Impacts of Element Diffusion on Bond Breakage of Cemented Carbide Cutter

2.25Cr1Mo0.25V is an H₂S-resistant steel widely used in such fields as petroleum and chemical industries, thanks to its excellent high-temperature physical and chemical properties. During the machining of 2.25Cr1Mo0.25V heavy forging parts, the carbide cutting tools are prone to breakage. There are many causes of such a failure, among which the bond breakage is particularly remarkable. To put it more visually, the continuous cutting takes away the material from the tool rake face, resulting in tool failure.

In fact, bond breakage is commonplace in many popular iron-carbon alloys, nickel-based alloys and titanium alloys. After cutting stainless steel and other materials with cemented carbide tools, some scholars pointed out that the element diffusion of congeners will bond the chips with the rake face and the loss of tungsten will reduce the hardness of tool material, leading to bond breakage [1-4]; In addition, they also conducted a series of diffusion experiments, established the theoretical model of element diffusion in the tool, and determine the damage threshold. Through the cutting of 508III steel with cemented carbide tools, Cheng et al. [5] identified the bonding layer formed on the tool-chip interface, under the action of force-thermal coupling field, as the fundamental cause of bond breakage, and concluded that bond breakage of cemented carbide tools is a shared problem in the cutting of various chip materials. Eiji [6] explored the role of pressure in the adhesion phenomenon, suggesting that the large normal pressure can bring two solid materials closer to the distance of atomic scale and thus bind the two interfaces. Focusing on the high-speed machining of Ti-6Al-4V, Zhang et al. [7] attributed the element diffusion to the high temperature and concentration gradient on the tool-chip interface, and advised to extend the tool life through the control over the diffusion of chip elements to the tool direction. Targeting low-temperature nitriding iron-based alloys, Tong et al. [8] argued that the grain boundary of the material serves as a fast diffusion channel for atoms, and the element diffusion may produce compounds of varied compositions or phases under certain conditions. Shenouda et al. [9] found that the Ni₂Si coating and the Si (100) substrate diffused through the crystal boundary at low temperature (453~473 K), forming a NiSi phase. This finding reveals that element diffusion can create new compounds or phases, which differ from the original compounds or phases in physical and chemical properties. Christensen et al. [10] carried out first-principles study on the bonding strength of cemented carbide materials, and drew the following conclusion: WC-Co enjoys a better bonding strength than TiC-Co because of its edge in bonding energy, as high bonding energy implies strong load transfer ability, high hardness and good strength. This conclusion sheds new light on the microscopic research of bond breakage [11].

Despite the fruitful results, the previous studies on bond breakage, bonding energy and element diffusion of tool-chip surface only concentrate on the macroscopic analysis of dynamic cutting under the continuum hypothesis, failing to examine the cutting process from the microscopic perspective. As a matter of fact, micro mechanism is involved in the dynamic process during the diffusion and property change of tool materials after diffusion. On the microscale, the atoms and molecules are discrete and their diffusion cannot be fully explained by existing macroscopic theories. This calls for new theories that can accurately describe the element diffusion and bonding energy on the microscale [12] and associate the descriptions with the dynamic cutting process.

In light of element diffusion, this paper sets up a rational microscale model of cemented carbide and 2.25Cr1Mo0.25V based on the specific working conditions in the cutting process. Inspired by molecular dynamics (MD) theory, the deterioration layer model of cemented carbide was obtained through MD simulation; the bonding energy and interaction parameters between WC and Co, Fe, Cr, Mo, V and other elements were calculated, and the influence of element diffusion on bond breakage was discussed under specific working conditions from the microscopic perspective.

3.1 Discussion of diffusion features

Wang et al. [20] suggested that diffusion is the only transport method in solid materials. When two chemically intimate solids (e.g. iron and carbon) are put together and heated to a certain temperature, the atoms of these solids will mutually diffuse to form a new alloy. Once solid diffusion occurs, the atoms in the solids will move in a direction that reduces the concentration difference, that is, down the energy gradient [21]. This is because the atoms, under the action of various factors, tend to leave the initial equilibrium positions in seek of new equilibrium positions.

