CHIN. PHYS. LETT. Vol. 29, No. 11 (2012) 116201
An Effective Solution for the Best Set of Beveling Parameters of the Cubic
High-Pressure Tungsten Carbide Anvil *
HAN Qi-Gang(韩奇钢)1** , ZHANG Qiang(张强)1 , LI Ming-Zhe(李明哲)1 , JIA Xiao-Peng(贾晓鹏)2 ,
LI Yue-Fen(李月芬)3 , MA Hong-An(马红安)2
2
1
Roll-forging Research Institute, Jilin University, Changchun 130025
National Lab of Superhard Materials, Jilin University, Changchun 130012
3
College of Earth Sciences, Jilin University, Changchun 130061
(Received 9 June 2012)
Determining the best set of beveling parameters is an advantageous characteristic of the geometrical conditions
for a cubic high-pressure tungsten carbide (WC) anvil, but it is almost impossible to deduce experimentally
(much affected by defects in the material). In order to remove the affection of defects in materials, we investigate
computational stress analyses in different beveling parameters of WC anvils by the finite element method. The
results indicate that the rate of cell pressure transmitting and failure crack in the WC anvil monotonically increases
with the bevel angle from 42∘ to 45∘ . Furthermore, there are two groups of actual users of beveled anvils, one
group preferring 41.5∘ , which can decrease the rate of failure crack in WC anvil, the other group preferring 42∘ ,
which can increase the rate of cell pressure transmitting. This work would give an effective solution to solve the
problem of the design of a cubic high-pressure WC anvil experimentally and will greatly help to improve the
cubic high-pressure WC anvil type high pressure techniques.
PACS: 62.50.−p, 07.35.+k, 07.05.Tp
DOI: 10.1088/0256-307X/29/11/116201
High pressure techniques have attracted the wide
attention of scientists and engineers, which have been
used in the fields of physics, advanced materials, and
geophysics widely.[1−3] Nowadays, the most commonly
used apparatus for academic research and industrial
applications are belt, cubic, tetrahedral, and split
sphere apparatus.[4−6] In these apparatus and systems, the cubic high-pressure apparatus (CHPA) that
employs cemented tungsten carbide (WC) anvils is the
most popular apparatus.[7,8] In CHPA, six cubic WC
anvils with a square anvil tip forming a cubic cell are
actuated by three pairs of hydraulic rams so that the
sample assembly is compressed, as shown in Fig. 1(a).
Typically, three adjacent anvils are held in fixed positions while the other three are mobile. CHPA can
accommodate much larger sample volumes than the
other types of apparatus and can be adjusted accurately in HPHT. Furthermore, the pressure of the sample cell in CHPA can rise faster to the pressure of
synthesis.
There are two kinds of WC anvils used for CHPA,
as shown in Figs. 1(b) and 1(c). One is 45∘ off, which
passes a corner of anvil top square (called a no bevel
anvil), the other has a bevel with an angle smaller
than 45∘ (called a bevel anvil). The no bevel anvil
often blows out more easily than the bevel anvil, because the bevel can increase the value of the pressure
on the gaskets between adjacent anvils. In order to
decrease the rate of the blow out, the gasket between
the no bevel anvils needs to be longer than that of
the bevel anvil, but this will increase the time of sample pressure up to 30 min and decrease the rate of cell
pressure transmission. Thus, in most research and
commercial organizations, the most widespread use of
a cubic high-pressure anvil is the bevel anvil, which
has advantages for the formation of the gaskets between bevel anvils, and the pressure of the sample cell
can rise faster than the pressure of synthesis (it only
takes 2 min).
If the best set of beveling parameters is deduced
for the WC anvil, it will be very useful to improve
the cubic anvil high pressure techniques. However, it
is very hard to deduce these parameters for a cubic
high-pressure anvil, because the experimental results
containing the breaking of anvils is much affected by
factors such as defects in the material, which are not
related to the geometrical condition of the anvil. From
this viewpoint, computational stress analysis in the
anvil is one of the most important ways to construct a
whole image of the problem, which is a fast, cheap and
non-destructive method. In this study, a considerable
number of beveling parameters have been tuned by
the finite element method (FEM), so as to increase
the performance of the CHPA and to make an effective solution for the design of a high-pressure anvil
(and remove the affected by defects in the material).
In order to study the beveling parameters of WC
anvils, we only need to simulate the stress and its
distribution under the highest pressure point (synthesized pressure), because the fracture cracks in anvils
mostly occur at the highest pressure point, during
the phase of maintaining the ram load. In this work,
we are not interested in the complicated deformation
process of pyrophyllite cube (gasket) in the process
of increasing pressure and the length of bevel, which
have been studied by us and reported in Refs. [9,10].
* Supported by the National Natural Science Foundation of China under Grant No 11204102, the China Postdoctoral Science
Foundation under Grant No 2011M500592, Shanghai Key Laboratory of Digitized Auto-Body under Grant No 2010001, and Jilin
University Science Foundation.
** Corresponding author. Email: [email protected]
© 2012 Chinese Physical Society and IOP Publishing Ltd
116201-1
CHIN. PHYS. LETT. Vol. 29, No. 11 (2012) 116201
We model the case in which the gasket has been
compressed (after tremendous deformation) and has
reached a fixed pressure point, at which industry diamond can be synthesized. Based on the principle
of symmetry, the cubic symmetric system can be divided into four equivalent parts by a set of two planes
crossing each other at right angles. After make the
simplifying approximation, we only need to simulate
the stress of the 1/4 set under the highest pressure
point.
Fig. 2(a), and the enlarged view of the anvil is shown in
Fig. 2(b). Some of the nodal numbers are also shown
for the convenience of subsequent discussion. A uniform load is applied along the base of the anvil. The
relationship between the load and the system oil pressure is that load = 14.2×oil pressure. All nodes on the
outer surface of the pyrophyllite cube and the supporting ring are the DOF constraints, all nodes on the
symmetric surface are symmetry constraints (these are
carried out by program option).
(a)
(b)
(b)
45O
(a)
(c)
α 46O
Anvil
Supporting ring
46O
Pyrophyllite
y

