International Journal of Minerals, Metallurgy and Materials Volume 16, Number 2, April 2009, Page 215
Materials
Thermal residual stress analysis of coated diamond grits Zi-qian Huang1), Bo Xiang2), Yue-hui He1), and Bai-yun Huang1) 1) State Key Laboratory of Powder Metallurgy, Central South University, Changsha 410083, China 2) Zhejiang Huayou Cobalt Co. Ltd., Tongxiang 314500, China (Received 2008-04-13)
Abstract: Residual stresses of coated diamond grits were analyzed by a finite element unit cell model. Diamond grits coated with four types of metals, W, Mo, Ti, and Cr, were considered. The numerical results show that compressive stress occurs in the diamond particles and tensile stress occurs in the metal matrix; compressive stress is concentrated in the diamond sharp corner; interface stresses decrease by more than 1000 MPa with a metal interlayer; plastic deformation of the matrix begins near the sharp corner of diamond grits and extends toward the peripheral zone. Stress concentration dramatically decreases due to plastic deformation of the matrix. The deposition of transition metals on a diamond surface can dramatically promote the adhesion between diamond grits and the metal bond. Key words: diamond grit; residual stress; interlayer; finite element method
[This work was financially supported by the National Natural Science Foundation of China (No.50323008).]
1. Introduction Diamond is the hardest material and is widely used as cutting, grinding, and polishing tools [1-3]. Presently, diamond tools for saw cutting and drilling are often manufactured by powder metallurgy at the sintering temperature of 700-900qC [4-6],but with oxidation at 700qC and graphitization at 1000qC for diamond grits, which influence the performance of the tools. Furthermore, there is rather high interface energy between diamond grits and metal substrate [7-9]; large difference of thermal expansion coefficients, which reduces the holding force of the interface, makes diamond grits separate from the metal matrix. Thus, strengthening the performance of oxidation resistance, graphitization resistance, and pull-out prevention is the main factor for improving the lifetime of diamond tools [10-12]. As mentioned above, the bonding strength between diamond and metal substrate decides the machining lifetime of diamond tools. How to improve the bonding strength is a great question for many researchers. Metallization of the diamond surface can reduce the interface energy between diamond grits and metal maCorresponding author: Zi-qian Huang, E-mail:
[email protected] © 2009 University of Science and Technology Beijing. All rights reserved.
trix and make carbide form [13]. Investigations show that there is good bonding between diamond grits and the coating [14-15] because of the interface formed by the compounds like tungsten carbide, titanium carbide, molybdenum carbide and so on. The improvement of interface bonding strength is because of the relaxation of residual stress by a coated interlayer. The changes of interface stresses and matrix plastic deformation are the main factors for the improvement of material performance. Therefore, it is necessary to discuss the mechanism of thermal stress relaxation and the effects of different elements on the bond strength. In this study, the variations of thermal residual stresses with sintering temperature were analyzed by a finite element unit cell model of plane strain, and the effects of plastic deformation on stress relaxation were also considered.
2. Numerical modeling Diamond tools were manufactured by the powder metallurgy method. Diamond grits were coated with the transition metal by vacuum slow vapor deposition. Diamond grits and the bond metal powder were mixed and cold-pressed to compacts. The sintering temperaAlso available online at www.sciencedirect.com
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ture was between 750 and 900qC. The thermal residual stress was created as a result of the differences in thermal expansion coefficients between diamond grits and the matrix after a temperature drop from sintering temperature to room temperature. In diamond tools, the distribution of diamond grits is discrete; the homogenous distribution of diamond grits in the metal substrate was assumed. A unit cell with a diamond particle and the surrounding partial matrix was analyzed. The morphology of the diamond particles is considered as hexagonal. The edge of the substrate is square. The geometric model of the finite element plane strain method is shown in Fig. 1. The diameter of the diamond particle is about 200 Pm, and the interlayer thickness is around 10 Pm. Microstress is considered in this model, and the main problem here is the interface stresses between diamond grits and the bond metal, which lead to crack initiation and the pull-out of diamond grits. The mechanical and thermal properties of the materials are shown in Table 1. Here, the thermal expansion coefficients are assumed to vary with temperature. The bond metal is characterized as an isotropically hardening elastic-plastic solid, and the diamond grit is assumed to be linear elastic. The two phases are considered to remain perfectly bonded. The yield strength of the matrix is 400 MPa. The temperature changes gradually from 800qC to room temperature and the temperature gradient is ignored. The boundary condition is that the displacement y for the top edge is the same, so is the displacement x for the right edge; the displacement x of the left edge and the displacement y of the bottom edge are fixed.
Fig. 1. Finite element unit cell model for 2-dimensional plane strain.
