Finite Element Analysis of Surface Residual Stress in Functionally Gradient Cemented Carbide Tool

Gradient structure and elemental distribution of the FGCC-T5 tools

The original materials chosen to use are WC, TiC, and cobalt (with proportions amounting to 85 %, 5 %, and 10 %, respectively). The FGCC-T5 cutting tools were prepared using the previously-described microwave-assisted nitriding sintering method [9, 20, 21]. After production, cross-sectional metallographic specimens were prepared. The gradient structure and elemental distribution of the FGCC-T5 tools were analyzed using EPMA (Figure 1).

Figure 1:

The microstructure of FGCC-T5 cross-sectional metallographic specimens (EPMA, sintering temperature is 1400 °C, holding time is 15 min).

Figure 1(a) shows the backscattered electron image of the FGCC-T5 surface. The surface of the tool is formed from two layers: a grey gradient layer (approximately 10 μm thick) and a bright-white substrate layer. During the nitriding sintering process, titanium diffuses to the surface and forms (Ti, W) (C, N) because titanium and nitrogen have a high affinity for each other. At the same time, the space left due to titanium diffusion is filled by tungsten and cobalt coming from the outer layer. Figure 1(b)–(f) shows the results of the EPMA analysis of the FGCC-T5 samples. It can be seen that the gradient layer is divided into two parts: an outer layer rich in titanium and nitrogen (but deficient in tungsten and cobalt) and an intermediate layer rich in cobalt. As shown in Figure 1(d), the thicknesses of the two layers are essentially equal. Figure 2 shows XRD patterns obtained from the FGCC-T5 tools. It is apparent that the main diffraction peak from the FGCC-T5 surface is due to TiCN. Some small diffraction peaks due to WC and Co can also be seen to exist concurrently. The diffraction peaks measured mainly correspond to the surface components of the tool (as the XRD diffraction depth is about 10 μm). Combining the EPMA results, an outer layer rich in Ti and N is verified. They also show that the TiCN was formed by the nitridation of TiC. An outer layer rich in TiCN will improve the wear resistance of the tools. In addition, the intermediate layer which is rich in cobalt will improve the toughness of the tools and help prevent cracks extending to the substrate.

Figure 2:

XRD patterns of the gradient layer.

Gradient component distribution model

Based on the EPMA results, a simplified structural model for the component distribution function of the FGCC-T5 was established (Figure 3). In order to facilitate our calculations, the gradient layer was divided into multi-layers. The layers with the lowest and highest volume fractions of cobalt are referred to as the Co-poor and Co-rich layers, respectively. Transition layer 1 occurs between the Co-poor and Co-rich layers – transition layer 2 occurs between the Co-rich layer and substrate. The position of Co-rich layer ranges from the Co-poor layer to the substrate according to the thickness ratio between transition layer 1 and transition layer 2. From the surface to the substrate, the FGCC-T5 component distribution is characterized by a gradual decrease in TiCN, a gradual increase in WC, and a parabolic trend (opening downwards) in Co.

Figure 3:

Model of three-component distribution.

In order to better describe the volume fraction of each component, a three-component gradient distribution function was proposed based on a power-law function. In the function, the pores and sintering additives are not taken into account because they have relatively small proportions. The volume fractions of Co, WC and TiCN along the surface-to-substrate direction are given, respectively, by:

In these expressions, ξ (or k) denotes the ratio between the distance from an arbitrary position (or to the Co-rich layer) to the surface and the total thickness of the gradient layer. The quantities f_p, f_r, and f_s are the volume fractions of each component in the Co-poor layer, Co-rich layer, and substrate, respectively. Finally, n₁ and n₂ are distribution indices.

The volume fraction of a component varies with the sintering parameters employed, which can be described using the different distribution indices. The volume fraction of Co changes from the surface to substrate according to the different distribution indices, as shown in Figure 4. It was found that the distribution function used to describe the composition could properly describe the experimental results.

Figure 4:

Volume fraction of Co with different distribution indices.

Finite element modeling

The residual stress of the FGCC-T5 as it cooled from the sintering temperature to room temperature was analyzed using finite element analysis software (ANSYS). The value of the stress and its distribution within the gradient layer were studied. A cylindrical cutter model was used for finite element analysis (Figure 5) and so the origin of the coordinates was chosen to be at the geometrical center of the cylindrical tool section. Directions X and Z are taken to be along the radial and axial directions, respectively. The gradient distribution of each component was calculated using the three-component function. The substrate and gradient layer thicknesses were assigned to d₁ and d₂ in the FEM, respectively. The thickness of the gradient layer of the FGCC-T5 was too small (relative to the thickness of the substrate), so that only part of the substrate was studied in the calculation model.

Figure 5:

Model of finite element analysis.

