Behaviour of corner surface cracks in V-H rolling
process of steel slabs
L iu Xianghua 1,Y u Hailiang, L i Changsheng, Z hao Xianming
1. INTRODUCTION
The vertical–horizontal (V-H) rolling process is often used to accomplish width reduction. For its importance, researchers widely applied finite element method (FEM) to solve V-H rolling problems. For example, K. Mori et al [1] using a rigid-plastic formulation and Huisman et al [2] using an elastic-plastic finite element formulation investigated the deformation of slab edging, Zhao et al [3] researched an influence of vertical roll on the bar camber, Liu et al [4] analyzed the effect of edger share on the slab profile with explicit dynamic FEM. Meantime, the whole V-H rolling process has been studied by Nikaido [5], Xiong [6], and Chung et al [7], the effect of rolling parameters on the slab deformation was simulated, and the temperature field, velocity field and stress field during V-H rolling have been obtained.
A few research works deal with the behaviour of cracks during rolling processes. Esa Ervasti et al [8] analyzed the behaviour of cracks on slab surface by the explicit dynamic FEM, Nobuki YUKAWA et al [9]
simulated the behaviour of rectangle cracks on the slab corner by rigid-plastic FEM.
In order to know the closure and growth of transversal cracks on slab corner during multi-pass V-H rolling processes, a numeral simulation was carried out by the explicit dynamic FEM and updating geometric method on the platform of LS-DYNA. The influence of vertical roll shape on the behaviour of cracks on slab corner was discussed which are significance for understanding original defect deformation and it proved a new way to investigate the closure and growth of cracks on the slab corner.
2. FEM SIMULATION 2.1 Simulation conditions
Taking the roughing passes of hot strip mill as the simulation object, the main equipment and technology parameters are as follows: the diameter of horizontal roll 1150mm, the diameter of vertical roll 980mm, three kind of vertical rolls were used: flat roll (scheme 1); grooved roll with RX ＝50 mm (scheme 2); grooved roll with RX ＝80 mm (scheme 3). The groove dimension of vertical roll is shown in Figure1. The dimension of slab before rolling is 1200×250mm.
The main chemical composition of the steel are: C 0.18%, Si 0.32%, Mn 0.82%. The yield stress model used in the simulation is as follows:
T T e F D C B A +=ε
εσ&, (1) where ε- strian, ε
&- srain rate, T -deformation temperature, A, B, C, D, F-constant, e -nature logarithms. A “V” shape crack on the slab corner was regarded as two independent surfaces. The dimensions of
the crack are shown in Figure 2. The rolling parameters and computing conditions are shown in table 1.
Table 1 Rolling parameters and computing conditions
V-stand H-stand Pass Number width /mm
thickness /mm
Rolling temperature/℃
Coefficient of friction
1200 250
- -
1 1150 240 880 0.35
2 1100 240 862 0.35
3 1050
240
840 0.35
The State Key Laboratory of Rolling & Automation （ Northeastern University ）, China
Figure1Groove dimensions of V-roll Figure2 Initial dimensions of ‘V’ shape crack 2.2 FEM model
In the simulation, multi-pass V-H (V1-H1-V2-H2-V3-H3) rolling processes have been done. Owing to the symmetry, 1/4 of slab and rolls were taken as simulating object in the geometric model. The rolls were considered to be rigid. The finer element was meshed near the slab edge in order to describe the V shape crack and see the local deformation in detail, as Figure 3. The number of element is about 23540 in total, and the computation time is about 12 hours for one rolling pass on a PC computer with pentiun 4 cpu.
The hexahedral element with 8 nodes was used in the 3-D simulation The boundary conditions are as follows: Z=0, u y=0; Y=0, u z=0. The FEM mesh of the 2nd pass and the 3rd pass were obtained by updating geometry method, modifying material parameters, boundary conditions, and deformation conditions.
Figure3 Meshing of slab with crack
3. RESULTS AND ANALYSIS
3.1 Deformation of cracks
The simulation results of the crack deformation in V-H rolling are shown in table 2. From which we can find that both the flat vertical roll and the grooved vertical roll are helpful to the slab corner crack closure during vertical rolling, but during horizontal rolling, the deformation of cracks is different as the vertical roll shape changed.
