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Investigation on stress distribution and wear behavior of brazed polycrystalline cubic boron nitride superabrasive grains: Numerical simulation and experimental study
Wear 376-377 (2017) 1234–1244
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Investigation on stress distribution and wear behavior of brazed polycrystalline cubic boron nitride superabrasive grains: Numerical simulation and experimental study Yejun Zhu a, Wenfeng Ding a,n, Tianyu Yu b, Jiuhua Xu a, Yucan Fu a, Honghua Su a a b
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China Department of Aerospace Engineering, Iowa State University, Ames, IA 50010, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2016 Received in revised form 16 November 2016 Accepted 5 December 2016
The polycrystalline cubic boron nitride (PCBN) superabrasive grains, which are comprised of microcrystalline CBN particles and AlN ceramic binder, have a distinguished advantage in self-sharpness during grinding by means of controllable fracture wear. The present work intends to clarify the mechanism of grain fracture based on the analysis of brazing-induced residual stress and the resultant stress in grinding; as such, the grain fracture wear could be predicted and controlled effectively. A finite element model based on Voronoi tessellation method has been first established for PCBN grains. The effects of embedding depth, volume fraction, and grinding loads on the stress distribution within PCBN grains are discussed. It is found that the distribution patterns of microcrystalline CBN particles generally have less influence on grain fracture. Large tensile stress is produced at the interfaces of microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler. Particularly, the largest tensile stress is generated near the grain vertex in the case of the embedding depth of 50%, volume fraction of 80%, and uncut chip thickness of 0.6 μm. The simulation results are verified experimentally through characterizing the wear topography evolution of brazed PCBN grains in grinding. & 2017 Elsevier B.V. All rights reserved.
Keywords: PCBN grains Stress distribution Wear behavior FEA analysis Voronoi tessellation method
1. Introduction The polycrystalline cubic boron nitride (PCBN) superabrasive grains are synthetized by microcrystalline CBN particles and AlN ceramic binder under the conditions of high temperature and high pressure [1]. The isotropic structure of PCBN grains overcome the drawback of anisotropic monocrystalline CBN grains, which tend to a cleavage in grinding due to limited slipping planes [2]. On the other hand, with the assistance of brazing technology, the monolayer brazed superabrasive grinding wheels solve the issue of grains premature pullout, which improves the life of grinding wheels compared with the electroplated superabrasive wheels [3]. The performance in machining nickel-based superalloys and titanium alloys could be improved effectively by the monolayer brazed PCBN grinding wheels [4]. However, recent research has found that, the fracture of AlN binder material can result in PCBN grains fracture [5]. Usually, the tensile stress within a grain is the dominating factor that causes grain fracture, however, the n
Corresponding author. E-mail addresses: [email protected] (W. Ding), [email protected] (T. Yu). http://dx.doi.org/10.1016/j.wear.2016.12.048 0043-1648/& 2017 Elsevier B.V. All rights reserved.
influence of stress distribution on the wear behavior of brazed PCBN grains during grinding has not been clarified clearly. The dimension of PCBN grains in grinding usually ranges from 100 μm to 400 μm, which makes the stress measurement difficult [6,7]. In comparison, the simulation and prediction of stress distribution in some materials based on finite element analysis (FEA) has been widely utilized in the recent years. For instance, Zohdi [8] simulated the stress distribution produced in the cooling process of additive manufacturing of the heated particulate mixture depositions. Matteo et al. [9] and Barrena et al. [10], respectively, investigated the characteristic of stress distribution in brazed steel/ceramic joints with the FEA. Wang et al. [11] predicted the residual stress in Si3N4/Invar with FEA and found the residual stress decrease significantly with increasing of Cu foil thickness in the multi-layered system. Moreover, Suh et al. [12], Akbari et al. [13], Meng et al. [14] and Chen et al. [15] simulated the distribution of residual stress in diamond grains during the brazing process, and found that the largest tensile stress occurred along the bonding interface. Because the PCBN grains are comprised of microcrystalline CBN particles and AlN ceramic binder, the numerical microstructure should be investigated first in order to simulate the stress
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distribution in the finite element model. The Voronoi tessellation method has been applied in several studies to simulate numerical microstructures in FEA [16,17]. For example, Espinosa et al. [18], Warner et al. [19] and Zhou et al. [20] have used the FEA based on Voronoi tessellation method to investigate the failure behavior of brittle materials. In addition, Li et al. [21] combined the FEA and the Voronoi tessellation technique to investigate the mechanical property of the tungsten-based bulk metallic glass matrix composites. In general, the simulation results agreed well with those tested in the experiment. Accordingly, the numerical microstructures of PCBN grains can be created effectively using the Voronoi tessellation method. In this article, the finite element model combined with the Voronoi tessellation techniques was first established for analyzing stress distribution in PCBN grains, which contain the residual stress produced during brazing process and the resultant stress generated in grinding. Additionally, the influence of embedding depth, volume fraction and grinding loads on the stress distribution and grain fracture wear were discussed. Finally, the grinding experiment was conducted to verify the stress simulation results by characterizing the wear topography evolution of brazed PCBN grains.
In order to investigate stress distribution for PCBN grains, a random microstructure model has been constructed by using the Voronoi tessellation method. The typical Voronoi tessellation method could be generally described as follows: (i) a set of seeds are randomly spread in a 2D space; (ii) the space is partitioned into polygonal Voronoi cells with the partitioning line of the perpendicular bisector of the segment that joins two seeds [21]. In the present work, in order to build the inner microcrystalline CBN particles and AlN binder for PCBN grains according to the Voronoi tessellation method, a new parameter Vf, which describes volume fraction, is introduced. Fig. 1 schematically displays a convex polygon of original particle with the solid line, which is similar with the shape utilized in the Voronoi cell. The coordinate centroid, c, can be calculated as follows: n
∑ (xi + xi + 1)(xi yi + 1 − xi + 1yi ) + yi + 1 )(xi yi + 1 − xi + 1yi )
i=1
Fig. 1. Schematic of the Voronoi cell.