The analysis of the residual stress of the FGCC-T5 was simplified using the two-dimensional axial symmetry of the problem in view of the cylindrical symmetry of the cutter. A four-node thermal-stress coupling element was used in the FEM. Boolean algebra was used to handle the gradient layer to ideally bond the multi-layers, and these were combined with the substrate of the tool. Parts of the gradient layer where a drastic change in stress occurred were meshed more densely in order to increase accuracy.

The overall temperature field in the model was assumed to change consistently, and the nitriding–sintering and room temperatures were set to T₁=1400 °C and T₂=20 °C in the first instance, respectively. Studies by Bouchafa et al. [22, 23] reported that the effects of a temperature-dependent elastic modulus and thermal expansion coefficient on residual stress are small. Thus, such effects were not taken into account in the present work.

According to our EPMA results, the ratio of the thicknesses of transition layer 1 to transition layer 2 was approximately 1:1, indicating that k=0.5 in eqs (1) and (2). The volume fractions of Co and WC in the Co-poor layer were 5 % and 7 %, respectively, and those in the Co-rich layer were 35 % and 12 %, respectively. We set n₁=n₂=1 to give linear relationships between the volume fractions and the distance from the surface to an arbitrary position in the first analysis. Residual stress nephograms of the FGCC-T5 are shown in Figure 6.

Figure 6:

The residual stress nephograms of FGCC-T5 (a-sectional view, b- cross-sectional view).

The distance-dependent residual stress distributions corresponding to different sintering temperatures are shown in Figures 7 and 8. It can be seen from Figure 7 that the highest residual compressive stress is located in the Co-poor layer. Then, this gradually changes to residual tensile stress which peaks in the Co-rich layer. Afterwards, the residual tensile stress gradually falls and finally approaches zero in the substrate. The maximum residual compressive and tensile stresses in the gradient layer simultaneously increase with increasing sintering temperature. The change in the compressive stress in the Co-poor layer is shown in Figure 8. The compressive stress rapidly increases at first and then changes more slowly with increasing distance from the knifepoint. It can be seen that the lowest compressive stress occurs at the knifepoint due to stress concentration. This thereby became the weakest area of the tool during the cutting process. The compressive stress of the knifepoint increased only slightly with an increase in sintering temperature. At the same time, the location of the region of maximum compressive stress occurred further from the knifepoint in a smaller range.

Figure 7:

The effect of sintering temperature on residual stress in gradient direction.

Figure 8:

The effect of sintering temperature on residual surface stress.

Feasibility of the finite element method

The residual stress in the FGCC-T5 surface was detected using XRD, which is based on Bragg’s law [24]. When X-rays of wavelength λ are irradiated onto a sample, the relationship between the spacing of the crystal planes and inclination angle can be obtained [25]. The residual stress can be calculated using Bruker Leptos software. Figure 9 shows a comparison of the experimental and simulated values of the maximum residual compressive stress. It can be seen that the experimental compressive stress increases from 498 to 581 MPa as the fabrication temperature increases from 1380 to 1460 °C. From 1380 to 1400 °C, the simulated values are essentially consistent with the detected values – small differences (3–6 %) are observed, however, over the range 1400–1460 °C. These differences can be attributed to the intensified nitridation that occurs at the higher fabrication temperatures, which leads to greater Co enrichment in the Co-rich layer and more TiCN appearing in the Co-poor layer.

Figure 9:

The maximum compression stress of FGCC-T5 by different sintering temperatures.

Effect of gradient distribution index

The beneficial effect of residual stress on cutting performance can be greatly improved by altering the gradient distribution by controlling the parameters involved in the sintering process. The effect of changing the gradient distribution indices on the residual stress should therefore be explored. As shown in Figure 4, when the distribution index is 1, the component volume fraction changes linearly according to the factor ξ. When the distribution index is smaller (or bigger) than 1, the component volume fraction changes more quickly the closer one is to the Co-rich layer (or Co-poor layer). The effects of varying indices n₁ and n₂ on the residual stress of samples sintered at 1400 °C are shown in Figure 10. It can be seen that for a fixed n₂ (or n₁) and increasing n₁ (or n₂), the maximum residual compressive stress of the gradient layer decreases (or increases). On the other hand, the maximum residual tensile stress increases (or decreases). When n₁ = 0.5 and n₂ = 2.5, the maximum residual compressive stress of the FGCC-T5 was 612 MPa, and the maximum residual tensile stress was 527 MPa. Research by Nomura [3] has shown that when the surface residual compressive stress of a tool reaches 500 MPa, one can be assured that no damage will occur to the tool even in the severest of cutting conditions. Our work indicates that smaller n₁ and bigger n₂ values contribute to the formation of higher residual compressive stress at the surface of the FGCC-T5, and this will thereby improve the tool’s cutting performance.

