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2002 ABAQUS Users’ Conference

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Numerical Simulation of the Forming of a Seamless Elbow Using Abaqus.

E. Salas Zamarripa1, M.P. Guerrero Mata

1, R. Colás

1, P. Fodor

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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 Empresas Riga S.A. de C.V.

Carretera Monterrey-Laredo Km 24.2, Ciénega de Flores, N.L. 65550 MEXICO

Abstract

By means of the commercial package Abaqus™, using its explicit module, a model for the high temperature

forming of a seamless elbow was achieved. The results of the strain and stress distributions predicted by the

numerical model were compared with the results experimentally obtained by the visioplasticity method. For

both models a straight seamless pipe of 2.7 cm internal diameter, 6 mm thickness and 31.7 cm long, was used

as preform. The mechanical properties of the material were introduced into the package from the results of a

set of axial compression tests carried out at high temperature, 800 °C. The material used for the forming

process and for the testing was an ASTM A-106 steel. The tools were model as an undeformable solid.

It is hope to used the numerical model to perform a further optimization of the tools, in order to improve the

thickness uniformity of the elbows.

Introduction

The forming of seamless elbows is a hot working procedure based on plastic deformation and cyclic heating,

care has to be taken to ensure the dimensional uniformity of the final thickness of the elbow. The practice has

shown that the final shape of the deformed piece depends on the shape of the tooling. Different designs of

tools 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 tooling design [1,2].

An horizontal press is used for forming the elbows, and the change of shape involved is accomplished when

the performs are forced through a mandrel that is located at the end of the extension shaft, Figure 1 shows a

diagram of the forming operation.

The elbows are fabricated from straight seamless steel pipe of low to medium carbon steel, the starting shapes

are cut depending on the size and wall thickness of the final product.

Numerical simulation has been used in the past to model the forging process above described [3], however,

those trails have been came out with not very good results. Since the problem to solve is a difficult one,

however this new model tries to overcome the limitations of the others using the explicit module.

Experimental Procedure

In order to gain a deeper understanding and a better control of the process different studies and experimental

trails have been carried out, these are reported in detail in other works [3,4], first the problem of the cyclic

heating was attacked and afterwards the deformation problem. Samples were taken from seamless pipes

before the process to obtain the material properties, the samples were machine into cylindrical samples of

10mm diameter and 15mm height, the lubricant used at the plant was also used during the axial compression

testing, tests were performed at 800°C. The results of the testing were averaged and used into the numerical

model, Table 1 reports the values. The visioplasticity method was used to find the final strains and stress

develop during the forming of the elbow. To carry out the test, a grid was scribed on the seamless pipe, the

gridded pipe is presented in Figure 2, as well as the mandrel. In Figure 3 the formed elbow can be seen with

2002 ABAQUS Users’ Conference 2

the grid on it. The values of the grid are measured and recorded before and after the deformation and the using

the slip line field theory the stresses and strains are found [5-7].

The pipe used for the visioplasticity was 2.7 cm internal diameter, 6 mm thickness and 31.7 cm long, was

divided at 30° obtaining 12 segments of 1.5 cm each and 19 segments of 1.5 cm of the long.

Numerical Procedure

For the numerical model the commercial finite element package Abaqus™, was used. The model was

obtained in three dimensions (3D); using the explicit module, only half of the geometry was simulated. The

geometry of the mandrel was created in the preprocessor of the package Ansys then imported to Abaqus via

iges files, whereas the pipe was directly created in Abaqus. The stresses and strains were analysed throughout

the whole process as well as the shape of the elbow. Temperature was not taken into account, but the

properties of the material were those at the working temperature. The initial materials properties and the

hardening parameters were fed into the model as a table from the results of a series of compression tests

performed in a previous work (Table 1) [3]. The boundary conditions were taken from the information

gathered from the process plant. In the model a fixed displacement was imposed over the extremes of the

perform not in contact with the mandrel. The elements used in the model were for the mandrel R3D4, to

simulate a undeformable rigid surface, and for the pipe the type used was C3D4, Figure 4 shows the mandrel

and the seamless pipe with the mesh before deformation. The temperature changes associated to the forming

process, although are very imported, for this model were neglected.

