstructure Visualization 4.2. 4.2. Microstructure Microstructure Visualization Visualization Figure 8 shows the microstructure variation at the center point during different deformation Figure 8shows shows themicrostructure microstructure variation at the center point during different deformation zones. The 8white region represents thevariation matrix structure and colored grains represent DRX nuclei or Figure the at the center point during different deformation zones. zones. The white region represents the matrix structure and colored grains represent DRX nuclei or DRXwhite grains. It is obvious thatthe dynamic firstand appear at grain boundaries their high energy The region represents matrix nuclei structure colored grains representfor DRX nuclei or DRX DRX grains. It isinto obvious that dynamic nuclei appear at grain their high energy and then recrystallized grains. In appear thefirst backward zone,boundaries a few DRXfor nuclei are formed in grains. It isgrow obvious that dynamic nuclei first at grainslip boundaries for their high energy and then and then grow into recrystallized grains. In the backward slip zone, a few DRX nuclei are formed in the grain boundary and the grain is almost equiaxed of small deformation. The grow into recrystallized grains. In theshape backward slip zone, a fewbecause DRX nuclei are formed in the grain the grain and boundary and the recrystallized grain shape isgrain almost because of small deformation. The recrystallization and sizeequiaxed areof increased sharply in the cross shear zone, boundary thefraction grain shape is almost equiaxed because small deformation. The recrystallization recrystallization fraction andgrain recrystallized grain size are increased sharply in the cross zone, as shownand in Figure 8b. The large strain increases the sharply deformation energy the material, which fraction recrystallized size are increased in the cross inside shear zone, asshear shown in as shown in Figure 8b. The large strain increases the deformation energy inside the material, which promotes process of recrystallized grains. Furthermore, rises quickly in Figure 8b. the Thegrowth large strain increases the deformation energy insidethe thetemperature material, which promotes promotes the growth process of recrystallized grains. Furthermore, the temperature rises quickly in the cross shear zone due to the large heat energy induced by deformation energy, which enhances the growth process of recrystallized grains. Furthermore, the temperature rises quickly in the cross the zone the energy large heat energy induced bywithin deformation energy, which enhances the cross thermally activated motion of atoms and the material. As a result, the shear zoneshear due to the due largeto heat induced bymolecules deformation energy, which enhances the thermally the thermally activated motion of atoms and molecules within the material. As a result, the recrystallization from 1.8% in Figure 8a to 10% Figure and the average grain activated motion fraction of atomschanges and molecules within the material. As a in result, the8b recrystallization fraction recrystallization fraction fromIn in Figure 8a toaverage 10%there ingrain Figure 8breduces and thefrom average grain size reduces 100 μmchanges to8a 93.2 the forward slip is a size slight increase of strain and changes fromfrom 1.8% in Figure to μm. 10% in1.8% Figure 8b and thezone, 100 µm to size reduces from 100 μm to 93.2 μm. In the forward slip zone, there is a slight increase of strain recrystallization fraction. 93.2 µm. In the forward slip zone, there is a slight increase of strain and recrystallization fraction.and recrystallization fraction.
200μm 200μm
200μm 200μm
200μm 200μm
(a) backward slip zone (b) cross shear zone (c) forward slip zone (a) backward slip zone (b) cross shear zone (c) forward slip zone Figure 8. 8. Microstructure Microstructure under underconditions conditionsii== 1.1 1.1 and and SS == 40 40 mm mm at at the the center center point point of of the the plate. plate. Figure Figure 8. Microstructure under conditions i = 1.1 and S = 40 mm at the center point of the plate.