1 2
n
∑ (xi yi + 1 − xi + 1yi ) i=1
(2)
Afterwards, the segments connect the centroid with each vertex are drawn. N triangles have been partitioned from the outer particle. The dashed lines, as displayed in Fig. 1, describe the newly-born particle. Assume that each of the vertices in the newly-born particle is located in the dashed line, and its edge is parallel to the corresponding one of the original particle. The shape of newly-born particle will be similar to that of the original particle, and the volume fraction Vf can be determined as:
Vf =
Ai ′ , i ′+ 1, c Ai, i + 1, c
(3)
where Ai ′ , i ′+ 1, c is the area of newly-born particle and Ai, i + 1, c is the area of original particle. Due to the similarity of the newly-born particle and original one, a relationship between the coordinates of newly-born particle and original particle exist, as follows:
(4)
⎧x =x − ⎪ i′ c ⎨ ⎪ ⎩ yi ′ = yc −
Vf (x c − xi ) Vf (yc − yi )
(5)
Accordingly, the size and shape of newly-born particle can be determined by utilizing Eqs. (1) and (5). In the present work, the Voronoi tessellation process was coded with the MATLAB 2010b software. In the FEA model, the maximum size of the microcrystalline CBN particles within a PCBN grain is chosen as 20 μm. As a result, a number of 625 randomly distributed seeds can be created in an area of 0.5 mm 0.5 mm, as displayed in Fig. 2(a); meanwhile, a 2D Voronoi tessellation process has been performed with these seeds (Fig. 2(b)). Then, the volume fraction Vf is taken into consideration based on Eqs. (1) and (5), and the results are shown in Fig. 2(c). Finally, the 2D Voronoi diagram has been transferred into the finite element software ABAQUS. 2.2. Finite element model of the brazing-induced residual stress within PCBN grains
i=1 n
∑ (yi
A=
The coordinates of vertes i’ can be obtained by combining Eqs. (3) and (4):
2.1. Numerical microstructure construction of PCBN grains using Voronoi tessellation techniques
⎧ 1 ⎪ xc = A ⎪ ⎨ ⎪ 1 ⎪ yc = A ⎩
where xi and yi are the coordinates of vertex i , n is the sum of vertices number in the original particle; A refers to the area of the original particle, the value of which can be calculated as:
(y − yi ′ )2 Ai ′ , i ′+ 1, c (x − xi ′ )2 = c = c 2 (x c − xi ) (yc − yi )2 Ai, i + 1, c
2. Finite element model
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(1)
As described in Section 2.1, the microstructure of PCBN grain has been constructed and applied into FEA. In order to be consistent with the PCBN grains used in the grinding experiment, the 2D Voronoi diagram has been trimmed off and a shape of regular hexagon is constructed with the grain side length of 200 μm (maximum diameter 400 μm). A square of the AISI 1045 steel substrate with the height of 5 mm and width of 2 mm is built; as such, the area of metallic substrate is 10 mm2, which is about 200 times larger than that of the PCBN grain. Under such conditions, the size of metallic substrate used will not affect the stress distribution in the PCBN grain. Particularly, the concept of embedding depth refers to the depth of a grain embedded in the bonding alloy [22]. For instance, the 40% embedding depth means that the distance from the highest interface between the grain and the Ag-CuTi bonding alloy to the bottom of the grain is about 40% of the diameter of the grain, as displayed in Fig. 3. The element type used is CPS8R. Fig. 4 shows the meshed finite element model with the embedding depth of 40%, the
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Fig. 2. Evolution of the Voronoi tessellation diagram: (a) seeds spreading; (b) the Voronoi diagram; (c) generation of the microcrystalline CBN particles within a PCBN grain.
grain middle vertex, then to the top vertex; particularly, Path II includes the embedding area, bonding interface and the grinding force area and three vertex points are also connected. Path III is similar to Path I, and it is along the grain top boundary, which is from grain edge center to the vertex. 2.3. Materials properties and brazing procedures
Fig. 3. Schematic diagram of brazed PCBN grains.
microcrystalline CBN particle size of 20 μm and the grain side length of 200 μm, which contains 16,382 elements and 59,054 nodes. Moreover, it can be seen from Fig. 4(a), the node displacement in the bottom surface and that on the right and left surface along x (horizontal) axis are all defined as zero. The node displacement along y (vertical) axis in the bottom surface is also defined as zero. In addition, three reference paths are selected to characterize the brazing-induced residual stress in the PCBN grain, as illustrated in Fig. 4(c). They are represented as Path I, II and III, respectively, with directions denoted by arrows. For example, Path I is along the bottom of the grain, which starts from the center of the grain edge to the vertex of the hexagon. Path II is the most complex one, which starts from the grain bottom vertex to the
According to the previous work [4], (Ag72Cu28)95Ti5 (wt%) alloys are utilized as the brazing filler material to join PCBN grains and AISI 1045 steel substrate in the vacuum furnace, a brazing temperature of 920 °C with the hold time of 5 min is used as optimal operation parameters. In order to ensure a good joining at the interface of PCBN grain-bonding alloy and bonding alloy-metallic substrate, the heating and cooling rate in the brazing cycle is set as 10 °C/min [2,23]. Moreover, the differential thermal analysis (DTA) has indicated that the solidification temperature of Ag-Cu-Ti filler alloy is around 800 °C [23]. Meanwhile, the brazing-induced residual stress would not be produced in both the heating stage and the cooling stage from the brazing temperature to the solidification temperature. As a consequence, a cooling condition from solidification temperature (800 °C) to the room temperature (20 °C) is used in the present simulation. As listed in Table 1, the material properties (e.g., Young’s modulus, Poisson’s ratio, thermal expansion coefficient, and yield strength) are provided either from the manufacturers or from literatures [24–26]. Particularly, in order to save the computation load, some assumptions are made. For example, all materials used in the model are regarded as isotropic and rigid plastic.
Fig. 4. Finite element model for the brazing-induced stress distribution in a PCBN grain: (a) boundary conditions, (b) meshing diagram, (c) three paths selected for stress distribution analysis.
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Table 1 Materials properties utilized in the present finite element simulation. Properties
Materials
Young’s modulus E/GPa
Microcrystalline CBN particle
AlN binder
Ag-Cu-Ti filler alloy
909
320
100 (293 K) 90 (500 K) 80 (700 K) 70 (800 K) 67 (900 K) 0.35 16.7 (293 K) 18.0 (500 K) 19.0 (700 K) 20.0 (800 K) 20.5 (900 K) 230 (293 K) 170 (473 K) 100 (700 K) 70 (800 K) 20 (900 K)
Poisson’s ratio μ Thermal expansion coefficient α/10 6 K 1
0.12 4.92
0.23 4.5
Yield strength ss/MPa
–
–
AISI 1045 steel
210 (293 K) 185 (600 K) 160 (800 K) 0.26 9.1 (293 K) 13.09 (500 K) 13.71 (700 K) 14.18 (800 K) 14.6 7(900 K) 360 (293 K) 263 (600 K) 179 (800 K) 78 (900 K)
Fig. 5. Schematic illustration of monolayer brazed PCBN wheel in grinding: (a) grinding behavior, (b) the loading zone on the grain vertex. Table 2 Relationship between the grinding forces and uncut chip thickness of single grain. Uncut chip thickness agmax (μm)
Normal grinding forces Fn (N)
Tangential grinding forces Ft (N)
0.6 2 4 8
2.6 3.5 4.6 9.4
1.4 1.5 2.2 4.9
Meanwhile, the PCBN grain micro-cracks are ignored and it is considered as a continuum body. In addition, the material creep behavior, solubilization and diffusion behavior during the brazing process are not taken into account as well due to their limited influence.
2.4. Loading of grinding forces on the PCBN grains After the brazing-induced stress distribution has been analyzed, the grinding forces can be loaded on the vertex region on the grain top surface. In fact, the cutting depth of a single grain in the PCBN wheel, is different than the wheel depth of cut (such as d in Fig. 5(a)) and it can be described by the uncut chip thickness agmax, as shown in Fig. 5(b). For this reason, the quantitative correlation between the uncut chip thickness, agmax, and the grinding force on each grain has been listed in Table 2. It should be noted that, the grinding force versus uncut chip thickness is obtained based on finite element simulation of the grinding process with a single grain, which has been reported in our previous work [27] and the effect of wheel speeds vs, depth of cut ap and workpiece infeed speed vw has been considered. Furthermore, as illustrated in Fig. 5(b), the normal and tangential forces listed in Table 2 are uniformly loaded on the grain
Fig. 6. Contour maps of residual stress distribution from brazing process: (a) Single grain-bond; (b) Grain bond interface.
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Fig. 7. Contour maps of resultant stress distribution in grinding wheel: (a) Single grain-bond; (b) Stress concentration from polycrystalline structure.
Fig. 8. Maximum in-plane principal stress distribution along Path I in PCBN grains with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding, (c) stress at point A and B.
vertex region in the present simulation of the resultant stress. The loading zone of the grain is solely determined by agmax. As such, the finite element model of the resultant stress, which contains the brazing-induced stress and the force-induced stress, has been established.
