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Finite element simulation of cold rolling process of steel metal sheet using AbaqusTM.

L.G. Díaz-Samaniego1, M.P. Guerrero Mata1, R. Colás1, R. Viramontes2, C. Lizcano2

1Universidad Autónoma de Nuevo Léon, Fac. de Ing. Mecánica y Eléctrica Pedro de Alba S/N, Cd. Universitaria, San Nicolás de los Garza, N.L. 66450 MEXICO

2 Hylsamex S.A. de C.V. Ave. Munich 101, San Nicolás de los Garza, N.L. 66452 MEXICO

This work presents a finite element model for the cold rolling process of a steel strip that was achieved with the commercial software AbaqusTM. The model was computed considering an elastic-plastic behaviour of the material, low carbon steel, using the explicit module. The results obtained were validated by comparing them with those taken from the process. The mechanical properties of the material used for modeling were taken from a set of tensile tests carried out on samples taken at different reductions of the cold rolling process. The aim of this work is to predict the final conditions within the strip and the required operational parameters in an efficient way. The model assumes that the work rolls are rigid surfaces and that the friction is uniform throughout the bite zone. The elements in the mesh for the strip are C3D8R (8-node linear brick, reduced integration hourglass control), the boundary conditions imposed are angular velocity, displacement and symmetry on the “y” axis.

1. Introduction

One of the principal concerns of manufacturing companies is their economics, therefore it is necessary to have a good efficiency of processes, which is difficult to obtain as it requires highly qualified technical manufacturing knowledge, which can usually is gained through years of experience, but it is also possible to acquire such experience based on a scientific investigation.

In order to determine the influencing parameters on forming processes with more precision to optimize them, it is necessary a fundamental understanding of the process. Usually, process parameters, such as the roll speed , back and frontal tension and applied load are varied until a stable and economic manufacturing process is founded . On the other hand, parameters such as the number of steps, lubricant, roll surface and final conditions provide information concerning the economic efficiency of the process.

The above procedure is time consuming and costly, and can only be influenced and accelerated by the experience input of the worker. The rise in computing power and the development of new, more powerful calculating algorithms, is being transferred to manufacturing technologies. Simulation can be used in various areas of the rolling process. It is possible to determine the

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mechanical loads, back and frontal tension and the number of required passes . The understanding of rolling is deepened and can be used for systematic optimization. Cold rolling of strips is a procedure based on plastic deformation, care has to be taken to ensure the dimensional uniformity of the final thickness of the sheet. Practice has shown that the final shape of the deformed piece depends on the shape of tooling and on the properties of the material. The material is reduced in thickness by compressive forces applied on the material by two opposite rolls. The rolls rotate to stretch out the metal sheet and s imultaneously press the material between them, Figure 1 (Dieter,1988). Figures 2 shows a diagram of the rolling process. Different steps are used in the process, therefore the aim of this work is to obtain a reliable model of the process in order to use it to perform a further optimization of the process.

The model requires constitutive equations to calculate the response of the material. The most common formulations, are derive from the power law (Ludwik, 1909):

0nKσ σ ε= +

where σ and ε are, respectively the instantaneous values of true stress and true strain , σ0 , the yield stress, Κ, the strength coefficient , and n is the strain hardening exponent. A better prediction of strength at high levels of strain can be obtained by means of the exponential equation proposed by Voce (Voce,1948):

( )0 0 exp( )s cσ σ σ σ ε= + − −

where σs is the saturation and C is a coefficient that is determined from experimentation.

2. Experimental procedure

The sheet is fabricated from of low to medium carbon steel strip, the starting material is hot rolled band, that is reduced by a series of successive passes.

In order to obtain the properties of the material, samples were taken from different reductions of the rolling process, the samples were machine into plane specimens for tensile testing according to ASTM-E8 standard.

The tests were performed at room temperature and at constant crosshead speed of 50 mm/min. The results were averaged and used into the numerical model, Table 1 reports the values, that result fro m the use of an exponential equation in which σ0 , σs, C, take the values of 295 MPa, 830 MPa, 0.55, respectively and ε is true strain.

(1)

(2)

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3. Numerical procedure

For the numerical model the package ABAQUS™ was used. The model was developed in three dimensions (3D); using the explicit module, only half of the geometry was simulated. Geometries of the strip and the roll were created in ABAQUS /CAE. Figure 3 shows this geometry and Table 2 presents the dimensions for the three reductions. The stresses, strains and reaction forces were analyzed throughout the whole process as well as the shape of the strip. Temperature increase was not taken into account.

The initial properties of the material and the hardening parameters were feed into the model as a table, Table 1. Boundary conditions were imposed according to information obtained from the process plant.

The elements used in the model were, for the strip C3D8R to simulate a deformable solid , 21,000 elements were used for the strip and the roll was simulated as an analytical rigid surface, Figure 4 show the roll and the strip mesh before deformation.