In asymmetrical shear rolling, asymmetrical strain distribution and temperature distribution In asymmetrical shear asymmetrical strain distribution andand temperature distribution will In asymmetrical shearrolling, rolling, asymmetrical strain distribution distribution will result in heterogeneous microstructure distribution. Figure 9 shows thetemperature microstructure variation result in heterogeneous microstructure distribution. Figure 9 shows thethe microstructure variation at will result in positions heterogeneous distribution. Figure 9 shows microstructure variation at different in themicrostructure cross shear zone. The grains at the surface point are elongated more different positions in the cross shearshear zone. zone. The grains at the surface point arepoint elongated more seriously at different positions in the cross The grains at the surface are elongated more seriously compared to the center point and the lower surface point is obviously subjected to the comparedcompared to the center point and the lower surface pointsurface is obviously subjected to the largest to strain. seriously to the center point and the lower point is obviously largest strain. Meanwhile, the number of dynamic nuclei at the surface is larger subjected than that at the the Meanwhile, number ofthe dynamic nuclei at the surface than that at thethan center because largest strain.the Meanwhile, number of surface dynamic nuclei is at larger the surface is larger that at the center because the large strain rate at the is beneficial to generate more nuclei, according to the large strainthe ratelarge at the surface is beneficial toisgenerate more nuclei, according to Equation (3). center because strain rate at the surface beneficial to generate more nuclei, according to Equation (3). However, the recrystallized grain size is smaller than that at the center point. Due to However, (3). the recrystallized size is smaller that at the center point. to the sufficient heat Equation thegrain recrystallized grainthan sizeand is smaller than the that at Due the center point. to the sufficientHowever, heat exchange with the work roll emulsion, temperature at the Due surface exchange withheat the work roll and emulsion, the roll temperature at the surface decreases sharply during the sufficient exchange with the work and emulsion, the temperature at the surface decreases sharply during rolling process, which hinders the grain growth; meanwhile, the decreases sharply duringis rolling process, grain growth; from meanwhile, the temperature at the center increased becausewhich of the hinders thermal the energy transferred deformation temperature at the center is increased because of the thermal energy transferred from deformation
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rolling process, which hinders the grain growth; meanwhile, the temperature at the center is increased because thermal energy transferred from energy. A DRX lowerprocess; temperature will increase energy.of A the lower temperature will increase thedeformation critical energy for the as a result, despite the energythe forrecrystallization the DRX process;fraction as a result, despitepoints the large strain, the fraction thecritical large strain, of surface is smaller thanrecrystallization that of the center point. ofThe surface points is smaller than that of the center point. The recrystallization fraction is 20.1% at the recrystallization fraction is 20.1% at the center point, which is larger than that at the upper center point, which is larger than that at the upper surface (13.2%) and lower surface (15.5%). surface (13.2%) and lower surface (15.5%).
200μm
(a) upper surface point
200μm
(b) center point
200μm
(c) lower surface point Figure 9. Microstructure under conditions i = 1.1 and S = 40 mm during the cross shear zone. Figure 9. Microstructure under conditions i = 1.1 and S = 40 mm during the cross shear zone.
The movement asymmetry of the speed ratio and geometry asymmetry of the offset distance The asymmetrical movement asymmetry of the ratio and geometry between asymmetry of the offset distance during shear rolling arespeed the obvious distinction symmetrical rolling. The during asymmetrical shear rolling are the obvious distinction between symmetrical rolling. The effects of the speed ratio on the average grain size and recrystallization fraction at the centereffects point of the speed ratio on the grain size and recrystallization fraction at the theaverage center point are depicted in Figure 10. average The recrystallization fraction increases sharply and grain are size depicted in Figure 10. The recrystallization fraction increases sharply and the average grain size is is refined remarkably when the speed ratio varies from 1.0 to 1.2. The strain and temperature both refined remarkably when the speed ratio varies from 1.0 to 1.2. The strain and temperature both increase with the ascending speed ratio, which promotes the DRX process and grain refinement. increase with ascending speeddown ratio,by which promotes the DRXthe process However, thethe increase rate slows sequentially increasing speedand ratiograin (fromrefinement. 1.2 to 1.3), However, the increase rate slows down by sequentially increasing the speed ratio (from 1.2 to 1.3), which indicates that a further increase of speed ratio has limited effect on grain refinement. The which indicates that a further increase of speed ratio has limited effect on grain refinement. The effect effect of the offset distance on the average grain size and recrystallization fraction is shown in Figure of offset the offset average grain size and recrystallization fraction is shown inthe Figure 11. 11.the With thedistance increase on of the distance, the recrystallization fraction decreases, while average With the increase of the offset distance, the recrystallization fraction decreases, while the average grain grain size increases. The actual pass reduction will decrease with the ascending offset distance, size increases. actualequivalent pass reduction will decrease the ascending in a resulting in aThe smaller strain. The offset with distance is mainly offset used distance, to reduceresulting the bending smaller equivalent strain. The offset distance is mainly used to reduce the bending behavior of behavior of the plate in asymmetrical shear rolling. Therefore, a proper offset distance should bethe set plate in asymmetrical shear rolling. Therefore, proper distance should be set by taking into by taking into consideration bending behavior aand grainoffset refinement. consideration bending behavior and grain refinement.