3. Numerical results 3.1. Stress distribution without coating High stress concentration occurs in the sharp interface due to the large differences of thermal expansion coefficient between diamond grits and the metal matrix. Fig. 2 shows the distribution of equivalent Von
Mises stress after a temperature drop from 800qC to room temperature without a metal interlayer. It can be found that equivalent stresses mainly concentrate in a diamond particle, and they are quite small in the metal matrix; there is a large stress gradient from the diamond grit to the matrix; stress singularity occurs in the sharp corner of the diamond particle; the maximum value of the equivalent stress is 5012 MPa and the minimum is 2241 MPa, which is about a half of the maximum. Here is the condition of elastic deformation for diamond grits and the metal bond, actually the true value of stresses should be lower than 5012 MPa for the plastic flow of the metal matrix. Fig. 3 shows the distribution of principal total strain. It can be seen that strains mainly concentrate in the sharp interface between diamond grits and the metal matrix; the maximum strain is 0.028 and the minimum is 0.0035. It is concluded that there is a small strain and large stress in the diamond particle, i.e. large stress and strain gradient occurs in the sharp interface. Table 1. Mechanical and thermal parameters for material calculation Material W Mo Ti Cr Diamond particle Co, Ni
0.28 0.32 0.22 0.3
Linear expansion coefficient / 106 K1 (20-800qC) 4.59-8 4.98-8.5 8.35-10 6.2-9.2
1050
0.2
1-4
210
0.32
13-16
Young’s modulus / GPa 406 317 116 289
Poisson’s ratio
Fig. 2. Contour plot of the equivalent Von Mises stress without an interlayer.
3.2. Stress distribution with a metal interlayer As mentioned above, high stress concentration occurs in the sharp interface, which results in the decrease of interface strength and the pull-out of diamond grits. The deposition of the strong carbide-forming metal on a diamond surface can dra-
Z.Q. Huang et al., Thermal residual stress analysis of coated diamond grits
matically promote the adhesion between diamond grits and the matrix. The thermal expansion coefficient for the coated metal should be between diamond grits and the substrate. Four types of transition elements, W, Mo, Ti, and Cr, were considered. The effects of the four elements are to be considered by numerical calculation. Fig. 4 shows the distribution of equivalent Von Mises stress with Ti as an interlayer after a temperature drop from 800qC to room temperature. It can be found that the equivalent stresses concentrate in the interfaces of the interlayer, stress concentration occurs in the sharp corner of a diamond particle, and the maximum value is 4016 MPa. The stress in the interlayer is smaller than that in the substrate and diamond particle, the minimum value is 1271 MPa in the matrix. Fig. 5 shows the stress variation with the sintering temperature for the four types of elements. It reveals that the equivalent Von Mises stress increases in the following order: Ti
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mum value of the equivalent stress is 5012 MPa without an interlayer and 4016 MPa with a metal interlayer. In fact, these values should be lower because there is no consideration of plastic deformation of the metal bond. Actually, the metal substrate is an elastic-plastic material; plastic deformation of the substrate has a significant effect on stress redistribution. In this section, the bond metal is characterized as an elastic-plastic solid hardened isotropically, and the diamond particle is assumed to be linear elastic. Fig. 6 shows the distribution of equivalent Von Mises stress with consideration of plastic deformation. Compared with section 3.1, the maximum decrease is from 5012 to 3033 MPa, which decreases by 39%. Fig. 7 shows the evolution of the plastic constraint zone in the metal substrate. It is found that the plastic constraint zone begins from the sharp corner of diamond grits and extends to the peripheral zone.
Fig. 4. Distribution of the equivalent Von Mises stress with a Ti interlayer.
Fig. 5. Variation in equivalent Von Mises stress with sintering temperature for four types of interlayer.
Fig. 3. Contour plot of principal total strain without aninterlayer.
3.3. Effects of plastic deformation on stress relaxation From the above sections, it is found that the maxi-
Fig. 8 shows the comparison of elastic and elastic-plastic deformation with a metal interlayer. It can be seen that the equivalent stress is above 4000 MPa for elastic deformation and decrease by 1000 MPa for elastic-plastic deformation. As for the four metals, the highest stress is in chromium and the lowest is in titanium, and tungsten and molybdenum exhibit moderate
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stress. Also, from this, it can be observed that Ti is the
Fig. 6.
best interlayer metal.
Distribution of the equivalent Von Mises stress with consideration of plastic deformation.
Fig. 7.
Evolution of the plastic constraint zone in the metal matrix.
mond grits. Thermal residual stresses decrease by 25% because of the coated diamond technology. Among the four types of metals, the Ti coating is the best for residual stress relaxation. Plastic deformation of the substrate begins near the sharp corner of diamond grits and extends toward the peripheral zone. Residual stresses decrease by 39% because of plastic deformation of the metal substrate.
References Fig. 8. Comparison between elastic and elastic-plastic deformation of the matrix.
4. Conclusions The deposition of strong carbide-forming metal on a diamond surface can dramatically promote the adhesion between diamond grits and the metal bond. Numerical results show that compressive stresses occur in diamond grits and tensile stresses develop in the metal bond; there is great stress gradient in the interface and stress singularity in the sharp corner of dia-
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