Paper
Simulation of Retention of a Diamond Particle in a Matrix of Diamond-Impregnated Tools
2016 Volume 63 Issue 7 Pages 697-700
Details
2016 Volume 63 Issue 7 Pages 697-700
The main objectives of the paper are numeric calculations of retention of diamond particle in metallic-diamond segments of circular saws. The segments are produced by means of the technology of powder metallurgy. The analysis has been preformed for cobalt, cobalt-iron and cobalt-tungsten sinters. The effective use of diamond impregnated tools is strongly depended on the retentive properties of the metal matrix, which must hold diamond grits firmly. Due to mismatch between thermal expansion coefficients of the matrix and diamond, the mechanical fields are generated in the matrix at diamond surroundings. The fields play a major role for retentive properties of matrix. It has been postulated that the potential retentive capability of a matrix can be associated with the amount of elastic and plastic deformation energy which occurs in the matrix around diamond particles.
Diamond tools designed to cut construction materials and natural stone include circular saws with blade segments soldered to a steel disc (Fig. 1). The segments—the cutting elements of the saw—are produced using powder metallurgy.
Views of a circular saw disc.
The process of production of metal-diamond segments involves mixing the metal matrix powder with the natural or synthetic diamond powder, which is followed by die pressing and sintering or hot pressing1–3).
The specimens to be examined were produced by hot pressing. The pressing was performed in the atmosphere of an inert gas (nitrogen)1). The process parameters were selected experimentally and they were as follows: pressure 35–40 MPa, duration 2 min. and temperature 850–980 °C (Table 1). The specimens were produced from the following elementary powders: SMS cobalt, EF (Extrafine) cobalt and 400 mesh cobalt. Additionally, one matrix was produced using 50 percent by mass of EF cobalt powder + 50 percent by mass of CN (Carbonyl) iron powder and another matrix was produced using 80 percent by mass of EF cobalt powder + 20 percent by mass of WP30 tungsten powder. The mechanical properties of the matrix materials were determined experimentally2,3), as depicted in Table 1.
| Material symbol | Chemical composition | Pressing parameters | Rm [MPa] | R0.2 [MPa] | ΔL/L [%] |
|---|---|---|---|---|---|
| Co(SMS) | 100 % Co SMS | 850 °C/35 MPa/2 min | 865 | 405 | 19.5 |
| Co(EF) | 100 % Co Extrafine |
850 °C/35 MPa/2 min | 954 | 634 | 9.5 |
| Co(400) | 100 % Co 400 mesh |
950 °C/35 MPa/2 min | 743 | 540 | 1.7 |
| Co(EF)Fe | 50 % Co Extrafine 50 % Fe CN |
900 °C/35 MPa/2 min | 527 | 494 | 1.3 |
| Co(EF)W | 80 % Co Extrafine 20 % WP30 |
980 °C/40 MPa/2 min | 927 | 632 | 1.4 |
The coefficients of thermal expansion for cobalt, iron, tungsten and diamond are given in Table 24–6). The coefficients for the CoFe sinter and CoW sinter were assumed to be proportional to the amount of metals in the sinters.
| Temperature [K] | Cobalt [K−1] | Iron [K−1] | Tungsten [K−1] | Diamond [K−1] |
|---|---|---|---|---|
| 300 | 13.4·10−6 | 12.0·10−6 | 4.4·10−6 | 1·10−6 |
| 600 | 16.5·10−6 | 13.1·10−6 | 4.7·10−6 | 3·10−6 |
| 1200 | 18.0·10−6 | 13.4·10−6 | 4.8·10−6 | 6·10−6 |
An important property of the matrix material is retention of diamond particles (Fig. 2a) during the operation of the tool. The retention occurs as a result of mechanical bonding. Mechanical bonding is achieved during cooling, which follows hot pressing. Compared with metals, diamond has a very low coefficient of thermal expansion, which causes that diamond particles are squeezed by the shrinking matrix1). Mechanical bonding is dependent on the elastic and plastic properties of the matrix. Retention of a diamond particle with respect to the mechanical properties of the matrix was analyzed in Refs.7–9). The most essential parameters affecting retention are the elastic and plastic energies of the deformed matrix around a diamond particle (Fig. 2b)8–10).
a) Fracture of a segment with diamond particles, b) numerical model of a diamond particle with the plastic zone (grey color).