z

x
WC have been used as structural components
in large volume high-pressure apparatus for many
decades. There is a relatively extensive set of measurements for the uniaxial compressive behavior of WC
and a modest body of literature on the deformation
and strength of WC. We used the values of Poisson’s
ratio 𝜐 = 0.21, Young’s modulus 𝐸𝑥 = 605 GPa, and
the failure stress 𝜎𝑓 = 6.20 GPa, based on a useful
study of the mechanical properties of WC by Getting
et al., which provide the rheological information necessary to facilitate realistic numerical analysis of high
stressed structural components constructed from WC
(the applicability of these date to the structural analysis and design is discussed in Ref. [11]). The supporting ring is made of steel. We used 𝐸𝑥 = 210 GPa,
𝜐 = 0.295, and 𝜎𝑓 = 1.47 GPa.[12] A linear elastic, perfectly plastic model with the von Mises plasticity condition 𝜎VM = 𝜎𝑓 was used, where 𝜎VM and 𝜎𝑓 are the
von Mises stress and the failure strength, respectively.
The material exists with a probability of failure, when
𝜎VM ≥ 𝜎𝑓 .[13] The von Mises stress in the anvil is assumed to be smaller than 6.21 GPa, so the value of the
von Mises stress does not exceed the failure strength
of the WC, and the failure cracks in WC anvils do not
reach the highest pressure point. The shear stress criterion has not been used in this work, although it is
better and safer than that based on a von Mises stress
criterion, because it is very difficult to measure the
dependence of shear stress in WC anvils experimentally (we have performed finite-element simulations to
study the shear stress of WC anvils and Ref. [14]).
A 20-node element (SOLID95) was used in the 3D
model meshes, and all elements were fully isoperimetric. The contact elements (Targe170 and Contact174) were selected and applied to the contact surface in a set. The finite element model is shown in

α
     
Fig. 2.
(Color online) The simplified approximation
model: (a) the finite element model, (b) the enlarged view
of the anvil.
9
Value of vertical stress (GPa)
Fig. 1. (Color online) The model of a cubic high-pressure
WC anvil: (a) CHPA, (b) the no bevel anvil, and (c) the
bevel anvil.

