Extrusion process modelling of the non-rounded products: a 2-D approach.

Ghiban, Nicolae ; Chelu, Gheorghe ; Serban, Nicolae 等

1. INTRODUCTION

Products with non-rounded complex geometrical sections can be obtained only by extrusion, a plastical forming process, which generally leads to nonuniformities in final product. The main problem in extrusion is the equilibration of the yielding rates and the place of final cavities.

The aim of the present paper is to put in evidence by a modern modelling method the difference between two positions of the die cavity, optimum and respectively non-optimum position, in comparison with other researchers (Altan et al., 1994), (Ulysse, 2002).

2. MATERIALS AND METHODS OF INVESTIGATION

The modelling of the direct extrusion with the finite element method is based on a COSMOS M 1.65 program (COSMOS, documentation, 1997). A structural analytical program was used, which nonlinear subprograms allow the study of the plastic forming process up to the first plastically formed zones and non on the effective plastic forming process in the considered regime. The modelling was established for the direct extrusion process of the "yalle piece", made on brass CuZn39Pb3. Two situations were considered: one situation in which the displacement of the die cavity from the longitudinal axis is null (the so called optimum position), which leads to the uniformity of the mechanical properties of the product and another situation which corresponds to a displacement about 20 mm from the longitudinal axis of the die cavity (the so called non-optimum position).

These situations were considered taking into account other laboratory tests, made in (Ghiban, 1997). The charged curves and the yielding curve of the material were buildt considering: applied pressure of the semifinished product is 20 MPa; Young modulus E = 7.3 x [10.sup.4] MPa; plasticity modulus [E.sub.pl] = -0.087 N/[m.sup.2]; Poisson coefficient v = 0.4. The whole process was divided into 20 steps, during one second, in order to determinate the dynamics of the process.

The surface model used SHELL 4T elements, which simulated the nonlinear behavior of the medium plastic material. The surface model allows the determination of the distribution of total equivalent stresses and deformations (total, elastic and plastic) for both conditions (optimum and non-optimum position of the die cavity). COSMOS program may offer good results for comparing with other FEM based programs, like COMSOL or QFORM, (Zienkiewicz & Taylor, 2000), (Hartley et al., 1992).

3. RESULTS AND INTERPRETATION

The surface model for the "Yalle piece" is shown in figure 1 (a for optimum and b for the non-optimum position of the die cavity). The surface model has 218 nodes and 180 elements for the optimum position and respectively, 207 nodes and 170 elements for the non-optimum position of the die cavity. The charging is made linearly at forces in nodes from the end of the semifinished product in the opposite position of the die cavity.

The results regarding the variation of the main parameters of the direct extrusion process by modelling are presented in figures 2, 3, 4 and 5 and summarized in table 1. It can be seen that the surface model describes very well the situation on the rounded ends of the die, because in these places the maximum yield stress is obtained (and so, it is satisfied the Von Misses criterion). This model shows the differences in the distribution of all values for the equivalent stress, total and plastic deformations (both on x and on y direction) and on the angle-deformations. So, one may observe the symmetry of the distribution of all values obtained at the optimum position in comparison with inhomogeneity of all values obtained at the non-optimum position of the die cavity.

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4. CONCLUSIONS

The surface model based on COSMOS M 1.65 program may be successfully used in simulating and modelling the direct extrusion process. Using SHELL 4T elements, the authors put in evidence the difference between process parameters (equivalent stresses, total and plastic deformations, angle-deformation) obtained at direct extrusion of a brass "yalle piece", in two different situations: the optimum and the non-optimum position of the die cavity. These results are used in correct design and manufacture of the non-rounded direct extruded products. Future researches, based on the same program, may be done also for a tridimensional modelling approach.

5. REFERENCES

Altan, T.; Oh, S. & Gegel, H. (1994). Metal Forming Fundamentals and Applications, ASM, 1994;

COSMOS M 1.65 (1997). Documentation;

Ghiban, N. (1997). Studies and experimental researches about the non-rounded extruded profiles, Doctoral Thesis, University Politehnica Bucharest;

Hartley, P.; Pillinger, I. & Sturgess, C.E.N. (1992). Numerical Modelling of Material Deformation Processes, Springer Verlag;

Ulysse, P. (2002). Extrusion die design for flow balance using FE and optimization methods. International Journal of Mechanical Sciences, Vol. 44 (2002), pp. 319-341;

Zienkiewicz, O.C. & Taylor, R.L. (2000). Finite Element Method, Elsevier Butterworth-Heinemann, ISBN 0-7506-5049-4.