3. Results and discussion 3.1. Characterization of stress distribution in PCBN grains As a typical brittle material, the PCBN grains can bear high compressive stress but fracture easily under large tensile stress
[28,29]. Therefore, the values of the residual stress in brazed PCBN grains could be evaluated by the maximum in-plane principal stress. Figs. 6 and 7 show the contours of the maximum in-plane principal stress simulated during the brazing process and the grinding process, respectively. Here the embedding depth is 40%, and the volume fraction is 80% with the uncut chip thickness of 0.6 μm. Tensile stress has been observed in the microcrystalline CBN particles and compressive stress in the AlN binders. Moreover, the brazing-induced tensile stress in PCBN grains greatly concentrate in the interfaces among the microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler alloy (Fig. 6(b)), which are caused due to the thermal expansion coefficients mismatch. A large compressive stress occurs at the vertex of the PCBN grain,
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Fig. 9. Maximum in-plane principal stress distribution along Path II in PCBN grain with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding, (c) stress at point C and interface.
Fig. 10. Maximum in-plane principal stress distribution along Path III in PCBN grains with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding.
where the grinding force is loaded, as displayed in Fig. 7(b). Furthermore, the microcrystalline structure of the PCBN grains may affect their fracture behavior. However, it is out of the scope of the current study, which is investigating the effect of the
embedding depth, volume fraction and grinding loads as brazing and grinding parameters, on the stress distribution. Hence, the effect of the microcrystalline structure will be investigated in further research.
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Fig. 11. The component of PCBN grains with different volume fractions: (a) Vf ¼60%; (b) Vf ¼ 70%; (c) Vf ¼80%; (d) Vf ¼90%.
3.2. Influence of embedding depth on stress distribution in PCBN grains Figs. 8–10 quantitatively compare the maximum in-plane principal stress distribution along Path I, II and III, respectively, with the grain embedding depth varies from 20% to 50%. Here, the volume fraction is 80% and agmax is 0.6 μm. It can be observed from Figs. 8(a) and (b), along Path I, not only the brazing-induced residual stress but also the resultant stress in grinding just slightly changed. However, as described in the previous work [30], the grain fracture wear probably happens when the tensile stress in the grain are larger than its fracture strength; as such, the maximum tensile stress should be discussed. Two points along Path I (denoted as Point A and Point B in Fig. 8(a)) where the local maximum tensile stress occur are selected, as displayed in Fig. 8(c). It should be noted that, the resultant stress at Point A and B change less compared with the brazing-induced residual stress. Therefore, only the brazing-induced stress are analyzed here. With the embedding depth of about 20%, the tensile stress at point A is 1532 MPa and that at point B is 1073 MPa, respectively. The tensile stress at point A increases by 6.9% to 1638 MPa when the embedding depth increases to 40%. When the embedding depth further increases to 50%, the stress at point A decreases by 3.7% to 1578 MPa. However, the stress at Point B keeps almost constant. The stress distribution along Path II in PCBN grains with different embedding depth is displayed Fig. 9. Obviously, the brazing-induced stress along Path II is tensile, and the peak values are over 1000 MPa, which occur at the interface of the microcrystalline CBN particles/AlN binders. When the grinding
forces are applied, large tensile and compressive stress occur at the grain vertex, as illustrated in Fig. 9(b). The stress near the interface is affected by the embedding depth. Hence, the maximum stress in Path II (donated as point C), the stress in the vertex and the maximum stress near the interface are selected to investigate the stress distribution in the grain, as illustrated in Fig. 9(c). The tensile stress are 1315 MPa at point C, 35 MPa at the vertex and 821 MPa at the interface, respectively. Obviously, with the change of embedding depth, the brazinginduced stress at point C and at the vertex almost keep constant. In the opposite, when the embedding depth increases to 30%, the tensile stress at the interface increases by 8.9% to 894 MPa. In contrast, the stress decreases by 28% to 643 MPa, when the embedding depth increases to 50%. In addition, the resultant stress at point C and the interface change slightly, after the grinding forces are applied. In the opposite, the resultant stress at the vertex changes from tensile stress (35 MPa) to compressive stress ( 610 MPa). It’s noted that, point C is close to the vertex. The tensile stress at point C is over 1300 MPa, which may cause the PCBN grain micro-fracture wear. Fig. 10 shows the stress distribution along Path III in PCBN grains with different embedding depth. Along Path III, the influence of the embedding depth on the stress distribution is generally small. The maximum tensile stress is above 1200 MPa and that of compressive stress is around 610 MPa. As discussed above, the large stress usually exist in three paths in the PCBN grain. The large stress along Path I and in the interface along Path II could result in the grain macro-fracture wear, and the stress near the vertex and along Path III will cause
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Fig. 12. Maximum in-plane principal stress distribution along Path II in PCBN grains with different volume fraction: (a) brazing-induced stress, (b) resultant stress in grinding, (c) the largest brazing-induced stress in the range from 0 to 320 μm, from 320 to 400 μm and at the vertex, (d) the largest resultant stress in the range from 0 to 320 μm, from 320 to 400 μm and at the vertex.
Fig. 13. Resultant stress in the PCBN grain along Path II with different agmax: (a) full range, (b) narrow range.
the micro-fracture wear. Obviously, when the embedding depth is 50%, the stress along Path I and in the interface along Path II is lower than the others comprehensively. As such, the 50% embedding depth is selected. Meanwhile, the stress distribution along Path II is complex, which will affect the fracture wear of PCBN grain. Therefore, the stress distribution along Path II will be discussed in detail.
3.3. Influence of volume fraction on stress distribution within PCBN grains The PCBN grains are combined with microcrystalline CBN particles and AlN binder. As described in Ref. [22], the ratio of the materials in PCBN grains may affect the mechanical property of the grains. Fig. 11 displays the PCBN grain with the volume fraction
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uncut chip thickness on the stress distribution in the PCBN grain has been discussed. In order to increase the working life of the brazed grinding tools, the brazing-induced residual stress should be as low as possible to maintain fracture strength of the grain. However, during the attrition and fracture wear, the micro-fracture is preferred to occur on the grain top surface to maintain sharp edges. Therefore, the resultant stress should be large enough on the grain top surface. In conclusion, the most suitable stress distribution was obtained in the case of the embedding depth of 50%, volume fraction of 80% and uncut chip thickness of 0.6 μm.
4. Wear topography evolution of the brazed PCBN grain in grinding Fig. 14. Equipment of grinding experiment with brazed PCBN grinding wheel.