The amount of diamond grits in a segment of a metal-matrix diamond tool is determined basing on the so called diamond concentration. The 100 concentration is equivalent to 4.4 carats (0.2 g) of diamond per 1 cm3, which constitutes 25 % of the volume1). The matrix fragment selected for the computer simulation contained only one diamond particle, with a relative measure of concentration being 15.
The data were obtained with the finite element method using ABAQUS program ver. 6.1411). The 3D model with a truncated octahedral diamond particle was analyzed (Fig. 3a). The size of the particle (distance between the opposite square walls) was 350 μm. The calculations were performed for a deeply embedded particle and one protruding above the surface of a metal matrix (Fig. 3b).
a) Model of a diamond particle—truncated octahedron, b) model of a diamond particle protruding above the matrix surface.
A numerical analysis was conducted for a diamond particle with protrusion ranging from 25 μm to 150 μm, as well as for a particle with a negative protrusion value. Protrusion is the height of a diamond particle projecting above the matrix surface (Fig. 3b). Negative protrusion is the distance of the particle from the surface in the case of a particle completely submerged in the matrix.
For all the materials analyzed here, the strain energy of the matrix around a diamond particle was largely affected by protrusion.
The cooling of the diamond particle–metal matrix system was simulated for all the matrix materials tested. The total strain energy of the matrix around a diamond particle shows a clear relationship with protrusion of the diamond particle (Fig. 4). For protrusion ranging from 0 to 150 μm, the relationship is linear with different inclinations.
Total strain energy vs. protrusion.
The percentage share of the plastic strain energy in the total strain energy shows little influence on the type of the matrix material (Fig. 5). All the matrices indicate similar and uniform share of the plastic energy with regard to the particle protrusion.
Percentage share of the plastic strain energy in the total energy of a diamond particle.
The simulation was repeated for a diamond particle subjected to a load normal to the matrix surface. A maximum force applied to the diamond particle was 50 N.
The force acting on the particle contributes to a change in the stress field around the particle (Fig. 6). An increase in the energy of the matrix deformation resulting from the external load is significant. It constitutes more than ten percent of the strain energy caused by thermal shrinkage of the sinter during pressing. Table 3 gives an average increase in the energy of the matrix for a typical protrusion of 75 μm. The elastic energy of the particle increases more clearly than the energy of the matrix (Table 3).
Stress field [MPa] around a diamond particle in the CoW matrix with a protrusion of 75 μm, a) the particle without loading, b) the particle under loading.
| Matrix material | Increase in the total strain energy of the matrix | Increase in the plastic strain energy of the matrix | Increase in the elastic strain energy of the particle |
|---|---|---|---|
| Co(SMS) | 17 % | 21 % | 133 % |
| Co(EF) | 11 % | 12 % | 68 % |
| Co(400) | 12 % | 12 % | 62 % |
| CoFe | 26 % | 35 % | 64 % |
| Co(EF)W | 10 % | 9 % | 40 % |
The retention of the diamond particle in the matrix was assessed by performing a simulation of a pullout of the particle by an external force. A force normal to the surface as well as a tangential force were applied. The force needed to remove the particle show strong relationship with the particle protrusion (Fig. 7).
Force pulling a particle out of a matrix, upper line—force tangent to the matrix surface, lower line—force normal to the matrix surface, a) the Co(EF) Fe matrix, b) the Co(EF)W matrix.
The amount of force required to remove a particle out of the matrix shows correlation with the total strain energy of the matrix around the particle (Fig. 8). In their previous works8–10), the authors suggested that the plastic strain energy of the matrix can be used as an indicator of retention of the diamond particle. The results of the computer simulations confirm the thesis that the strain energy of the matrix caused by thermal shrinkage during cooling is a measure of retention of a diamond particle in a metal matrix.
Force vs. energy of the Co(SMS) matrix, upper line—force tangent to the matrix surface, lower line—force normal to the matrix surface.
The following conclusions have been drawn from the analysis:
The total strain energy (i.e. elastic and plastic energies) of the matrix deformation around the diamond particle can be a good estimator of the retention properties of the metal matrix. Further research should focus on numerical modelling of abrasive and erosive wear of the matrix to verify all the results.