Table 1. The process parameters of the direct extrusion by
surface modelling

 Value Step 1

a) optimum position of the die cavity

Equivalent stress (MPa) 1.02

Total deformation ([10.sup.-5]) 1

[[epsilon].sub.x] total (10-6) 0.25

[[epsilon].sub.x] plastic ([10.sup.-6]) 0.137

[[epsilon].sub.x] total ([10.sup.-6]) 3.2

[[epsilon].sub.y] plastic ([10.sup.-6]) 1.2

[[gamma].sub.xy] (MPa) [+ or -] 0.101

b) non-optimum position of the die cavity

Equivalent stress (MPa) 0.947

Total deformation ([10.sup.-5]) 0.942

[[epsilon].sub.x] total ([10.sup.-6]) 0.14

[[epsilon].sub.y] plastic ([10.sup.-6]) 0.092

[[epsilon].sub.y] total ([10.sup.-6]) 4.9

[[epsilon].sub.y] plastic ([10.sup.-6]) 1.75

[[gamma].sub.xy] (MPa) [+ or -] 0.092

 Value Step 5

a) optimum position of the die cavity

Equivalent stress (MPa) 5.12

Total deformation ([10.sup.-5]) 5

[[epsilon].sub.x] total (10-6) 1.24

[[epsilon].sub.x] plastic ([10.sup.-6]) 0.94

[[epsilon].sub.x] total ([10.sup.-6]) 6.7

[[epsilon].sub.y] plastic ([10.sup.-6]) 2.8

[[gamma].sub.xy] (MPa) [+ or -] 0.61

b) non-optimum position of the die cavity

Equivalent stress (MPa) 4.74

Total deformation ([10.sup.-5]) 4.7

[[epsilon].sub.x] total ([10.sup.-6]) 0.94

[[epsilon].sub.y] plastic ([10.sup.-6]) 0.37

[[epsilon].sub.y] total ([10.sup.-6]) 8.3

[[epsilon].sub.y] plastic ([10.sup.-6]) 4.7

[[gamma].sub.xy] (MPa) [+ or -] 0.34

 Value Step 10

a) optimum position of the die cavity

Equivalent stress (MPa) 10.7

Total deformation ([10.sup.-5]) 10

[[epsilon].sub.x] total (10-6) 2.56

[[epsilon].sub.x] plastic ([10.sup.-6]) 1.86

[[epsilon].sub.x] total ([10.sup.-6]) 15.01

[[epsilon].sub.y] plastic ([10.sup.-6]) 7.2

[[gamma].sub.xy] (MPa) [+ or -] 0.82

b) non-optimum position of the die cavity

Equivalent stress (MPa) 9.47

Total deformation ([10.sup.-5]) 9.42

[[epsilon].sub.x] total ([10.sup.-6]) 1.72

[[epsilon].sub.y] plastic ([10.sup.-6]) 0.97

[[epsilon].sub.y] total ([10.sup.-6]) 15.1

[[epsilon].sub.y] plastic ([10.sup.-6]) 10.8

[[gamma].sub.xy] (MPa) [+ or -] 0.52

 Value Step 16

a) optimum position of the die cavity

Equivalent stress (MPa) 16.4

Total deformation ([10.sup.-5]) 16.1

[[epsilon].sub.x] total (10-6) 4.85

[[epsilon].sub.x] plastic ([10.sup.-6]) 2.75

[[epsilon].sub.x] total ([10.sup.-6]) 27.3

[[epsilon].sub.y] plastic ([10.sup.-6]) 13.8

[[gamma].sub.xy] (MPa) [+ or -] 2.3

b) non-optimum position of the die cavity

Equivalent stress (MPa) 14.2

Total deformation ([10.sup.-5]) 14.2

[[epsilon].sub.x] total ([10.sup.-6]) 3.78

[[epsilon].sub.y] plastic ([10.sup.-6]) 2.65

[[epsilon].sub.y] total ([10.sup.-6]) 34.5

[[epsilon].sub.y] plastic ([10.sup.-6]) 25.4

[[gamma].sub.xy] (MPa) [+ or -] 1.96

 Value Step 20

a) optimum position of the die cavity

Equivalent stress (MPa) 19.7

Total deformation ([10.sup.-5]) 44.5

[[epsilon].sub.x] total (10-6) 15.3

[[epsilon].sub.x] plastic ([10.sup.-6]) 8.2

[[epsilon].sub.x] total ([10.sup.-6]) 85

[[epsilon].sub.y] plastic ([10.sup.-6]) 54.3

[[gamma].sub.xy] (MPa) [+ or -] 7.65

b) non-optimum position of the die cavity

Equivalent stress (MPa) 19.3

Total deformation ([10.sup.-5]) 21.2

[[epsilon].sub.x] total ([10.sup.-6]) 16.7

[[epsilon].sub.y] plastic ([10.sup.-6]) 7.59

[[epsilon].sub.y] total ([10.sup.-6]) 48.2

[[epsilon].sub.y] plastic ([10.sup.-6]) 37.1

[[gamma].sub.xy] (MPa) [+ or -] 8.15