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Materials Processing Technology

E L S E V I E R Journal of Materials Processing Technology 55 (1995) 5 10

Strength analysis and optimization for both the cylinder and the anvil of a BELT-type ultra-high-pressure apparatus by FEM

Wang Qiang a, He Fang b, Lu Wei a, Li Dejun c, Z.R. Wang d'* "Jinan Foundry and Metalforming Machinery Research Institute, No. 464 Jingshi Road, Jinan 250022, People 'S Republic of China

b Shandong Institute of Building Materials, Jinan 250022, People's Republic of China CAD Laboratory, Shandong Polytechnic Universi.tv, Jinan 250014, People's Republic of China

d Division of Metal Forming, ~435, School qfMaterials and Engineering, Harbin Institute of Technology, Harbin 150001, People's Republic of China

Industrial summary

BELT-type ultra-high-pressure apparatus has been used widely to synthesize diamond and CBN. Because of the critical service conditions in the chamber (6 GPa pressure and 1500°C temperature), cracks are very likely to appear in both the cylinder and the anvil of the BELT, resulting in a short working life.

FEM-analysis models of both the cylinder and the anvil are presented, which have been verified by comparison of the press tonnage between practice and models. In accordance with the FEM-analysis results, the maximum principal stress within the cylinder is either the maximum axial stress near to the outer surface or the maximum tangential stress near to the inner surface, depending on the magnitude of the pre-stress acting on the outer cylindrical surface by shrink rings. It is the maximum principal stress which causes the brittle failure of the cylinder. The function of the shrink rings is of double character: the positive side is that they can decrease greatly the maximum tangential stress, whilst the negative side is that they can increase slightly the maximum axial stress. The influence of the shrink rings on the anvil is limited. It is the ultra-high compressive stress which causes the failure of the anvil. The influence of thermal stress on both the cylinder and the anvil is limited.

An optimization method is presented also, by means of which the maximum axial stress within the cylinder can be decreased by about 46%, therefore enabling the working life of the BELT to be extended greatly.

Keywords: BELT; FEM; Ultra-high-pressure

1. Introduction

The BELT-type ultra-high-pressure apparatus (herein- after called the BELT) was invented by Hall in 1953 [1] in order to synthesize diamond. Since the first successful production of artificial d iamond on 16 December 1954 at General Electric Research Laboratory, the BELT has been the most effective apparatus used in industry to synthesize diamond and CBN.

The BELT consists of one cylinder and two anvils made of sintered carbide (WC-Co), and corresponding shrink rings made of alloy steel (see Fig. 1). In the work- ing space of the chamber, the pressure is about 6 GPa, whilst the temperature is about 1500°C.

Because of the critical service conditions of the BELT, brittle cracks are very likely to appear in both the cylin- der and the anvil. Therefore, it is of great significance to understand the stress distributions in the BELT, in order to be able to take effective measurements to reduce the

* Corresponding author.

0924-0136/95/$09.50 ~ 1995 Elsevier Science S.A. All rights reserved SSD! 0 9 2 4 - 0 1 3 6 ( 9 5 ) 0 1 8 0 3 - M

magnitude of the maximum tensile stress, and to extend the working life of the BELT.

2. FEM-analysis models

Because the cylinder of the BELT is not a simple hollow tube, and the pressure acting on the inner surface is not evenly distributed, it is impossible to obtain the stress distributions by the classical Lam6 Equations. Therefore, the finite-element method (FEM) should be employed.

The FEM-analysis models of the cross-sections of both the cylinder and the anvil can be seen in Fig. 2, for which some assumptions have been made, as the following:

2.1. Pressure acting on the inner surface of the cylinder and pressure acting on the surface of the anvil

It is assumed that the pressure acting on the inner surface of the cylinder and the pressure acting on the

W. Qiang et aL / Journal of Materials Processing Technology 55 (1995) 5 10

Any i I

Fig. 1. Schematic diagram of the BELT.

surface of the anvil are evenly distributed, and the friction force can be neglected. The values of pressures have been determined to be Po = 5.4 GPa and P2 = 6 GPa, accord- ing to study of the mechanical properties of pyrophyllite, the material used in the synthesizing chamber (Ref. [2] ).

2.2. Pressures acting on the conical sealing part

The pressure acting on the conical sealing part of cylinder is given by Eq. (1) according to Ref. [3] :

P(s) = Poe-2~/~S, (1)

where P(s) is the pressure acting on the surface of the conical part; Po is the pressure acting on the inner cylin- drical surface; t is the sealing thickness; v is the inner friction coefficient of pyrophyllite; and S is local position coordinate. The pressure acting on the conical sealing part of the anvil can be determined with the same method also.

2.3. Frictional resistances acting on the conical sealing part

Because of the relative movement between the pyro- phyllite seal and the cylinder or anvil, there must be great frictional resistances acting on the conical surface, which should not be ignored. However, almost all investiga- tions in the past have not taken such frictional resistances into account (Refs. [3-5] ).