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0.234 83.2
0.2320.234
0.2260.228 0.2240.226 S=0mm S=30mm S=0mm S=50mm S=30mm S=70mm S=50mm S=70mm
0.2220.224 0.2200.222 0.2180.220 1.05 1.00
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Speed ratio i
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1.25 1.20
82.8 83.0 Average grain size/um
Average grain size/um
0.2280.230
DRX fraction
DRX fraction
0.2300.232
0.2160.218 1.00 0.216
S=0mm S=30mm S=0mm S=50mm S=30mm S=70mm S=50mm S=70mm
83.0 83.2
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1.00 82.0 1.30
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Speed ratio i 1.10 1.15
Speed ratio i
1.25 1.20
1.30 1.25
1.30
Speed ratio i
(a)
(b) (a)
(b)
Figure 10. Effect of speed ratio on (a): Recrystallization fraction and (b): Average grain size at the center point of Effect the plate. Figure speed ratio Recrystallization fraction and Average grain size Figure 10.10. Effect of of speed ratio onon (a):(a): Recrystallization fraction and (b):(b): Average grain size at at thethe
83.4
0.2320.234
83.2 83.4
0.2300.232
83.0 83.2
0.2280.230 0.2260.228 0.2240.226
i=1.0 i=1.05 0.2220.224 i=1.1 i=1.0 0.2200.222 i=1.2 i=1.05 i=1.3 i=1.1 0.2180.220 i=1.2 i=1.3 0.2160.218 -10 0 10 20 30 40 50 60 0.216 Offse distance S/mm -10 0 10 20 30 40 50
Offse distance S/mm
(a)
82.8 83.0
Average grain size /μm
Average grain size /μm
0.234
DRX fraction
DRX fraction
center point of the plate. center point of the plate. i=1.0 i=1.05 i=1.1 i=1.0 i=1.2 i=1.05 i=1.3 i=1.1 i=1.2 i=1.3
82.6 82.8 82.4 82.6 82.2 82.4 82.0 82.2
70
80
60
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-10 82.0 0 80
-10
10 0
20 30 40 50 60 70 Offse distance S/mm 10 20 30 40 50 60 Offse distance S/mm
80 70
80
(b)
(a) (b) Figure Figure11. 11.Effect Effectofofoffset offsetdistance distanceon on(a): (a):Recrystallization Recrystallizationfraction fractionand and(b): (b):Average Averagegrain grainsize sizeatatthe the center point of the plate. Figure 11.of Effect of offset distance on (a): Recrystallization fraction and (b): Average grain size at the center point the plate. center point of the plate.
5. Experiments 5. Experiments 5. Experiments An asymmetrical shear rolling mill is remolded by a symmetrical rolling mill as follows: two An asymmetrical shear rolling mill is remolded by a symmetrical rolling mill as follows: two work rolls a diametershear of 100 mm mill are driven by twobymotors to achieve a speed ratio (i = 1~4),two Anwith asymmetrical rolling is remolded a symmetrical rolling mill as follows: work rolls with a diameter of 100 mm are driven by two motors to achieve a speed ratio (i = 1~4), while therolls velocity lower of roll100 is fixed (0.0785 m/s). Different offset distances are achieved work withofa the diameter mm are driven by two motors to achieve a speed ratio (i =by 1~4), while the velocity of the lower roll is fixed (0.0785 m/s). Different offset distances are achieved inserting spacers withofdifferent thicknesses (0,(0.0785 2, 4 mm) between bearing of rolls and the by while the velocity the lower roll is fixed m/s). Different offset boxes distances are achieved by inserting spacers with different thicknesses (0, 2, 4 mm) between bearing boxes of rolls and frame. The material the plate is 7055 aluminum(0,alloy casting state, with compositions of (wt %) the inserting spacersofwith different thicknesses 2, 4atmm) between bearing boxes of rolls and the frame. The material of the plate is 7055 aluminum alloy at casting state, with compositions of 6.7Zn-2.6Mg-2.6Cu-0.15Fe-0.13Zr-0.12Si-0.06Ti, that isalloy machined into plates withcompositions different sizes. frame. The material of the plate is 7055 aluminum at casting state, with ofThe (wt %) (wt %) 6.7Zn-2.6Mg-2.6Cu-0.15Fe-0.13Zr-0.12Si-0.06Ti, that is machined into plates with different sizes. initial size of the plate is 150 mm (length) × 60 mmthat (width) × 20 mm (thickness). The initial rolling 6.7Zn-2.6Mg-2.6Cu-0.15Fe-0.13Zr-0.12Si-0.06Ti, is machined into plates with different sizes. The The initial size of the plate is 150 mm (length) × 60 mm (width) × 20 mm (thickness). The initial rolling temperature 410 °C and the plates are heated to the rolling temperature and then held for 30 min initial sizeisof the plate is 150 mm (length) × 60 mm (width) × 20 mm (thickness). The initial rolling temperature is 410 ◦ C and the plates are heated to the rolling temperature and then held for 30 min to acquire temperature balance in plates the heating furnace. Therolling plates temperature are immediately to 30 themin temperature is 410 °C and the are heated to the and