range from 60% to 90%. Fig. 12 shows the effects of volume fraction on the stress distribution along Path II after the brazing process and in the grinding process, respectively. Here, the agmax is 0.6 μm and the embedding depth is 40%. In order to avoid the grain macro-fracture wear and improve the life of grinding wheels, the stress along Path II in the range from 0 to 320 μm should be kept. Fig. 12(b) shows the largest tensile stress in the range from 0 to 320 μm, the range from 320 μm to 400 μm along Path II and the stress at the vertex, respectively. After the brazing process, the maximum tensile stress along Path II in the range from 0 to 320 μm is 1590 MPa when the volume fraction is 60%. The maximum tensile stress in the range from 320 μm to 400 μm is 1391 MPa. When the volume fraction increases, the largest tensile stress in the range from 0 to 320 μm greatly decreases by 50.7% to 783 MPa. However, the stress in the range from 320 μm to 400 μm increases by 18.9% to 1654 MPa first, then decreases by 50.5% to 818 MPa. The stress at the vertex keep in the range from 50 MPa to 200 MPa, which are tensile ones. When the grinding forces are applied, the largest tensile stress in the range from 0 to 320 μm and the range from 320 to 400 μm almost keep constant. However, the stress at the vertex changes from tensile stress into compressive stress. The largest stress changes around 600 MPa. It is obvious that, when the volume fraction is 80%, the resultant stress in grinding is low in the range from 0 to 320 μm and that is large in the range from 320 to 400 μm, which indicates that the grain micro-fracture wear may occur. 3.4. Influence of grinding loads on resultant stress in PCBN grains During the grinding process, different grinding parameters may be utilized to meet various machining requirements. In this case, the effect of grinding loads on the resultant stress is investigated. In this section, four groups of grinding forces (e.g., normal Fn and tangential Ft) are applied on the grain vertex region after brazing process, as listed in Table 2. The volume fraction is fixed as 80% and the grain embedding depth is selected as 40%. Moreover, according to Fig. 5, area of the loading zone will increase with the increase of agmax. Fig. 13 shows the resultant stress distribution along Path II. Obviously, the stress distribution on the grain vertex is affected significantly by the grinding force. As illustrated in Fig. 13(b), the resultant stress in the area (x ¼385 μm) is 1361 MPa when agmax is 0.6 μm. With agmax increases to 8 μm, the stress can decrease by 75.7% to 330 MPa. In the opposite, the maximum compressive stress changes from 614 MPa to 1220 MPa, with agmax increase from 0.6 μm to 8 μm. Therefore, in order to reduce the grain macro-fracture wear, the agmax should be selected around 0.6 μm. The influence of the embedding depth, volume fraction and the
The measurement of stress distribution within PCBN grains is very difficult and with low accuracy at present. However, the topology evolution can provide valuable information during grinding process. Grinding tests have been designed and conducted with the monolayer brazed PCBN grinding wheel; as such, the stress simulation results could be indirectly verified based on the wear topography evolution of the PCBN grains. The grinding equipment is displayed in Fig. 14. The nickel-based superalloy Inconel 718 is used as the workpiece material. The wheel speed is 120 m/s with the feed rate of 1.7 m/min and the cutting depth is 10 μm; as such, the uncut chip thickness is 0.6 μm. Three grinding passes are conducted with the grinding length of 60 mm. The wear topography of PCBN grain was collected using the 3D optical microscope (Hirox KH-7700), and the grains’ height was also measured. Moreover, the 3D profiles of the grains were reconstructed based on the Matlab 2010b software, which made it easy to characterize the grain topography evolution. In addition, in order to quantitatively evaluate the grain fracture wear during the grinding process, the surface fractal dimension Ds was calculated. The detailed calculation method of surface fractal dimension has been reported in Ref. [31]. In general, if micro-fracture wear happens on the grain surface, the micro cutting edges can be formed, which usually enlarges the surface fractal dimension Ds. On the contrary, when the large fracture wear occurs, the micro cutting edges reduce, and the surface fractal dimension Ds decreases to a certain extent. Fig. 15 provides the wear topography evolution of PCBN grain during the grinding process, and the evolution of the grain height. The surface fractal dimension is also displayed in Fig. 16. Obviously, the original grain has several cutting edges, and the grain height h and fractal dimension Ds are 336.9 μm and 2.0563, respectively. After the first grinding pass, a few part of microcrystalline CBN particles fall off from the PCBN grain due to the large resultant stress in grinding. The height h decreases by 3.27% to 325.9 μm; however, the fractal dimension Ds increases to 2.0589, which indicates that the number of micro cutting edges increase and the grain self-sharpening occurs. After the second grinding pass, the height h further decreases by 3% to 316.1 μm, and the fractal dimension continuously increases. After the third grinding pass, the grain height h decreases by 4.68% to 301.4 μm, and the fractal dimension Ds decreases by 1.15% to 2.0409. The wear of brazed PCBN grain is still dominant by the micro fracture. As described in the simulation, the resultant stress in the grain top surface was large that the micro fracture might occur on the grain top surface. Hence, the FEA model in the present work is verified valid by the wear topography evolution of brazed PCBN grains.
5. Conclusion Based on the investigation above, the conclusions have been drawn as follows:
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Fig. 15. Typical wear topography evolution of the brazed PCBN grain during grinding.
Fig. 16. Evolution of the grain height and surface fractal dimension in grinding.
(1) The finite element model based on Voronoi tessellation method was established for analyzing the stress distribution within PCBN grains. (2) The brazing-induced residual stress in PCBN grains is mainly concentrated in the interfaces among the microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler alloy. (3) The influence of the microcrystalline CBN particles distribution on fracture within the PCBN grain is weak and can be ignored. (4) In the case of the embedding depth of 50%, volume fraction of 80% and uncut chip thickness of 0.6 μm, the large tensile stress is predicted near the vertex of the PCBN grain. (5) The wear of brazed PCBN grain is mainly dominant by the micro fracture in grinding, which verified that the resultant stress induced micro fracture on the grain top surface.
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Acknowledgements This work is financially supported by the National Natural Science Foundation of China (Nos. 51235004 and 51375235), the Fundamental Research Funds for the Central Universities (Nos. NE2014103 and NZ2016107) and the Funding for Outstanding Doctoral Dissertation in NUAA (No. BCXJ16-06). The corresponding author, Dr. Wenfeng Ding, also thanks the support from Prof. Liangchi Zhang during his visiting in UNSW Australia.
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[13] M. Akbari, S. Buhl, C. Leinenbach, R. Spolenak, K. Wegener, Thermomechanical analysis of residual stresses in brazed diamond metal joints using Raman spectroscopy and finite element simulation, Mech. Mater. 52 (2012) 69–77. [14] F.L. Meng, A.G. Liu, H.H. Sun, M.H. Guo, FEA of thermal effects on brazed cold diamond grit, Trans. Indian Inst. Met. 68 (5) (2015) 829–838. [15] Y. Chen, Y.C. Fu, H.H. Su, J.H. Xu, H.J. Xu, The effects of solder alloys on the morphologies and mechanical properties of brazed diamond grits, Int. J. Refract. Met. Hard Mater. 42 (2014) 23–29. [16] P. Alveen, D. Carolan, D. McNamara, N. Murphy, A. Ivanković, Micromechanical modelling of ceramic based composites with statistically representative synthetic microstructures, Comput. Mater. Sci. 79 (2013) 960–970. [17] P. Alveen, D. McNamara, D. Carolan, N. Murphy, A. Ivanković, The influence of microstructure on the fracture properties of polycrystalline cubic boron nitride, Comput. Mater. Sci. 109 (2015) 115–123. [18] H.D. Espinosa, P.D. Zavattieri, A grain level model for the study of failure initiation and evolution in polycrystalline brittle materials, Part I: Theory Numer. Implement. Mech. Mater. 35 (2003) 333–364. [19] D.H. Warner, J.F. Molinari, Micromechanical finite element modeling of compressive fracture in confined alumina ceramic, Acta Mater. 54 (2006) 5135–5145. [20] T.T. Zhou, C.Z. Huang, H.L. Liu, J. Wang, B. Zou, H.T. Zhu, Crack propagation simulation in microstructure of ceramic tool materials, Comput. Mater. Sci. 54 (2012) 150–156. [21] H. Li, K. Li, G. Subhash, L.J. Kecskes, R.J. Dowding, Micromechanical modeling of tungsten-based bulk metallic glass matrix composites, Mater. Sci. Eng. A 429 (2006) 115–123. [22] W.F. Ding, Y.J. Zhu, L.C. Zhang, J.H. Xu, Y.C. Fu, W.D. Liu, C.Y. Yang, Stress characteristics and fracture wear of brazed CBN grains in monolayer grinding wheels, Wear 332–333 (2015) 800–809. [23] W.F. Ding, J.H. Xu, M. Shen, H.H. Su, Y.C. Fu, B. Xiao, Joining of CBN abrasive grains to medium carbon steel with Ag-Cu/Ti powder mixture as active brazing alloy, Mater. Sci. Eng.: A 430 (2006) 301–306. [24] A. Klett, R. Freudenstein, M.F. Plass, W. Kulisch, Stress of c-BN Thin films: a parameter investigation, Surf. Coat. Technol. 116 (1999) 86–92. [25] J. Chen, X.W. Xu, B.Y. Yuan, J.X. Deng, X.R. Xing, Thermal expansion of cubic boron nitride, Acta Metall. Sin. 39 (9) (2003) 952–954. [26] Editorial Board, Practical Handbook for Engineering Materials, 2nd Edition, Standards Press of China, Beijing, 2002. [27] J.B. Dai, W.F. Ding, L.C. Zhang, J.H. Xu, H.H. Su, Understanding the effects of grinding speed and undeformed chip thickness on the chip formation in highspeed grinding, Int. J. Adv. Manuf. Technol. 81 (2015) 995–1005. [28] G.M. Zheng, J. Zhao, Z.J. Gao, Q.Y. Cao, Cutting performance and wear mechanisms of Sialon-Si3N4 graded nano-composite ceramic cutting tools, Int. J. Adv. Manuf. Technol. 58 (1) (2012) 19–28. [29] X.H. Zhang, Z.H. Deng, G.Y. Chen, Y.H. Ren, L.L. Wan, W. Liu, G.F. Zhang, A theoretical and experimental study on laser-induced deterioration in wet grinding of Al2O3 engineering ceramic, Int. J. Adv. Manuf. Technol. 82 (9) (2016) 1949–1957. [30] W. Graham, C.M. Voutsadopoulos, Fracture wear of grinding wheels, Int. J. Mach. Tools Des. Res. 18 (2) (1978) 95–103. [31] Q. Miao, W.F. Ding, J.H. Xu, C.Y. Yang, Y.C. Fu, Fractal analysis of wear topography of brazed polycrystalline cBN abrasive grains during grinding nickel super alloy, Int. J. Adv. Manuf. Technol. 68 (2013) 2229–2236.