Results

In Figure 5 shows the deformed mesh of the elbow, one to one comparison was not possible with the

experimental tests, because of the mesh used for the pipe, however, two elements in the upper part of the

elbow and two in the lower one, were identified and the values of equivalent plastic strain and Von Mises

stress were compare with the results obtained with the visioplasticity method.

Figure 6 and 7 show the Von Mises stresses for the upper and lower sides of the pipe when half the

deformation has been achieved. Figure 8 presents the plastic equivalent strain.

Table 2 contains the values of the deformation found experimentally, the values are reported according to

angular position, only six positions were reported, since only half the geometry was simulated, according to

the symmetry.

Figure 8 and Table 2 can be compared and the trend of the strain is similar in both cases, for the upper part of

the pipe or elbow, the strains are very low and for the lower part, inner part of the curvature of the mandrel,

the strains are very high, by a factor of two, in both cases the numerical and the experimental model. However

for the numerical the difference between the upper and lower parts is different by a factor of 3. Although the

final results of the numerical model have not been found, it is expected that these will follow a similar path.

The difference between the numerical and the experimental model can be explained in term of the thermal

contributions.

Conclusions

A better model should be perused before carry out any optimization, the model must include the thermal

effects, also different meshes could be used and analyze the advantages.


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References 1. J.C. Gelin, O. Ghouati, The inverse approach for the determination of constitutive equations in metal

forming, Annals of the CIRP, Manufacturing Technology, 1995, Vol. 44, No.1, pp 189-192.

2. D.R.J. Owen, The Design and Optimisation of Forging Systems by Numerical Simulation, Bench

Mark, December 1993, pp 36-41.

3. J. A. López Cavazos, Master thesis, Universidad Autónoma de Nuevo Léon, 2001.

4. A. Rodríguez, M. Mezzetti, P. Fodor, R. Colás, Forming of seamless pipe fittings, Journal of

materials processing technology, articule in press accepted November 2001.

5. J.H. Beynon, C.M.Sellars, Strain Distribution Patterns during Plane Strain Compression Testing,

Journal of Testing and Evaluation, January 1985, No.13, pp28-38.

6. N.R. Chitkara, M.A. Butt, A General Numerical Method of Construction of Axisymmetric Slip-Line

Fields, Int. Journal of Mechanical Science, 1992, Vol. 34 No. 11, pp 833-848.

7. G.E Dieter, Mechanical Metallurgy, McGraw Hill Inc. 4th. Ed. 1988.

Tables

Table 1

ε σ (Mpa)

0.0182 101.14

0.0323 113.84

0.0456 122.93

0.0598 129.85

0.0735 135.35

0.0873 140.17

0.1011 144.17

0.1331 152.11

0.1790 161.40

0.2249 168.94

0.2707 175.68

0.3165 180.51

0.3322 181.60

0.4079 185.84

0.4536 187.06

0.5402 188.92

Table 2

ε Angular position

1.25 15

1.07 45

0.94 75

0.80 105

0.67 135

0.62 165


Figures

Figure 1 Diagram of the furnace and ancillary equipment required for forming the elbows [1].

Figure 2 a) Madrel use in the forming operation, b) gridded seamless pipe.


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Figure 3 Final shape of the gridded elbow.

Figure 4 Mandrel and pipe meshed, before deformation.


Figure 5 Mandrel and pipe meshed, after deformation.

Figure 6 Von Mises Stress for half the total deformation of the pipe, upper side of the pipe.


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Figure 7 Von Mises Stress for half the total deformation of the pipe, inner side of the pipe.

Figure 8 Equivalent plastic strain at half deformation of the pipe.


Acknowledgment The authors thank the support and facilities provided by CONACYT, SIREYES, FIME-

UANL, Mexico, as well as the material and industrial facilities provided by Empresas Riga,

S.A. de C.V. M.P.G.M. recognizes the support provided by PAICYT-UANL

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