Scheme 1 shows the crack closure and growth conditions with flat vertical roll, the cracks could be closed well after V-H rolling processes. However, after vertical rolling, there is a little open of the crack on the slab top surface, but it closes well on side surface. After horizontal rolling, it is a little open of the crack on the slab side surface , but it closes well on top surface.
Scheme 2 and 3 show the conditions of the crack closure and growth when a grooved vertical roll was used. From which we found that the crack on the slab side surface closed well and the crack on slab top surface opened a little after vertical rolling when changing the inner radius RX. After horizontal rolling, the crack open with different degree, and at the same pass, the width of the crack on side
surface is wider than that on top surface. Meantime, it is clear that the influence of RX on the crack on the side surface is less than that on the top surface of slab.The crack is not just from “V” shape to “Y” shape and the whole crack has a little leaning during V-H rolling process.
Table 2 Crack shape from FE-simulations
“
”rolling direction
Scheme number
V 1 H 1 V 2 H 2 V 3 H 3
Side surface
1
Top surface
Side surface
2
Top surface
Side surface
3
Top surface
Further analysis to the crack deformation, as shown in figure 4, where 1, 2, 3 represent 3 kinds of simulation schemes, from which we can find that the crack width gradually reduce as the rolling pass increasing.
0.0
0.40.81.21.62.02.42.8
3.232
C r a c k w i d t h /m m
Pass number/N
1
Figure4 Crack width after H-rolling
3.2 Contact pressure on inside surfaces of the crack
During rolling process, two crack surfaces might contact each other, for that the crack inner will appear contact pressure. It is significance to analyze contact pressure during rolling process for studying the closure and growth of crack.
Figure 5 shows the contact pressure on crack inner surfaces for the first pass, where figure 5 a shows the contact pressure when flat vertical roll is used and figure 5 b shows the contact pressure when grooved vertical roll is used. In vertical rolling, it can be found that when flat vertical roll is used, the
maximum contact pressure is about 70~80 MPa, when grooved vertical roll is used, the maximum contact pressure rose to 110 MPa. The pressure in scheme 3 is 10 MPa more than in scheme 2. In horizontal rolling, the contact pressure becomes 0 MPa when using grooved vertical roll, but the contact pressure still exists when using flat vertical roll. From figure 5 b, we can find that the contact pressure fluctuates greatly, which might be affected by changing of friction condition in deformation zone.
The results show that the crack close well when using flat vertical roll and it might open again when using grooved vertical roll after multi-pass of V-H rolling processes.
-1001020304050607080a)
Flat V-roll C o n t a c t p r e s s u r e /M P a
Time /s
C o n t a c t p r e s s u r e /M P a
Time /s
b)Grooved V-roll
Figure5 Contact pressure during 1st pass V-H rolling process
Figure 6 shows the maximum contact pressure in each pass during multi-pass V-H rolling. Where, figure 6 a shows the contact pressure of the crack for each pass both scheme 1 and scheme 2. We found that the contact pressure is among 70~80 MPa during V 1, V 2, V 3 rolling process and 0 during H 1, H 2, H 3 when the grooved vertical roll is used. When employing a flat vertical roll, there exists contact pressure in the crack on slab corner during V 1, H 1, V 2, H 2, V 3, H 3 rolling processes, but all of the values are less than 60 MPa. Because the contact pressure become 0 after horizontal rolling when grooved vertical roll is employed, so the contact pressure during vertical rolling was analyzed, as shown in figure 6 b, which shows the maximum values of contact pressure of the crack during V 1, V 2, V 3 rolling process both scheme 2 and scheme 3. From the figure 6 b, we found that the value of contact pressure on the inner surfaces of the crack increases with the inside radius RX increasing during V 1 rolling pass. But during V 2 and V 3 rolling passes, the value of contact pressure decreases with the increasing of the inside radius RX .