The diffusion degree must be quantified to accurately measure the effect of temperature on diffusion. Thus, the diffusion coefficient (D) was introduced, which can describe how fast the solute atoms diffuse in the solvent. Then, the mean square dislocation (MSD) of each atom in the system was computed by the Forcite module. Taking the MSD as an intermediate variable, the D of each atom can be derived by the Einstein method [22].

The MSD can be calculated as:

$\operatorname{MSD}(t)=\frac{1}{n} \sum_{i=1}^{n}\left\langle\left|r_{i}(t)-r_{i}(o)\right|^{2}\right\rangle$        (1)

where, r_i(t) is the position of the atom i at time t; n is the number of atoms in the system.

The D can be expressed as:

$D=\frac{1}{6} \frac{\partial}{\partial t}\left[\frac{1}{n} \sum_{i=1}^{n}\left\langle\left|r_{i}(t)-r_{i}(o)\right|^{2}\right\rangle\right]$        (2)

The expression is usually simplified as:

$D=\frac{1}{6}(M S D)$         (3)

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Figure 12. MSD-time curve of main elements

The atom positions at each time point were fitted on Matlab, yielding the MSD-time curve of the main elements in cemented carbide and 2.25Cr1Mo0.25V (Figure 12). To ensure the accuracy of the D, the non-Einstein diffusion region was removed during the fitting of the MSD curve.

Table 2. The D value of each main element (Ų/ps)

The fitted MSD value of each element was substituted into equation (3) to obtain the D value of each main element at the corresponding temperature. The specific values are listed in Table 2.

As shown in Table 2, the D value is positively correlated with the diffusion ability of an atom. Under each temperature, the 2.25Cr1Mo0.25V atoms moving towards the cemented carbide had greater D values than the cemented carbide atoms moving towards the 2.25Cr1Mo0.25V. This means each 2.25Cr1Mo0.25V atom boasts greater diffusion ability than its counterpart in cemented carbide. From Figure 12 and Table 2, it can be seen that the diffusion degree increased with the temperature, and peaked at 1,286 K. The trend is consistent with the Fick’s law of diffusion.

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Figure 13. Tool-chip interface

Eiji explained that the role of pressure in the diffusion process is to press the two materials into the range of atomic range [6]. As shown in Figure 13, the interface between cemented carbide and 2.25Cr1Mo0.25V is rough during the machining. On the microscale, the protrusions and gullies continued to spread on the surfaces of the two metals. In general conditions, it is difficult to make atoms enter the range of atomic force on either side of the interface. In other words, the diffusion conditions are hard to achieved under normal conditions. During the cutting process, however, the cutting force is sufficiently large, such that the two metal surfaces are in close contact. In this case, many atoms can enter the range of atomic force. From the microscopic angle, the high pressure of the cutting process only ensures the close contact of the two atomic layers. In the simulation, the distance between the two materials was on the angstrom level, which is well within the range of atomic force. Thus, pressure is not an important influencing factor of solid diffusion, and is neglected in our discussion.

As mentioned above, temperature and concentration gradients are two leading factors affecting diffusion. In our research, the MD simulation lasted only 50 ps and the opposite atom concentration was zero in the microscale models of cemented carbide and 2.25Cr1Mo0.25V. Thus, there existed a concentration gradient to initiate the diffusion. As a result, the effect of temperature on diffusion is discussed in details below.

The expression of the D can be rewritten as [23]:

$D=\alpha^{2} P \Gamma$       (4)

where, α² is the square of atomic diffusion distance; P is the probability of atomic diffusion; Γ is the frequency of atomic diffusion.

Unlike those in liquids and gases, the diffusion of elements in solids needs to overcome the huge bonding energy, i.e. the energy barrier. That is why the solid diffusion is very slow under normal conditions. Fortunately, the high temperature of the cutting process creates a favorable condition for solid element diffusion. In the cutting environment, the atomic diffusion distance hinges on the temperature and the microscopic mechanism of atomic diffusion.