Figure 10:

The effect of different gradient distribution indices on residual stress.

Effect of geometric shape

The knifepoint is directly in contact with the work-piece during the cutting process. Any crack that is initiated in a weak area of the knifepoint will subsequently propagate to the substrate. The analysis above has shown that a right-angled knifepoint provides an asymmetrical residual stress on the surface of the FGCC-T5. Also, the strength of the knifepoint will be reduced if the compressive stress decreases. Figure 11 shows the distribution of residual stress corresponding to chamfered and rounded-edge knifepoints. Among the three different types of knifepoint (Figures 6(b) and 11), the residual stress of a rounded-edge knifepoint is the most homogeneous.

Figure 11:

Residual stress distribution of different geometric shape (a) chamfered, (b) rounded-edge.

The effect of having rounded cutting edges of different radii was also studied (Figure 12). With an increase in radius, the maximum residual surface compressive stress of the tool is reduced while the compressive stress at the knifepoint shows a parabolic trend (opening upwards) and the parabola’s peak occurs at a radius of 20 μm. The maximum residual surface compressive stress of the tool and residual compressive stress at the knifepoint changed modestly as the radius of the rounded cutting edge changed. Both values of compressive stress were close to each other when the radius reached 300 μm. Hence, weaknesses in the knifepoint can be avoided by using a knifepoint with a rounded design.

Figure 12:

The effect of different rounded cutting edge radius on residual stress.

Effect of substrate thickness

The residual stress of the FGCC-T5 in the gradient direction after cooling from a fabricating temperature of 1400 °C to room temperature is shown in Figure 13 for varying substrate thicknesses from 50 to 150 μm. The thickness of the gradient layer and radius of the rounded cutting edge were set 10 and 20 μm, respectively. As the thickness of the substrate increases, the maximum residual compressive stress of the gradient layer decreases. At the same time, the residual tensile stress in the Co-rich layer increases. The residual stress at the knifepoint decreases with increasing substrate thickness, but the differences between the values of the stress for the various thicknesses are small. As residual compressive stress plays an important role in strengthening the tool, the thickness of substrate should be appropriately reduced on the promise of better performance.

Figure 13:

The effect of substrate thickness on residual stress in gradient direction.

Effect of the thickness of the gradient layer

The gradient layer is in direct contact with the work-piece at the surface of the tool. Therefore, it is necessary to study the effect of the thickness of the gradient layer on the residual stress. Figure 14 shows the residual stress of the FGCC-T5 in the gradient direction as the thickness of the gradient layer is changed from 50 to 150 μm. The thickness of the substrate and radius of the rounded cutting edge were set to 75 and 20 μm, respectively. As can be seen from Figure 14(a), as the gradient layer thickness increases, the maximum residual compressive stress of the gradient layer increases from 531 to 712 MPa. However, the compressive stress at the knifepoint (which had a maximum value of 557 MPa when the thickness of the gradient layer was 10 μm), first increased and then decreased. The effect of different gradient layer thicknesses on the residual stress in the gradient direction is shown in Figure 14(b). As the gradient layer thickness increases, the distribution of the residual stress in the gradient direction changes little. On the other hand, the region of residual tensile stress increases. Lengauer et al. [26] found that a gradient tool with a 7 μm-thick grade zone produced the best performance in their turning tests. In our work, the compressive stress at the knifepoint exceeded 500 MPa when the gradient layer thickness was between 6 and 18 μm. According to Nomura’s criterion [3], therefore, in order to improve the tool’s resistance to breakage during the cutting process, the gradient layer thickness should be controlled to be in the range between 6 and 18 μm.

Figure 14:

The effect of gradient layer thickness on residual stress (a) compressive stress, (b) residual stress in the gradient direction.

Effect of position of the Co-rich layer

Residual stress is caused by the change in thermal expansion coefficient in the gradient direction. Here, the thermal expansion coefficient is mainly affected by the position of the Co-rich layer. The Co-rich layer lies between the Co-poor layer and substrate and its position varies by changing the thickness ratio of transition layers 1 and 2.

When the thickness ratio of transition layers 1 and 2 increases from 1:7 to 7:1, the maximum residual compressive stress decreases, and the maximum tensile stress in the Co-rich layer increases (Figure 15). For smaller thickness ratios, the Co-rich layer is closer to the surface of the FGCC-T5, and so the compressive stress in the Co-poor layer is bigger (because the change in the components occurring between the Co-rich and Co-poor layers is more rapid). Therefore, it is important to control the position of the Co-rich layer so that it is close to the tool’s surface and to reduce the layer thickness ratio, provided this does not affect the integrity of the tool’s surface gradient layer.

Figure 15:

The effect of the Co-rich layer position on residual stress.