2.4. Pre-stress from the shrink rings

The cylinder and the anvil are pre-stressed in the radial direction by several shrink rings, in order to be able to withstand the high pressure present in the cylinder cham- ber or on the anvil surface. Therefore, an evenly distrib-

uted pressure acting on the outer cylindrical surface is assumed.

2.5. Thermal stress

By calculating the temperature field on the basis of the boundary temperature, the thermal stress field can be obtained also and taken into account in the FEM analy- sis.

2. 6. Verification o f the FEM-analysis models

The successful analysis of the BELT by FEM depends greatly on the precision of the analysis model. The press tonnage calculated from the analysis model is 9703 kN. Compared with the press tonnage in practice of 9500 kN, the relative error is 2.1%.

3. Results and discussions of the F E M analysis

A powerful FEM code ANSYS is employed to carry out the FEM analysis using 4-node isoparametric axisymmetric elements, Fig. 2 also giving the correspond- ing meshes. Usually both the cylinder and the anvil are made of sintered carbide YG9, the properties are given in Table 1.

3.1. Stress distribution within the cylinder

Fig. 3 gives the distribution of the three stress compo- nents within the cylinder when the pre-stress effected by shrink rings is 2.0625 GPa.

Because sintered carbide is a brittle type of material, the major reason causing cylinder failure is the maximum

g( Qiang et al. / Journal of Materials Processing Technology 55 (1995) 5 10 7

A (a)

I

t / / i / 2 / | IIII//~/

P, (b)

Fig. 2. FEM-analysis models and meshes: (a) cylinder; (b) anvil.

Table 1 Properties of carbide YG9

Items Unit Value

Specific gravity (p) g/cm 3 14.5 Elastic modulus (E) GPa 570 Poisson's ratio (~) 0.23 Coefficient of heat conduction (2) W/m°C 75.3 Coefficient of thermal expansion (c 0 mm/mm.°C 5 x 10-6 Specific heat (C) Cal/kg.°C 130

principal stress. It has been proven by FEM analysis that the maximum principal stress is either the maximum tangential stress on the inner surface or the maximum axial stress on the outer surface, depending on the magni- tude of the pre-stress.

From FEM-analysis results, it is known that the max- imum tangential stress is influenced greatly by the pre- stress, and decreases from 2.474 G P a to zero if the pre- stress increases from 0 to 2.0625 GPa. On the other hand, the maximum axial-stress component will increase with the pre-stress. It can be seen from Fig. 3(c) that the maximum axial stress is 1.21 GPa, which is sufficiently great to damage the cylinder. Therefore, the function of the pre-stress is of double character: the positive side is

(a)

(b)

Fig. 3. Distribution of the stress components within the cylinder when the prestress is 2.0625 GPa: (a) radial stress at; (b) tangential stress at; (c) axial stress a~.

8 W. Qiang et al. / Journal of Materials Processing Technology 55 (1995) 5-10

(c)

Fig. 3. Continued.

the effective reduction of the maximum tangential stress existing at the inner cylindrical surface, which could result in brittle failure in a vertical cross-section; the negative side is the slow increase of the maximum axial stress existing at the outer cylindrical surface, such that the opportunity of brittle failure in a horizontal cross section is increased.

The radial-stress component is always compressive, the greatest compressive stress (ar)max = -- 6.08 GPa be- ing reached at the point marked MN.

3.2. Stress distribution within the anvil

Fig. 4 shows the distribution of the three stress compo- nents within the anvil when the pre-stress effected by the shrink rings is 1 GPa.

It is verified by FEM-analysis results that within the small area near to the anvil surface, material is com- pressed in three directions, with the maximum stress components being (~r)max = -- 3.52 GPa, (trz)max = -- 9.18 GP a and (trt)max = -- 4.51 GPa. It is the ultra-

high compressive stress that causes the damage to the anvil.

The function of the shrink rings was also investigated by changing the magnitude of the pre-stress from zero to 1.5 GPa, finding that the pre-stress is beneficial in effect- ing decrease in the maximum principal stress, i.e. the maximum principal stress decreases from 0.546 to 0.152 GPa when the pre-stress increases from zero to 1.5 GPa. Compared with the cylinder, the function of the shrink rings for the anvil is not so obvious. On the other hand, the maximum principal stress within the anvil is much less than that in the cylinder. Therefore, the

t . 2 1

gX

l_

I I

(b)

l -9.18

(c) Fig. 4. Distribution of stress components within the anvil when the pre- stress is 1 GPa. (a) radial stress at; (b) tangential stress tr,; (c) axial stress tY z.

- 1 . 48

i ,'o

W. Qiang et aL / Journal of Materials Processing Technology 55 (1995) 5-10 9

6

g ¢J

Fig. 5. Distr ibut ion of the thermal principal stress within the anvil.