Contents lists available at ScienceDirect
Wear journal homepage: www.elsevier.com/locate/wear
Investigation on stress distribution and wear behavior of brazed polycrystalline cubic boron nitride superabrasive grains: Numerical simulation and experimental study Yejun Zhu a, Wenfeng Ding a,n, Tianyu Yu b, Jiuhua Xu a, Yucan Fu a, Honghua Su a a b
College of Mechanical and Electrical Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China Department of Aerospace Engineering, Iowa State University, Ames, IA 50010, USA
art ic l e i nf o
a b s t r a c t
Article history: Received 3 September 2016 Received in revised form 16 November 2016 Accepted 5 December 2016
The polycrystalline cubic boron nitride (PCBN) superabrasive grains, which are comprised of microcrystalline CBN particles and AlN ceramic binder, have a distinguished advantage in self-sharpness during grinding by means of controllable fracture wear. The present work intends to clarify the mechanism of grain fracture based on the analysis of brazing-induced residual stress and the resultant stress in grinding; as such, the grain fracture wear could be predicted and controlled effectively. A finite element model based on Voronoi tessellation method has been first established for PCBN grains. The effects of embedding depth, volume fraction, and grinding loads on the stress distribution within PCBN grains are discussed. It is found that the distribution patterns of microcrystalline CBN particles generally have less influence on grain fracture. Large tensile stress is produced at the interfaces of microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler. Particularly, the largest tensile stress is generated near the grain vertex in the case of the embedding depth of 50%, volume fraction of 80%, and uncut chip thickness of 0.6 μm. The simulation results are verified experimentally through characterizing the wear topography evolution of brazed PCBN grains in grinding. & 2017 Elsevier B.V. All rights reserved.
Keywords: PCBN grains Stress distribution Wear behavior FEA analysis Voronoi tessellation method
1. Introduction The polycrystalline cubic boron nitride (PCBN) superabrasive grains are synthetized by microcrystalline CBN particles and AlN ceramic binder under the conditions of high temperature and high pressure [1]. The isotropic structure of PCBN grains overcome the drawback of anisotropic monocrystalline CBN grains, which tend to a cleavage in grinding due to limited slipping planes [2]. On the other hand, with the assistance of brazing technology, the monolayer brazed superabrasive grinding wheels solve the issue of grains premature pullout, which improves the life of grinding wheels compared with the electroplated superabrasive wheels [3]. The performance in machining nickel-based superalloys and titanium alloys could be improved effectively by the monolayer brazed PCBN grinding wheels [4]. However, recent research has found that, the fracture of AlN binder material can result in PCBN grains fracture [5]. Usually, the tensile stress within a grain is the dominating factor that causes grain fracture, however, the n
Corresponding author. E-mail addresses: [email protected] (W. Ding), [email protected] (T. Yu). http://dx.doi.org/10.1016/j.wear.2016.12.048 0043-1648/& 2017 Elsevier B.V. All rights reserved.
influence of stress distribution on the wear behavior of brazed PCBN grains during grinding has not been clarified clearly. The dimension of PCBN grains in grinding usually ranges from 100 μm to 400 μm, which makes the stress measurement difficult [6,7]. In comparison, the simulation and prediction of stress distribution in some materials based on finite element analysis (FEA) has been widely utilized in the recent years. For instance, Zohdi [8] simulated the stress distribution produced in the cooling process of additive manufacturing of the heated particulate mixture depositions. Matteo et al. [9] and Barrena et al. [10], respectively, investigated the characteristic of stress distribution in brazed steel/ceramic joints with the FEA. Wang et al. [11] predicted the residual stress in Si3N4/Invar with FEA and found the residual stress decrease significantly with increasing of Cu foil thickness in the multi-layered system. Moreover, Suh et al. [12], Akbari et al. [13], Meng et al. [14] and Chen et al. [15] simulated the distribution of residual stress in diamond grains during the brazing process, and found that the largest tensile stress occurred along the bonding interface. Because the PCBN grains are comprised of microcrystalline CBN particles and AlN ceramic binder, the numerical microstructure should be investigated first in order to simulate the stress
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distribution in the finite element model. The Voronoi tessellation method has been applied in several studies to simulate numerical microstructures in FEA [16,17]. For example, Espinosa et al. [18], Warner et al. [19] and Zhou et al. [20] have used the FEA based on Voronoi tessellation method to investigate the failure behavior of brittle materials. In addition, Li et al. [21] combined the FEA and the Voronoi tessellation technique to investigate the mechanical property of the tungsten-based bulk metallic glass matrix composites. In general, the simulation results agreed well with those tested in the experiment. Accordingly, the numerical microstructures of PCBN grains can be created effectively using the Voronoi tessellation method. In this article, the finite element model combined with the Voronoi tessellation techniques was first established for analyzing stress distribution in PCBN grains, which contain the residual stress produced during brazing process and the resultant stress generated in grinding. Additionally, the influence of embedding depth, volume fraction and grinding loads on the stress distribution and grain fracture wear were discussed. Finally, the grinding experiment was conducted to verify the stress simulation results by characterizing the wear topography evolution of brazed PCBN grains.