-10
01020304050607080
C o n t a c t p r e s s u r e
/M P a
Rolling pass
(
a )
40
5060708090
C o n t a c t p r e s s u r e /M P a
Rolling pass
(
b )
Figure 6 Contact pressure during multi-pass V-H rolling process
3.3 Position of the node on slab corner
Tracking position changing of nodes on slab corner is helpful to know the movement of the original crack .Figure 7 shows the tracking map of the surface nodes’ position. Figure 7 a shows the position
distribution of crack surface nodes’ after vertical rolling in the third pass, figure 7 b shows that after horizontal rolling
From Figure 7 we found that the slab corner original defects gradually overturn to the top surface when using flat vertical roll, and it keeps on the corner when using grooved vertical roll.
(a) V 3 pass Y d i r e c t i o n /
m
m
(b) H3 pass
Corner conditions
Figure 7 Tracking position of the nodes on slab corner
3.4 Experiment
According to the scheme 1, the experiment of the closure and growth of transversal crack during multi-pass V-H rolling process was done in authors’ laboratory.
The φ
300 mm mill is adopted in the vertical rolling, and the φ
180 mm mill is adopted in the horizontal rolling. The pure lead of slab was used, and the profile of slab is 120×25 mm. The transversal crack with ‘V’ shape was made by a knife in slab corner. The height of crack on top surface is 5 mm, which on side surface is 5 mm, and the width of crack is 0.5 mm. During rolling process, according to the
rolling schedule V
1
-H
1
-V
2
-H
2
-V
3
-H
3
the experiment is investigated. The rolling velocity is 200 mm/s. The reduction in width of vertical rolling for each pass is 5 mm, and the reduction in height of horizontal rolling is 1 mm.
The behaviour of transversal crack on slab corner during multi-pass V-H rolling processes through FEM calculation and experiment is compared in table 3. From the table, we can see the closure and growth from the slab top surface and slab side surface in each pass. It is clear that the calculated
results are in good agreement with the experimental ones.
Table 3 Behaviour of crack between FEM and experimental results
Before rolling
V1
H1
V
2
H2V3H3
FEM
Top
Surface
Experiment
FEM
Top
surface
Experiment
4. DISCUSSIONS
From above analysis, it can be found that the crack opens again when grooved vertical roll used and the crack closes when the flat vertical roll used during horizontal rolling process. Compared the former and the latter, the main difference of slab deformation is the ‘dog-bone’ shape in vertical rolling, which brings different tensile stress in the slab corner in horizontal rolling. The stress on slab corner along the rolling direction under different apical of dog-bone shape was calculated, taking position of apical A equals to 120, 80, 60, 40, 20, 10 and 5 mm respectively as in figure 8, and the results as Figure 9.
σX
o
n
s
l
a
b
c
o
r
n
e
r
,
M
P
a
Distance of dog-bone apical(A),mm
Figure 9 shows the tensile stress on slab corner under different A, where all of the values are the max value of tensile stress along the contact arc. It can be found that the tensile stress on slab corner decreases with the decreasing of the apical position of dog-bone. When the apical position of dog-bone A equals to 5 mm, the max tensile stress is 75 MPa; when the apical position of dog-bone A equals to 120 mm, the max tensile stress attaches to 125 MPa, increasing by 66.7%.
5. CONCLUSIONS
(1) After multi-pass V-H rolling processes, the crack closes well when using flat vertical roll and the crack might open again when using grooved vertical roll.
(2) After vertical rolling, the contact pressure appears on the inner surfaces of the crack both using flat vertical roll and using grooved vertical roll, and the mean contact pressure when using grooved vertical roll is bigger than that when using flat vertical roll. After horizontal rolling, it becomes zero when using grooved vertical roll, and it still exists when using flat vertical roll.
(3) Using grooved vertical roll, the nodes on slab corner keep their original position, but using flat vertical roll it overturned to the top surface of the slab, which is the reason the defects on steel surface short distance from the slab edge come from the crack on the slab corner.
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Figure 9 Influence of A value on stress
of the corner in rolling direction
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