On the effect of temperature, the total energy of the system increases with the temperature, making it easier to reach the energy to activate the diffusion of each element. Besides, the vacancy concentration is high and the thermal motion of atoms is vigorous at high temperatures. In this case, an atom can easily enter the range of interaction between other atoms along the crystal gap and vacancies. The diffusion behavior of the atom is thus promoted. The diffusion speed is slow if the temperature is below the atomic recrystallization temperature, and much faster if otherwise. For industrial pure metal, the recrystallization temperature is 35 %~45 % of its melting point. For alloy, recrystallization temperature is 40 %~90 % of its melting point. As the main component of cemented carbide, the WC starts to melt under 3,143 K. Thus, the recrystallization temperature of WC falls in 1,421~2,856 K. The temperature measured in the cutting experiment was 800~1,286 K, failing to reach the recrystallization temperature of WC. However, the measured temperature fell in the recrystallization temperature range of 2.25Cr1mo0.25V. As a result, the 2.25Cr1Mo0.25V atom diffused much faster than W atoms and Co atoms in the cemented carbide.

The microscopic mechanism of atomic diffusion directly bears on the energy to activate atomic diffusion. The atoms in vacancies are the easiest to diffuse because they have the highest potential energy. Vacancy diffusion is the most common diffusion mechanism, followed by interstitial diffusion and quasi-interstitial diffusion. By contrast, the atoms at the lattice position have the lowest potential energy. Thus, a huge amount of energy is needed to activate translocation diffusion. As mentioned above, a vacancy concentration of 0.2 was set for the cemented carbide diffusion model. Hence, the atomic diffusion of 2.25Cr1Mo0.25V mainly followed the vacancy diffusion mechanism. With the growth of temperature, the atoms were more likely to surpass the energy barrier, and other diffusion mechanisms gradually emerged. As the cutting progressed, numerous Fe, Cr, Mo and V atoms entered the diffusion deterioration layer, and a large amount of W atoms were lost, leading to changes of tool material composition. Through this process, the tool material was deteriorated and its mechanical strength declined gradually. The bond breakage occurred when the strength dropped to a certain threshold (Figure 14).

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Figure 14. Diffusion deterioration layer

3.2 Discussion of Blends features

The mixing and separation between binary systems in the Blends module can be calculated by the Flory-Higgins model [19]:

$\frac{\Delta G}{R T}=\frac{\phi_{b}}{n_{b}} \ln \phi_{b}+\frac{\phi_{s}}{n_{s}} \ln \phi_{z}+\chi \phi_{b} \phi_{z}$       (5)

where, △G is the mixture free energy per mole of microscopic particles; Φ_i is the volume fraction of the i-th component; n_iis the miscibility of the i-th component; χ(chi) is the interaction parameter. The first two terms represent the mixing entropy and the last term reflects the interaction free energy.

In the diffusion deterioration layer of cemented carbide, WC and such elemental metals as Co, Fe and Cr appear as a solid solution. It is necessary to evaluate the solid solubility of each element before determining the structural stability of the diffusion deterioration layer. Here, the solid solubility is explored using the interaction parameter χ below:

$\chi=\frac{E_{\operatorname{mix}}}{R T}$      (6)

where, E_mix is the mixing energy; R is the gas constant; T is the absolute temperature. If χ is negative or small, the two particles have good miscibility at the current temperature. Otherwise, the two particles tend to separate. If the χ is sufficient large, the free energy of the mixture will overcome the mixed entropy and split the mixture into two separate phases.

As shown in Figure 15 below, when the cutting temperature was on the rise, the χ values of all atomic groups exhibited a downward trend and eventually tended to zero. This trend shows that the solid solubility of WC (base) and Co, Cr, Fe, Mo and V (screen) increases with the cutting temperature. Within the range of the cutting temperature, WC can forma stable solid solution alloy with proper concentrations of screen elements. With the decline in the cutting temperature, the solubility of WC and all screen elements were reduced, and the particles were more likely to be separated, adding to the difficulty in the formation of alloy.