In order to investigate stress distribution for PCBN grains, a random microstructure model has been constructed by using the Voronoi tessellation method. The typical Voronoi tessellation method could be generally described as follows: (i) a set of seeds are randomly spread in a 2D space; (ii) the space is partitioned into polygonal Voronoi cells with the partitioning line of the perpendicular bisector of the segment that joins two seeds [21]. In the present work, in order to build the inner microcrystalline CBN particles and AlN binder for PCBN grains according to the Voronoi tessellation method, a new parameter Vf, which describes volume fraction, is introduced. Fig. 1 schematically displays a convex polygon of original particle with the solid line, which is similar with the shape utilized in the Voronoi cell. The coordinate centroid, c, can be calculated as follows: n
∑ (xi + xi + 1)(xi yi + 1 − xi + 1yi ) + yi + 1 )(xi yi + 1 − xi + 1yi )
i=1
Fig. 1. Schematic of the Voronoi cell.
1 2
n
∑ (xi yi + 1 − xi + 1yi ) i=1
(2)
Afterwards, the segments connect the centroid with each vertex are drawn. N triangles have been partitioned from the outer particle. The dashed lines, as displayed in Fig. 1, describe the newly-born particle. Assume that each of the vertices in the newly-born particle is located in the dashed line, and its edge is parallel to the corresponding one of the original particle. The shape of newly-born particle will be similar to that of the original particle, and the volume fraction Vf can be determined as:
Vf =
Ai ′ , i ′+ 1, c Ai, i + 1, c
(3)
where Ai ′ , i ′+ 1, c is the area of newly-born particle and Ai, i + 1, c is the area of original particle. Due to the similarity of the newly-born particle and original one, a relationship between the coordinates of newly-born particle and original particle exist, as follows:
(4)
⎧x =x − ⎪ i′ c ⎨ ⎪ ⎩ yi ′ = yc −
Vf (x c − xi ) Vf (yc − yi )
(5)
Accordingly, the size and shape of newly-born particle can be determined by utilizing Eqs. (1) and (5). In the present work, the Voronoi tessellation process was coded with the MATLAB 2010b software. In the FEA model, the maximum size of the microcrystalline CBN particles within a PCBN grain is chosen as 20 μm. As a result, a number of 625 randomly distributed seeds can be created in an area of 0.5 mm 0.5 mm, as displayed in Fig. 2(a); meanwhile, a 2D Voronoi tessellation process has been performed with these seeds (Fig. 2(b)). Then, the volume fraction Vf is taken into consideration based on Eqs. (1) and (5), and the results are shown in Fig. 2(c). Finally, the 2D Voronoi diagram has been transferred into the finite element software ABAQUS. 2.2. Finite element model of the brazing-induced residual stress within PCBN grains
i=1 n
∑ (yi
A=
The coordinates of vertes i’ can be obtained by combining Eqs. (3) and (4):
2.1. Numerical microstructure construction of PCBN grains using Voronoi tessellation techniques
⎧ 1 ⎪ xc = A ⎪ ⎨ ⎪ 1 ⎪ yc = A ⎩
where xi and yi are the coordinates of vertex i , n is the sum of vertices number in the original particle; A refers to the area of the original particle, the value of which can be calculated as:
(y − yi ′ )2 Ai ′ , i ′+ 1, c (x − xi ′ )2 = c = c 2 (x c − xi ) (yc − yi )2 Ai, i + 1, c
2. Finite element model
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(1)
As described in Section 2.1, the microstructure of PCBN grain has been constructed and applied into FEA. In order to be consistent with the PCBN grains used in the grinding experiment, the 2D Voronoi diagram has been trimmed off and a shape of regular hexagon is constructed with the grain side length of 200 μm (maximum diameter 400 μm). A square of the AISI 1045 steel substrate with the height of 5 mm and width of 2 mm is built; as such, the area of metallic substrate is 10 mm2, which is about 200 times larger than that of the PCBN grain. Under such conditions, the size of metallic substrate used will not affect the stress distribution in the PCBN grain. Particularly, the concept of embedding depth refers to the depth of a grain embedded in the bonding alloy [22]. For instance, the 40% embedding depth means that the distance from the highest interface between the grain and the Ag-CuTi bonding alloy to the bottom of the grain is about 40% of the diameter of the grain, as displayed in Fig. 3. The element type used is CPS8R. Fig. 4 shows the meshed finite element model with the embedding depth of 40%, the
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Fig. 2. Evolution of the Voronoi tessellation diagram: (a) seeds spreading; (b) the Voronoi diagram; (c) generation of the microcrystalline CBN particles within a PCBN grain.
grain middle vertex, then to the top vertex; particularly, Path II includes the embedding area, bonding interface and the grinding force area and three vertex points are also connected. Path III is similar to Path I, and it is along the grain top boundary, which is from grain edge center to the vertex. 2.3. Materials properties and brazing procedures
Fig. 3. Schematic diagram of brazed PCBN grains.
microcrystalline CBN particle size of 20 μm and the grain side length of 200 μm, which contains 16,382 elements and 59,054 nodes. Moreover, it can be seen from Fig. 4(a), the node displacement in the bottom surface and that on the right and left surface along x (horizontal) axis are all defined as zero. The node displacement along y (vertical) axis in the bottom surface is also defined as zero. In addition, three reference paths are selected to characterize the brazing-induced residual stress in the PCBN grain, as illustrated in Fig. 4(c). They are represented as Path I, II and III, respectively, with directions denoted by arrows. For example, Path I is along the bottom of the grain, which starts from the center of the grain edge to the vertex of the hexagon. Path II is the most complex one, which starts from the grain bottom vertex to the
According to the previous work [4], (Ag72Cu28)95Ti5 (wt%) alloys are utilized as the brazing filler material to join PCBN grains and AISI 1045 steel substrate in the vacuum furnace, a brazing temperature of 920 °C with the hold time of 5 min is used as optimal operation parameters. In order to ensure a good joining at the interface of PCBN grain-bonding alloy and bonding alloy-metallic substrate, the heating and cooling rate in the brazing cycle is set as 10 °C/min [2,23]. Moreover, the differential thermal analysis (DTA) has indicated that the solidification temperature of Ag-Cu-Ti filler alloy is around 800 °C [23]. Meanwhile, the brazing-induced residual stress would not be produced in both the heating stage and the cooling stage from the brazing temperature to the solidification temperature. As a consequence, a cooling condition from solidification temperature (800 °C) to the room temperature (20 °C) is used in the present simulation. As listed in Table 1, the material properties (e.g., Young’s modulus, Poisson’s ratio, thermal expansion coefficient, and yield strength) are provided either from the manufacturers or from literatures [24–26]. Particularly, in order to save the computation load, some assumptions are made. For example, all materials used in the model are regarded as isotropic and rigid plastic.
Fig. 4. Finite element model for the brazing-induced stress distribution in a PCBN grain: (a) boundary conditions, (b) meshing diagram, (c) three paths selected for stress distribution analysis.
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Table 1 Materials properties utilized in the present finite element simulation. Properties
Materials
Young’s modulus E/GPa
Microcrystalline CBN particle
AlN binder
Ag-Cu-Ti filler alloy
909
320
100 (293 K) 90 (500 K) 80 (700 K) 70 (800 K) 67 (900 K) 0.35 16.7 (293 K) 18.0 (500 K) 19.0 (700 K) 20.0 (800 K) 20.5 (900 K) 230 (293 K) 170 (473 K) 100 (700 K) 70 (800 K) 20 (900 K)
Poisson’s ratio μ Thermal expansion coefficient α/10 6 K 1
0.12 4.92
0.23 4.5
Yield strength ss/MPa
–
–
AISI 1045 steel
210 (293 K) 185 (600 K) 160 (800 K) 0.26 9.1 (293 K) 13.09 (500 K) 13.71 (700 K) 14.18 (800 K) 14.6 7(900 K) 360 (293 K) 263 (600 K) 179 (800 K) 78 (900 K)
Fig. 5. Schematic illustration of monolayer brazed PCBN wheel in grinding: (a) grinding behavior, (b) the loading zone on the grain vertex. Table 2 Relationship between the grinding forces and uncut chip thickness of single grain. Uncut chip thickness agmax (μm)
Normal grinding forces Fn (N)
Tangential grinding forces Ft (N)
0.6 2 4 8
2.6 3.5 4.6 9.4
1.4 1.5 2.2 4.9
Meanwhile, the PCBN grain micro-cracks are ignored and it is considered as a continuum body. In addition, the material creep behavior, solubilization and diffusion behavior during the brazing process are not taken into account as well due to their limited influence.