transferred then held for to acquire temperature balance in the heating furnace. The plates are immediately transferred to the rolling mill in temperature less than 10 sbalance and theinheat during The the transfer period is disregarded. Due to to the to acquire the exchange heating furnace. plates are immediately transferred rolling mill in less than 10 s and the heat exchange during the transfer period is disregarded. Due to the rolling restriction capacity, reduction during is 2 mmthe and six rolling passes are conducted. millof inthe lessmill than 10 s andeach the pass heat exchange transfer period is disregarded. Due to the restriction of the mill capacity, each pass reduction is 2 mm and six rolling passes are conducted. A large speed ratio 1.2) capacity, and largeeach offset distance (S =is4 2mm) in the previous three the restriction of (i the= mill pass reduction mm are andapplied six rolling passes are conducted. A large speed ratio (i = 1.2) and large offset distance (S = 4 mm) are applied in the previous three rolling passes to acquire deformation. For the(Slast the speed turns to A large speed ratio (istrong = 1.2) shear and large offset distance = 4three mm)passes, are applied in theratio previous three rolling passes to acquire strong shear deformation. For the last three passes, the speed ratio turns to 1.1 and offset distance turns strong to 2 mm. rolling passes to acquire shear deformation. For the last three passes, the speed ratio turns to 1.1 and offset distance turns to 2 mm. After asymmetrical rolling, the specimens were cut at different positions (at the 1.1 and multi-pass offset distance turns to 2 mm. After multi-pass asymmetrical rolling, the specimens were cut at different positions (at the upper upper and lower surfacesasymmetrical as well as at the center) the plates by acut wire Then, After multi-pass rolling, thefrom specimens were at cutting differentmachine. positions (at the and lower surfaces as well as at the center) from the plates by a wire cutting machine. Then, the sections the upper sections were polished byas different abrasive paper and polishing and etched by and lower surfaces well astypes at theof center) from the plates by a wirepaste, cutting machine. Then, were polished by different types of abrasive paper and polishing paste, and etched by Keller’s reagent Keller’s reagent were (2.5 mL HNO3 by + 1.5 mL HCltypes + 1 mL + 95 mL H2O). The optical microstructures at by the sections polished different of HF abrasive paper and polishing paste, and etched (2.5 mL HNO3 + 1.5 mL HCl + 1 mL HF + 95 mL H2 O). The optical microstructures at different Keller’s reagent (2.5 mL HNO3 + 1.5 mL HCl + 1 mL HF + 95 mL H2O). The optical microstructures at
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different positions of the section plane were examined using a Leica DMI5000M image analyzer positions of the section planeChangsha, were examined using Leica DMI5000M image analyzer (Central (Central South University, China). Thea average single-circle-intercept grain sizesSouth were University, Changsha, China). The average single-circle-intercept grain sizes were measured using measured using the method described in the American Society for Testing and Materials (ASTM) the methodwhich described in the American Society Testing and of Materials (ASTM) which is standards, is beneficial for the grain sizefor measurement the material withstandards, obvious grain size beneficial grain size measurement of the material with obvious difference at different differencefor at the different positions. It should be guaranteed that there grain are atsize least 35 sections in each positions. It should guaranteed that there experiments are at least 35 sections in eachincircle to 12. improve the circle to improve the be accuracy. Metallography results are shown Figure A banded accuracy. experiments results arelarge shown in Figure 12. Ais banded appears on structure Metallography appears on the surface because of the strain, and there an anglestructure of inclination of the the surface because of the large strain, and there is an angle of inclination of the banded structure due banded structure due to the strong shear strain. The average grain sizes at the surface are smaller to thethat strong shear strain. Theand average grain sizes the surface smaller compared than that attothe than at the center point, a lower point hasatbetter grain are refinement an center upper point, a lower large point strain has better refinement compared to upper point. Therefore, large point. and Therefore, andgrain strong shear deformation is an beneficial