4. Results

Figures 5 and 6 show the Von Mises stresses for the strip while Figures 7 and 8 present the plastic equivalent strain. Table 3 presents the values obtained of the final dimension of the strip for the three reductions, the values shown in the Table are the average dimensions as well as the load required for the roll process, the error is also reported. Although the obtained results for the first reduction overestimated the real ones, the subsequent values of reductions are closer to the real ones.

5. Conclusions

It has been shown that if the properties of the material are known, it is possible to obtain a good numerical model of the rolling process and then predict the mechanical loads, back and frontal tension and number of reduction steps required to get the final thickness, all this towards the aim to predict the final conditions within the strip and the required operational parameters in an efficient way process.

6. Recommendations

It is important for subsequent models to consider the anisotropy of the strip in order to obtain a closer result to the real values. It is also recommendable to change the analytical rigid surface of the roll to a deformable solid and thus use tetrahedral elements as this element type has the possibility to move and rotate in three directions. This will allow for the roll distortion to be taken into account, also a more realistic model should consider the thermal contributions due to friction between roll and workpiece.

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7. References

1. ABAQUS /CAE /EXPLICIT user’s manual.

2. ASTM Standard E8, Methods of Tension Testing of Metallic Materials.

3. G.E. Dieter, Mechanical Metallurgy, McGraw-Hill Book Co., London,1988.

4. P.Ludwik, elemente der Technologischen Mechanik, Springe-Verlag OHG, Berlin, 1909.

5. E. Voce, J. Inst. Met. 74 537 (1948).

8. Tables

Table 1 Values of strain and stress for the three first reductions for a low carbon steel.

First reduction Second reduction Third reduction Strain ε mm/mm

Stress σ Pa

Strain ε mm/mm

Stress σ Pa

Strain ε mm/mm

Stress σ Pa

0 295000000 0 531856225 0 649577177

0.01844737 314105075 0.02842 546870862 0.00217 650287625

0.02844737 323400226 0.07842 571474582 0.05217 665904502

0.03844737 332527900 0.12842 593940255 0.07717 673196407

0.04844737 341491117 0.17842 614453678 0.10217 680164283

0.05844737 350292838 0.22842 633184499 0.12717 686822527

0.06844737 358935975 0.27842 650287625 0.15217 693184899

0.07844737 367423383 0.32842 665904502 0.17717 699264547

0.08844737 375757869 0.37842 680164283 0.20217 705074034

0.09844737 383942189 0.42842 693184899 0.22717 710625364

0.11844737 399871101 0.47842 705074034 0.25217 715930011

0.13844737 415231185 0.52842 715930011 0.27717 720998935

0.15844737 430042754 0.57842 725842611 0.30217 725842611

0.17844737 444325396 0.62842 734893814 0.32717 730471049

0.19844737 458097998 0.67842 743158473 0.35217 734893814

0.24844737 490416016 0.37717 739120044

0.29844737 519925621 0.40217 743158473

0.34844737 546870862

0.39844737 571474582

0.44844737 593940255

0.49844737 614453678

0.54844737 633184499

0.59844737 650287625

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Neutral point

entrance out

Table 2 Dimension of the strip for the three reductions and for the roll.

Strip

first reduction second

reduction third reduction

Length l (m) 0.2 0.2 0.2

Width w (m) 1.0033 1.0033 1.0033

Thickness t (m) 0.001016 0.0007366 0.000559

Roll

Length L (m) 1.3033

Diameter θ (m) 0.40513

Table 3 Results obtained of the width and thickness for the strip at different reductions.

Average Thickness

(mm)

% error Average width (mm)

% error Average Load

% error

First reduction

7.455 1.209 1.0038 0.051 829 20

Second reduction

5.645 1.029 1.0031 -0.014 763.95 4.14

Third reduction

14.410 2.1379 1.0037 0.041 762.28 2.806

9. Figures

Figure 1 The rolls rotate to stretch out the metal sheet and simultaneously press the material between them.

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Figure 2 Diagram of the rolling process

Figure 3 Geometry for the model, w,L and t depends on the reduction imparted, see Table 2.

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Figure 4 Aspect of the mesh f or the roll (rigid surface) and for the strip (type element C3D8R ) before reduction.

Figure 5 Distribution of Von Mises’ stress on the sheet after first pass.

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Figure 6 Zoom of distribution of Von Mises’ stresses on the sheet after first pass.

Figure 7 Distribution of equivalent plastic strain on the sheet after first pass.

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Figure 8 Zoom of distribution of equivalent plastic strain on the sheet after first pass.

10. Acknowledgment

The authors would like to thank Conacyt, Paicyt-UANL, FIME-UANL and Hylsamex S.A. de C.V. for the support and facilities provided to develop this work.