It can be seen from Figure 15(b) and Table 3, under the normal temperature of 298K, the χ values of WC and Mo were lower than those of other elements, and decreased with the increase of temperature. In terms of solid solubility, the WC has similar solubilities in Cr, V and Co, and an extremely high solubility in Mo. Thus, WC and Co can easily form a stable solid solution. Considering the low presence of Mo in the 2.25Cr1Mo0.25V alloy, the diffusion of Mo, Cr and V elements was not viewed as the main cause of bond breakage. This simulation result is consistent with the findings in previous research: when the cemented carbide is sintered, the WC is less soluble in Fe than in Co, and the mushy zone (the range of C content) is narrow in the WC-Fe system, making it difficult to obtain a solid solution two-phase alloy of WC-Fe [24].

Comparing Figure 15(c) and Table 3, it is observed that the χ curve of WC-Co was only slightly higher than that of WC-Fe. Co and Fe are congeners. With the rising temperature, the WC is more and more soluble in Co than in Fe. Thus, it can be concluded that WC-Fe and WC-Co have similar ranges of bond breakage temperature, and the small difference is negatively correlated with temperature. Under element diffusion, the WC is partially combined with Fe into WC-Fe alloy. However, this alloy may produce η phase (Fe_xW_xC_x) due to the carbon deficiency during metallurgy. The η phase exists as a malignant defect in the structure of cemented carbide, and seriously undermines the physical and chemical properties of the alloy. The η phase is often suppressed by carbon black, which is not available in the random diffusion process of our simulation. Thus, the physical and chemical properties of the tool material continued to worsen in the cutting process. When the deterioration reached a certain threshold, the tool material broke down and was carried away from the tool surface with the chips.

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Figure 15. Interaction parameter χ

Table 3. Results of blends simulation

3.3 Discussion of bonding energy

The strength of the bonding ability between crystals can be described as the bonding energy, which is defined as the difference between the total energy of a crystal and that of its N free atom states when the crystal is in a steady state. The bonding energy can also be understood as the energy released when a free atom (ion or molecule) is combined into a crystal, or the energy required to split a free atom off a crystal. The bonding energy between the atomic group of WC and that of any screen element helps to judge the fracture of cemented carbide under the cutting force and cutting vibration.

Bonding energy can quantify the strength of interface bonding. The higher the bonding energy, the more energy is needed to destroy the interface. The strength of interface bonding can be expressed as:

$W=\left(E_{\text {interface }}-E_{\mathrm{a}}-E_{\mathrm{b}}\right) / A$        (7)

where, E_interface is the total energy of the interface; E_a is the energy of surface a; E_b is the energy of surface b; A is the square of interface.

The directions of the bonding energy were calculated by the MS software. Note that the negative sign means the bonding between the two particles releases energy, and the absolute value stands for the level of bonding energy.

Table 3 shows that WC and Mo had stronger bonding energy than the combination between WC and any other screen element. As stated above, the low content of Mo in the 2.25Cr1Mo0.25V is not an important cause. The bonding energy of WC-Co was slightly higher than that of WC-Fe. From the simulation results and χ value analysis, it is known that Fe is the key element in the diffusion of cemented carbide. With the lowest bonding energy at normal temperature, the WC-Fe interface was the weakest and the most likely to break down in our research.

Under the same concentration, the bonding strength of WC-Co alloy is 1.5~2 times that of WC-Fe alloy. During the smelting of cemented carbide, a small amount of Cu is often added to enhance the performance of WC-Fe-based alloy. Even so, the bonding strength of WC-Fe-based alloys is only 60 %~70 % of that of WC-Co alloys. The diffusion deterioration layer of cemented carbide had even weaker mechanical properties and bonding ability than WC-Fe bonding, as multiple elements combined and multiple phases formed under the random diffusion in the cutting process. As a result, the material on the rake face of the cutting tool witnessed a decline in mechanical properties.

As shown in Figure 16, an unstable intermetallic compound was dissolved and formed in the range of the cutting temperature. If the cutting is interrupted, the changing temperature will break WC-Fe and other elemental bonding, creating local microcracks in the unstable solid solutions. The microcracks will develop between the tool materials, and eventually break the bond between WC and other element in the deterioration layer. The broken parts will leave the rake face of the cutting tool as chips.

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Figure 16. Diffusion deterioration layer of the bonding interface