Model Establishment of a Co-Based Metal Matrix with Additives of WC and Ni by Discrete Element Method
Abstract
:1. Introduction
2. Metal Matrix Discrete Element Method (DEM) Model Establishment and Calibration
2.1. Metal Matrix
2.2. Bonds in the Metal Matrix Model
- In the DEM model of the CoX matrix, which is without any additives, the bonded pair is only the Co–Co pair. The bond boundary of Co‒Co includes Co–Co bond1 and Co–Co bond2, which are a parallel bond and contact bond, respectively, as shown in Figure 4.
- In the DEM model of CoX–WC, the addition of WC particles introduces two new bonded pairs: WC–WC and Co–WC.
- In the DEM model of CoX–Ni, the addition of Ni particles introduces two new bonded pairs: Ni–Ni and Co–Ni.
- In the DEM model of CoX–WC–Ni, the simultaneous addition of WC and Ni introduces a new bonded pair: Ni–WC.
2.3. Microcosmic Parameters
2.3.1. Inversion Method for Microcosmic Parameters
2.3.2. Calibration of Microcosmic Parameters for CoX–WC–Ni
3. Experimental Setup
3.1. Metal Matrix Composition
3.2. Fabrication of Metal Matrix
3.3. Three-Point Bending Test and Compression Test
4. Calibration Results
5. Validation and Discussion
6. Concluding Remarks
- When building the DEM model of the diamond metal matrix, skeletal substances in the matrix are treated as particles in the model and bonding substances can be represented as parallel bonds between particles.
- Besides the parallel bond, the contact bond should be considered during the construction of the DEM model of the diamond segment matrix because of its elasticity.
- The step-by-step calibration of microcosmic parameters is effective for the DEM model of metal matrix with multiple additives.
- The constructed CoX–WC–Ni DEM model exhibited a satisfactory ability to predict TRS, and the error rate is less than 10%. It will be useful for the design of a metal matrix.
Author Contributions
Funding
Conflicts of Interest
References
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Percentage of WC | Number of WC Particles | WC–WC Bonds | WC–Co Bonds | ||
---|---|---|---|---|---|
Number | Proportion | Number | Proportion | ||
10% | 12,550 | 4959 | 1.9% | 60,956 | 24.6% |
5% | 6275 | 1241 | 0.5% | 32,929 | 13.3% |
3% | 3765 | 464 | 0.2% | 20,317 | 8.2% |
Metal Matrix | Particles in the Model | Bonded Pairs between Particles |
---|---|---|
CoX | Co | Co–Co |
CoX–WC | Co, WC | Co–Co, Co–WC, WC–WC |
CoX–Ni | Co, Ni | Co–Co, Co–Ni, Ni–Ni |
CoX–WC–Ni | Co, Ni, WC | Co–Co, Co–WC, WC–WC, Co–Ni, Ni–Ni, Ni–WC |
Ingredient | Average Granularity (µm) | Purity (%) |
---|---|---|
Cobalt (Co) | 48 | 99.7 |
Copper (Cu) | 48 | 99.5 |
Tin (Sn) | 74 | 98.0 |
Nickel (Ni) | 48 | 99.6 |
Tungsten carbide (WC) | 48 | 99.9 |
No. | Matrix | CoX (wt %) | WC (wt %) | Ni (wt %) |
---|---|---|---|---|
1 | CoX100 | 100 | 0 | 0 |
2 | CoX97–WC3 | 97 | 3 | 0 |
3 | CoX95–WC5 | 95 | 5 | 0 |
4 | CoX90–WC10 | 90 | 10 | 0 |
5 | CoX97–Ni3 | 97 | 0 | 3 |
6 | CoX94–WC3–Ni3 | 94 | 3 | 3 |
7 | CoX90–WC5–Ni5 | 90 | 5 | 5 |
8 | CoX80–WC10–Ni10 | 80 | 10 | 10 |
Particles | Particles | ||
---|---|---|---|
Co | WC | Ni | |
ρ, Density of particles, g/cm3 | 8.90 | 15.63 | 8.88 |
Ec, Elasticity modulus of particles, (Pa) | 1.3 × 1010 | 8 × 1011 | 9 × 109 |
μ, Friction coefficient | 0.80 | 0.05 | 0.80 |
Rmax/Rmin * | 1.13 | 1.13 | 1.13 |
Bonds | Microcosmic Parameters | Type of Particle Bonds | |||||
---|---|---|---|---|---|---|---|
Co–Co | WC–WC | Co–WC | Ni–Ni | Co–Ni | Ni–WC | ||
Contact bond | Normal strength (Pa) | 6 × 107 | 12 × 107 | 10 × 107 | 7 × 107 | 7.5 × 107 | 9.5 × 107 |
Shear strength (Pa) | 6 × 107 | 12 × 107 | 10 × 107 | 7 × 107 | 7.5 × 107 | 9.5 × 107 | |
Parallel bond | Elasticity modulus (Pa) | 1.3 × 109 | |||||
Normal strength (Pa) | 3 × 108 | ||||||
Shear strength (Pa) | 3 × 108 | ||||||
Radius multiplier | 1 |
The Content of WC | TRS | Ec | UCS | ||||||
---|---|---|---|---|---|---|---|---|---|
Experiment (MPa) | Simulation (MPa) | Error (%) | Experiment (GPa) | Simulation (GPa) | Error (%) | Experiment (MPa) | Simulation (MPa) | Error (%) | |
3% | 1054 ± 85 | 1180 | 11.9 | 13.9 ± 0.9 | 15.3 | 10.1 | 1713 ± 82 | 1819 | 6.2 |
5% | 1015 ± 79 | 1144 | 12.7 | 13.7 ± 0.7 | 14.2 | 3.7 | 1751 ± 77 | 1893 | 8.2 |
10% | 967 ± 82 | 1038 | 7.3 | 13.4 ± 0.8 | 13.7 | 2.2 | 1825 ± 83 | 1965 | 7.7 |
TRS | CoX90–(WC5–Ni5) | CoX80–(WC10–Ni10) |
---|---|---|
Simulation | 1110 MPa | 981 MPa |
Experimental | 1035 MPa | 923 MPa |
Error rate | 7.7% | 5.9% |
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Chen, X.; Huang, G.; Tan, Y.; Huang, H.; Guo, H.; Xu, X. Model Establishment of a Co-Based Metal Matrix with Additives of WC and Ni by Discrete Element Method. Materials 2018, 11, 2319. https://doi.org/10.3390/ma11112319
Chen X, Huang G, Tan Y, Huang H, Guo H, Xu X. Model Establishment of a Co-Based Metal Matrix with Additives of WC and Ni by Discrete Element Method. Materials. 2018; 11(11):2319. https://doi.org/10.3390/ma11112319
Chicago/Turabian StyleChen, Xiuyu, Guoqin Huang, Yuanqiang Tan, Hui Huang, Hua Guo, and Xipeng Xu. 2018. "Model Establishment of a Co-Based Metal Matrix with Additives of WC and Ni by Discrete Element Method" Materials 11, no. 11: 2319. https://doi.org/10.3390/ma11112319