Fig. 6. Distr ibut ion of the axial stress componen t cr z for the optimized design, when pre-stress is 2.0625 GPa.

damage mechanism for the anvil and that for the cylinder are different.

3.3. Distribution of temperature and thermal stress

The distributions of the temperature and the thermal stress within the cylinder and the anvil were obtained also by FEM analysis. Fig. 5 gives the field of the thermal principal stress within the anvil. In general, thermal stress is beneficial for the decrease of the tangential stress, but it also increases the axial stress to a certain degree. Al- though the influence of the thermal stress on the strength of the BELT is like pre-stress, it is very limited because of its small magnitude.

5.0

4.0 fe

3.0

I.OT = (o z)m~

0

-i.0 L f i i 0 0.5 1.0 1.5

ldl

,r'i M2 I I, t 2.02.2 2.5

4. Optimization of the BELT

Because the synthesizing pressure is concentrated at the middle part of the inner surface of the cylinder, and the pressure effected by the shrink rings is distributed over the whole area of the outer surface, elastic-bending deformation of vertical cross-sections must occur, result- ing in greater tensile axial stress. From the point of view of decreasing the bending deformation, the present authors paper introduce an optimization method: to con- centrate, relatively, the pre-stress on the outer surface of the middle of the cylinder: in other words, the new method is to decrease the height of the shrink rings.

FEM analysis has been performed retaining the pre- stress at 2.0625 GPa, but reducing the height of the shrink rings to 4.45 mm at each end of the cylinder, Fig. 6 giving the distribution of axial stress in this situation. For this new method, the maximum axial stress is only 0.662 GPa: Compared with that in Fig. 3(c), the maximum

P1 (GPa)

Fig. 7. Relationship between (at) max versus P1; (or:) max versus Pt for the optimized design.

axial stress has decreased by 46%. Although the max- imum tangential stress has increased from zero to 0.393 GPa, it is still in the safe range.

On the basis of the optimization method mentioned above, the relationship between (at)re, versus P1, and (a=) m~x versus P1 can be determined, where P1 is the pressure acting on the outer surface of the cylinder (see Fig. 7). The cross-point M is the so-called isostrength point. Consid- ering the influence of temperature on the material strength, the isostrength point should be moved slightly to the right. Therefore, the optimal pressure acting on the outer cylindrical surface is 2.2 GPa, and the optimal pre-stress is 2.05 GPa, which can be used in the deter- mination of the interference of the shrink rings.

10 ~ Qiang et al. /Journal of Materials Processing Technology 55 (1995) 5-10

5. Conclusions

(1) FEM-analysis models for the BELT are estab- lished, including synthesizing pressures, pre-stress, fric- tional resistance and thermal stress. The accuracy of the model has been verified by comparison of the press tonnage between the model and practice, where there is a relative error of 2.1%.

(2) In accordance with FEM-analysis results, max- imum principal stress is the main reason for the brittle failure of the cylinder, this being either the maximum tangential stress on the inner surface or the maximum axial stress on the outer cylindrical surface, depending on the magnitude of the pre-stress. The main cause of dam- age of the anvil is the ultra-high three-dimensional com- pressive stress which exists near to the surface of the anvil.

(3) The function of the pre-stress of the cylinder is of double character: great pre-stress can decrease, obvious- ly, the magnitude of the tensile tangential stress (by 247.4% ), but increases the axial stress slightly. Pre-stress in the anvil is not so important as that in the cylinder.

(4) The function of thermal stress is like that of pre- stress but its influence is limited.

(5) An optimization method aimed to decrease the magnitude of maximum axial stress existing within the

cylinder has been presented and verified by FEM analy- sis. By reducing the acting area to 4.45 mm at each end of the cylinder, the maximum axial stress can be reduced by about 46%.

Acknowledgements

The authors wish to thank Shandong Natural Science Foundation Committee for its financial support of the project: Study of the Failure Mechanism of BELT Ap- paratus for the Synthesis of Diamond and the Optimiza- tion Design (No. 91Fl175).

References

[1] H.T. Hall, Rev. Sci. Instr., 31 (1960) 125. [2] Q. Wang, Metal Forming Technol, 1 (1993) 42 (in Chinese). [3] J. Vrbka and Z. Knesl, in: Proc. 25th Annual Meeting European

High Pressure Res. Group, Potsdam, 1987, Akademie-Verlag, Berlin, 1988, p. 234.

[4] X.L. Yu, Y.N. Yan and Q.L. Liu, For#ing Stamping Technol. 3 (1985) 8 (in Chinese).

[5] H.S. Kim, M. Yoshikawa and O. Fukunaga, Program and Abstracts of Papers, 29th High Pressure Conf. Japan, Nov. 16-18, 1988, Fujisawa, p. 326 (in Japanese).