2.4. Loading of grinding forces on the PCBN grains After the brazing-induced stress distribution has been analyzed, the grinding forces can be loaded on the vertex region on the grain top surface. In fact, the cutting depth of a single grain in the PCBN wheel, is different than the wheel depth of cut (such as d in Fig. 5(a)) and it can be described by the uncut chip thickness agmax, as shown in Fig. 5(b). For this reason, the quantitative correlation between the uncut chip thickness, agmax, and the grinding force on each grain has been listed in Table 2. It should be noted that, the grinding force versus uncut chip thickness is obtained based on finite element simulation of the grinding process with a single grain, which has been reported in our previous work [27] and the effect of wheel speeds vs, depth of cut ap and workpiece infeed speed vw has been considered. Furthermore, as illustrated in Fig. 5(b), the normal and tangential forces listed in Table 2 are uniformly loaded on the grain
Fig. 6. Contour maps of residual stress distribution from brazing process: (a) Single grain-bond; (b) Grain bond interface.
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Fig. 7. Contour maps of resultant stress distribution in grinding wheel: (a) Single grain-bond; (b) Stress concentration from polycrystalline structure.
Fig. 8. Maximum in-plane principal stress distribution along Path I in PCBN grains with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding, (c) stress at point A and B.
vertex region in the present simulation of the resultant stress. The loading zone of the grain is solely determined by agmax. As such, the finite element model of the resultant stress, which contains the brazing-induced stress and the force-induced stress, has been established.
3. Results and discussion 3.1. Characterization of stress distribution in PCBN grains As a typical brittle material, the PCBN grains can bear high compressive stress but fracture easily under large tensile stress
[28,29]. Therefore, the values of the residual stress in brazed PCBN grains could be evaluated by the maximum in-plane principal stress. Figs. 6 and 7 show the contours of the maximum in-plane principal stress simulated during the brazing process and the grinding process, respectively. Here the embedding depth is 40%, and the volume fraction is 80% with the uncut chip thickness of 0.6 μm. Tensile stress has been observed in the microcrystalline CBN particles and compressive stress in the AlN binders. Moreover, the brazing-induced tensile stress in PCBN grains greatly concentrate in the interfaces among the microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler alloy (Fig. 6(b)), which are caused due to the thermal expansion coefficients mismatch. A large compressive stress occurs at the vertex of the PCBN grain,
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Fig. 9. Maximum in-plane principal stress distribution along Path II in PCBN grain with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding, (c) stress at point C and interface.
Fig. 10. Maximum in-plane principal stress distribution along Path III in PCBN grains with different embedding depth: (a) brazing-induced stress, (b) resultant stress in grinding.
where the grinding force is loaded, as displayed in Fig. 7(b). Furthermore, the microcrystalline structure of the PCBN grains may affect their fracture behavior. However, it is out of the scope of the current study, which is investigating the effect of the
embedding depth, volume fraction and grinding loads as brazing and grinding parameters, on the stress distribution. Hence, the effect of the microcrystalline structure will be investigated in further research.
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Fig. 11. The component of PCBN grains with different volume fractions: (a) Vf ¼60%; (b) Vf ¼ 70%; (c) Vf ¼80%; (d) Vf ¼90%.
3.2. Influence of embedding depth on stress distribution in PCBN grains Figs. 8–10 quantitatively compare the maximum in-plane principal stress distribution along Path I, II and III, respectively, with the grain embedding depth varies from 20% to 50%. Here, the volume fraction is 80% and agmax is 0.6 μm. It can be observed from Figs. 8(a) and (b), along Path I, not only the brazing-induced residual stress but also the resultant stress in grinding just slightly changed. However, as described in the previous work [30], the grain fracture wear probably happens when the tensile stress in the grain are larger than its fracture strength; as such, the maximum tensile stress should be discussed. Two points along Path I (denoted as Point A and Point B in Fig. 8(a)) where the local maximum tensile stress occur are selected, as displayed in Fig. 8(c). It should be noted that, the resultant stress at Point A and B change less compared with the brazing-induced residual stress. Therefore, only the brazing-induced stress are analyzed here. With the embedding depth of about 20%, the tensile stress at point A is 1532 MPa and that at point B is 1073 MPa, respectively. The tensile stress at point A increases by 6.9% to 1638 MPa when the embedding depth increases to 40%. When the embedding depth further increases to 50%, the stress at point A decreases by 3.7% to 1578 MPa. However, the stress at Point B keeps almost constant. The stress distribution along Path II in PCBN grains with different embedding depth is displayed Fig. 9. Obviously, the brazing-induced stress along Path II is tensile, and the peak values are over 1000 MPa, which occur at the interface of the microcrystalline CBN particles/AlN binders. When the grinding
forces are applied, large tensile and compressive stress occur at the grain vertex, as illustrated in Fig. 9(b). The stress near the interface is affected by the embedding depth. Hence, the maximum stress in Path II (donated as point C), the stress in the vertex and the maximum stress near the interface are selected to investigate the stress distribution in the grain, as illustrated in Fig. 9(c). The tensile stress are 1315 MPa at point C, 35 MPa at the vertex and 821 MPa at the interface, respectively. Obviously, with the change of embedding depth, the brazinginduced stress at point C and at the vertex almost keep constant. In the opposite, when the embedding depth increases to 30%, the tensile stress at the interface increases by 8.9% to 894 MPa. In contrast, the stress decreases by 28% to 643 MPa, when the embedding depth increases to 50%. In addition, the resultant stress at point C and the interface change slightly, after the grinding forces are applied. In the opposite, the resultant stress at the vertex changes from tensile stress (35 MPa) to compressive stress ( 610 MPa). It’s noted that, point C is close to the vertex. The tensile stress at point C is over 1300 MPa, which may cause the PCBN grain micro-fracture wear. Fig. 10 shows the stress distribution along Path III in PCBN grains with different embedding depth. Along Path III, the influence of the embedding depth on the stress distribution is generally small. The maximum tensile stress is above 1200 MPa and that of compressive stress is around 610 MPa. As discussed above, the large stress usually exist in three paths in the PCBN grain. The large stress along Path I and in the interface along Path II could result in the grain macro-fracture wear, and the stress near the vertex and along Path III will cause
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Fig. 12. Maximum in-plane principal stress distribution along Path II in PCBN grains with different volume fraction: (a) brazing-induced stress, (b) resultant stress in grinding, (c) the largest brazing-induced stress in the range from 0 to 320 μm, from 320 to 400 μm and at the vertex, (d) the largest resultant stress in the range from 0 to 320 μm, from 320 to 400 μm and at the vertex.
Fig. 13. Resultant stress in the PCBN grain along Path II with different agmax: (a) full range, (b) narrow range.
the micro-fracture wear. Obviously, when the embedding depth is 50%, the stress along Path I and in the interface along Path II is lower than the others comprehensively. As such, the 50% embedding depth is selected. Meanwhile, the stress distribution along Path II is complex, which will affect the fracture wear of PCBN grain. Therefore, the stress distribution along Path II will be discussed in detail.