40O
41O
42O
43O
44O
45O
8
7
6
5
4
3
2
1
0
1
2
3
4
5
6
7
8
9
10 11
Serial number of nodes in the Anvil
Fig. 3. (Color online) Graph showing the vertical stress
in a WC anvil with the same load.
Figure 3 shows the calculated vertical stress in a
WC anvil with the same load. The numbers of the
nodes that were used for the convenience of subsequent
discussion are illustrated by the nodes in Fig. 2(b)
(node 6 is on the edge of the anvil face). It can be
noticed that the value of vertical stress increases as
the angle of the bevel increases. For a sharper bevel,
the load is distributed more towards the center, causing a larger value of vertical stress. The greater vertical stress can achieve a more concentrated load in the
sample cell. Clearly, more concentrated load in the
sample cell can realize a higher sample pressure. Thus,
to attain the same cell pressure, the rate of cell pressure transmitting increases as the angle of the bevel
increases. The peak value of vertical stress lies on the
edge of the anvil face, which agrees with the experimental result reported by Forsgren et al.[15]
In order to compare the rate of failure crack in the
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CHIN. PHYS. LETT. Vol. 29, No. 11 (2012) 116201
8
7
(a)
Value of vertical stress (GPa)
6
5
4
3
2
40O
41O
42O
43O
44O
45O
1
(b)
6
5
4
3
1
2
3
4
5
6
7
8
9
10
Serial number of nodes in the anvil
Fig. 4. (Color online) Graph showing the same value of
vertical stress in the center of the square anvil tip (a), and
the von Mises stress in the WC anvil (b).
According to von Mises criterion, material failure
will occur when the magnitude of the von Mises stress
exceeds a critical value, the failure stress (6.20 GPa)
of the tungsten carbide. It is obvious that the peak
value of von Mises stress should be smaller than the
failure strength of the material. Unfortunately, the
peak value of von Mises stress is 6.32 GPa as the angle
of bevel increases to 43∘ (see Fig. 5), which exceeds the
failure stress (6.20 GPa). This will bring a great disadvantage to the performance of the anvils. The failure
cracks in anvils will arise in the process of synthesis
and its location around the bevel. However, the von
Mises stress is 6.19 GPa as the angle of bevel increases
to 42∘ , which does not exceed the failure strength of
the WC. Based on von Mises plasticity criterion, we
know that the failure cracks in anvils will not arise at
the highest pressure point, when the angle of bevel is
smaller than 42∘ . Thus, there are two groups in actual users of beveled anvils, one preferring 42∘ , which
can increase the rate of cell pressure transmitting, the
other preferring 41.5∘ , which can decrease the rate of
failure crack in a WC anvil.
Value of Von Mises stress (GPa)
WC anvil, we obtain the same value of vertical stress
on the center of the anvil face, by changing the load
on the finite model, as shown in Fig. 4(a). It is noticed that to gain the same value of sample pressure,
the load on the model is decreased as the angle of the
bevel increases. This will bring a great advantage to
enhance pressure limitation, when using the same hydraulic rams. The distribution of vertical stress is not
changed, which also agrees with the experimental result reported by Forsgren et al.[15] Figure 4(b) shows
the value of von Mises stress in WC anvil, with the
same vertical stress on the center of the anvil face. It
is noticed that the value of von Mises stress around
the bevel (from Node 6 to Node 9) is larger than in
the other location. The peak value of von Mises stress
is on the edge of the anvil face (node 6), and increases
obviously as the bevel angle increases. The distribution of von Mises stress agrees with the result reported
by Bruno et al.[16]
6.6
6.5
6.4
6.3
6.2
6.1
6.0
5.9
40
41
42
43
44
45
Angle of bevel (deg)
Fig. 5. Graph showing the von Mises stress in the edge
of the square top face of the WC anvil (node 6), when the
same value of vertical stress is attained in the center of
the square anvil tip.
In this work, we have given an effective solution
for the best set of beveling parameters of the cubic
high-pressure WC anvil without affecting the defects
in the material, which is very difficult to deduce experimentally. Our results indicate that to gain the
same cell pressure, the rate of cell pressure transmitting increases as the angle of bevel increases. Furthermore, the larger angle of bevel can bring a greater
advantage to enhance pressure limitation, when using
the same hydraulic rams. However, the rate of failure crack in the WC anvil also increases as the angle
of the bevel increases. There are two groups of actual users of beveled anvils, one preferring 41.5∘ and
the other preferring 42∘ , which can decrease the rate
of failure crack in a WC anvil and increase the rate
of cell pressure transmitting, respectively. This work
would give an effective solution for the design of a
high-pressure anvil and greatly help to improve the
cubic high-pressure techniques.
References
[1]
[2]
[3]
[4]
[5]
[6]
[7]
[8]
[9]
[10]
[11]
[12]
[13]
[14]
[15]
[16]
116201-3
Fan D W et al 2011 Chin. Phys. Lett. 28 126103
Tang L Y et al 2010 Chin. Phys. Lett. 27 016402
Lü S J et al 2009 Acta Phys. Sin. 58 6852 (in Chinese)
Liebermann R C 2011 High Press. Res. 31 493
Sung C M 1997 High Temp. High Press. 29 253
Abbaschian R et al 2005 Diam. Relat. Mater. 14 1916
Han Q G et al 2011 Cryst. Growth Design 11 1000
Han Q G et al 2009 Rev. Sci. Instrum. 80 096107
Li R et al 2007 High Press. Res. 27 249
Han Q G et al 2010 Rev. Sci. Instrum. 81 123901
Getting I C et al 1993 Pure Appl. Geophys. 141 545
Levitas V I and Zarechnyy O M 2007 Appl. Phys. Lett. 91
141919
Jiang C Y et al 2006 Elasticity Theory and Finite Element
Method Science (Beijing: Science Press) (in Chinese)
Han Q G et al 2009 High Press. Res. 29 457
Forsgren K F and Drickamer H G 1965 Rev. Sci. Instrum.
36 1709
Bruno M S and Dunn K J 1984 Rev. Sci. Instrum. 55 940