to grain refinement. strain and strong shear deformation is beneficial to grain refinement. Comparisons of experimental Comparisons of experimental and simulated average grain size are shown in Table 2. The results and simulated average sizehave are shown in Table 2. The results simulated by themodels. CA method simulated by the CA grain method a higher accuracy than those of the FEM The have DRX afraction higher and accuracy than those of the FEMdepend models.onThe DRXstrain fraction grain size mainly average grain size mainly strain, rate,and andaverage temperature in the FEM depend on strain, strain rate, and temperature in the FEM model, which ismethod an empirical model strains and is model, which is an empirical model and is calculated by the differential for different calculated by the However, differential method for of different strains ortheir temperatures. However, consists or temperatures. DRX consists DRX nuclei and growth, and the grainDRX morphology of DRX nuclei and their growth, and the grain morphology will significantly affect the number of will significantly affect the number of DRX nuclei and their growth process; as a result, the DRX DRX nuclei their growth process; as a result, DRXoffraction andmodel average changed. fraction andand average grain size is changed. Thethe error the FEM is grain over size 10%,iswhile the The error oferror the FEM is overis10%, maximum of themodel CA model 8.2%.while the maximum error of the CA model is 8.2%.
Figure 12. 12. Experimental during asymmetrical shear rolling: (a) Figure Experimentalmicrostructures microstructuresatatdifferent differentpositions positions during asymmetrical shear rolling: upper point; (b)(b) center point; (c) (c) lower point. (a) upper point; center point; lower point. Table 2. Comparisons of simulated and experimental average grain size in asymmetrical shear Table 2. Comparisons of simulated and experimental average grain size in asymmetrical shear rolling. rolling. Average Grain Sizesize Average grain
Upper PointPoint Upper
Experimental value/µm Experimental value/μm CA results/µm CA results/μm Error (CA) Error (CA) FEM results/µm FEM results/μm Error (FEM)
Error (FEM) 6. Conclusions
Center CenterPoint Point
36.4 36.4 38.5 38.5 5.8% 5.8% 40.2 10.4%40.2
39.1 39.1 40.7 40.7 4.1% 4.1% 44.8 44.8 14.6%
10.4%
14.6%
Lower Point Lower Point 33.1 33.1 35.8 35.8 8.2% 8.2% 36.4 36.4 10% 10%
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6. Conclusions (1)
(2)
(3)
(4)
(5)
Microstructure evolution models and CA models are established to study the DRX behavior of the plate in asymmetrical shear rolling. The effects of the speed ratio and offset distance on the DRX fraction as well as grain size during asymmetrical shear rolling are analyzed. The distributions of the DRX fraction and average grain size are asymmetrical in asymmetrical shear rolling and the lower part of the plate has a larger DRX fraction and finer grain than the upper part. The DRX fraction difference between the upper and lower surfaces increases with ascending speed ratio, but the variation of the offset distance has little effect on this difference. More sufficient DRX and finer grain can be obtained with ascending speed ratio, while the increase of the offset distance will slightly decrease the DRX fraction and increase the average grain size. A proper speed ratio should be selected to ensure sufficient DRX on the basis of small bending behavior of the plate, and the existence of the offset distance is mainly used to decrease the bending behavior of the plate during asymmetrical shear rolling. CA models have a higher accuracy than FEM models because they take comprehensive consideration of DRX nuclei, grain growth, and grain morphology.
Acknowledgments: This project is supported by National Natural Science Foundation of China (Grant Nos. 51705248, 51405520); Natural Science Foundation of Jiangsu province, China (Grant No. BK20170785); Open Research Fund of State Key Laboratory of High Performance Complex Manufacturing, Central South University (Kfkt2017-08); Scientific Research Staring Foundation for Talent Introduction of Nanjing University of Aeronautics and Astronautics (Grant No. 90YAH17038). Author Contributions: Tao Zhang and Shi-Hong Lu established numerical model and carried out the rolling experiment; Lei Li analyzed data and the results of experiments; Yun-Xin Wu and Hai Gong provided the experimental machine and managed the data information. Tao Zhang wrote the paper. Conflicts of Interest: The authors declare no conflict of interest.
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