3.3. Influence of volume fraction on stress distribution within PCBN grains The PCBN grains are combined with microcrystalline CBN particles and AlN binder. As described in Ref. [22], the ratio of the materials in PCBN grains may affect the mechanical property of the grains. Fig. 11 displays the PCBN grain with the volume fraction
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uncut chip thickness on the stress distribution in the PCBN grain has been discussed. In order to increase the working life of the brazed grinding tools, the brazing-induced residual stress should be as low as possible to maintain fracture strength of the grain. However, during the attrition and fracture wear, the micro-fracture is preferred to occur on the grain top surface to maintain sharp edges. Therefore, the resultant stress should be large enough on the grain top surface. In conclusion, the most suitable stress distribution was obtained in the case of the embedding depth of 50%, volume fraction of 80% and uncut chip thickness of 0.6 μm.
4. Wear topography evolution of the brazed PCBN grain in grinding Fig. 14. Equipment of grinding experiment with brazed PCBN grinding wheel.
range from 60% to 90%. Fig. 12 shows the effects of volume fraction on the stress distribution along Path II after the brazing process and in the grinding process, respectively. Here, the agmax is 0.6 μm and the embedding depth is 40%. In order to avoid the grain macro-fracture wear and improve the life of grinding wheels, the stress along Path II in the range from 0 to 320 μm should be kept. Fig. 12(b) shows the largest tensile stress in the range from 0 to 320 μm, the range from 320 μm to 400 μm along Path II and the stress at the vertex, respectively. After the brazing process, the maximum tensile stress along Path II in the range from 0 to 320 μm is 1590 MPa when the volume fraction is 60%. The maximum tensile stress in the range from 320 μm to 400 μm is 1391 MPa. When the volume fraction increases, the largest tensile stress in the range from 0 to 320 μm greatly decreases by 50.7% to 783 MPa. However, the stress in the range from 320 μm to 400 μm increases by 18.9% to 1654 MPa first, then decreases by 50.5% to 818 MPa. The stress at the vertex keep in the range from 50 MPa to 200 MPa, which are tensile ones. When the grinding forces are applied, the largest tensile stress in the range from 0 to 320 μm and the range from 320 to 400 μm almost keep constant. However, the stress at the vertex changes from tensile stress into compressive stress. The largest stress changes around 600 MPa. It is obvious that, when the volume fraction is 80%, the resultant stress in grinding is low in the range from 0 to 320 μm and that is large in the range from 320 to 400 μm, which indicates that the grain micro-fracture wear may occur. 3.4. Influence of grinding loads on resultant stress in PCBN grains During the grinding process, different grinding parameters may be utilized to meet various machining requirements. In this case, the effect of grinding loads on the resultant stress is investigated. In this section, four groups of grinding forces (e.g., normal Fn and tangential Ft) are applied on the grain vertex region after brazing process, as listed in Table 2. The volume fraction is fixed as 80% and the grain embedding depth is selected as 40%. Moreover, according to Fig. 5, area of the loading zone will increase with the increase of agmax. Fig. 13 shows the resultant stress distribution along Path II. Obviously, the stress distribution on the grain vertex is affected significantly by the grinding force. As illustrated in Fig. 13(b), the resultant stress in the area (x ¼385 μm) is 1361 MPa when agmax is 0.6 μm. With agmax increases to 8 μm, the stress can decrease by 75.7% to 330 MPa. In the opposite, the maximum compressive stress changes from 614 MPa to 1220 MPa, with agmax increase from 0.6 μm to 8 μm. Therefore, in order to reduce the grain macro-fracture wear, the agmax should be selected around 0.6 μm. The influence of the embedding depth, volume fraction and the
The measurement of stress distribution within PCBN grains is very difficult and with low accuracy at present. However, the topology evolution can provide valuable information during grinding process. Grinding tests have been designed and conducted with the monolayer brazed PCBN grinding wheel; as such, the stress simulation results could be indirectly verified based on the wear topography evolution of the PCBN grains. The grinding equipment is displayed in Fig. 14. The nickel-based superalloy Inconel 718 is used as the workpiece material. The wheel speed is 120 m/s with the feed rate of 1.7 m/min and the cutting depth is 10 μm; as such, the uncut chip thickness is 0.6 μm. Three grinding passes are conducted with the grinding length of 60 mm. The wear topography of PCBN grain was collected using the 3D optical microscope (Hirox KH-7700), and the grains’ height was also measured. Moreover, the 3D profiles of the grains were reconstructed based on the Matlab 2010b software, which made it easy to characterize the grain topography evolution. In addition, in order to quantitatively evaluate the grain fracture wear during the grinding process, the surface fractal dimension Ds was calculated. The detailed calculation method of surface fractal dimension has been reported in Ref. [31]. In general, if micro-fracture wear happens on the grain surface, the micro cutting edges can be formed, which usually enlarges the surface fractal dimension Ds. On the contrary, when the large fracture wear occurs, the micro cutting edges reduce, and the surface fractal dimension Ds decreases to a certain extent. Fig. 15 provides the wear topography evolution of PCBN grain during the grinding process, and the evolution of the grain height. The surface fractal dimension is also displayed in Fig. 16. Obviously, the original grain has several cutting edges, and the grain height h and fractal dimension Ds are 336.9 μm and 2.0563, respectively. After the first grinding pass, a few part of microcrystalline CBN particles fall off from the PCBN grain due to the large resultant stress in grinding. The height h decreases by 3.27% to 325.9 μm; however, the fractal dimension Ds increases to 2.0589, which indicates that the number of micro cutting edges increase and the grain self-sharpening occurs. After the second grinding pass, the height h further decreases by 3% to 316.1 μm, and the fractal dimension continuously increases. After the third grinding pass, the grain height h decreases by 4.68% to 301.4 μm, and the fractal dimension Ds decreases by 1.15% to 2.0409. The wear of brazed PCBN grain is still dominant by the micro fracture. As described in the simulation, the resultant stress in the grain top surface was large that the micro fracture might occur on the grain top surface. Hence, the FEA model in the present work is verified valid by the wear topography evolution of brazed PCBN grains.
5. Conclusion Based on the investigation above, the conclusions have been drawn as follows:
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Fig. 15. Typical wear topography evolution of the brazed PCBN grain during grinding.
Fig. 16. Evolution of the grain height and surface fractal dimension in grinding.
(1) The finite element model based on Voronoi tessellation method was established for analyzing the stress distribution within PCBN grains. (2) The brazing-induced residual stress in PCBN grains is mainly concentrated in the interfaces among the microcrystalline CBN particles, AlN ceramic binder and Ag-Cu-Ti filler alloy. (3) The influence of the microcrystalline CBN particles distribution on fracture within the PCBN grain is weak and can be ignored. (4) In the case of the embedding depth of 50%, volume fraction of 80% and uncut chip thickness of 0.6 μm, the large tensile stress is predicted near the vertex of the PCBN grain. (5) The wear of brazed PCBN grain is mainly dominant by the micro fracture in grinding, which verified that the resultant stress induced micro fracture on the grain top surface.
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Acknowledgements This work is financially supported by the National Natural Science Foundation of China (Nos. 51235004 and 51375235), the Fundamental Research Funds for the Central Universities (Nos. NE2014103 and NZ2016107) and the Funding for Outstanding Doctoral Dissertation in NUAA (No. BCXJ16-06). The corresponding author, Dr. Wenfeng Ding, also thanks the support from Prof. Liangchi Zhang during his visiting in UNSW Australia.
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