Figure 2 shows the microstructure of the surface layer of C45 steel grinded with different depths. As shown in Fig. 2, three zones can be distinguished in each ground surface layer. As shown by XRD and Energy-dispersive X-ray spectroscopy (EDS) (Figs. 3 and 4), oxides are present in the first, near- surface zone. The second zone shows deformed grains of ferrite and pearlite and the third zone has an unchanged structure. In the second zone, the distances between the ferrite and cementite lamellae are distinctly smaller than in the third zone. As shown by the metallographic observation, increasing the depth of grinding causes an increase in the thickness of the first zone and a simultaneous decrease in the thickness of the second zone. In the first zone of the sample ground to a depth of 2 µm there is magnetite Fe3O4 while in the sample ground to a depth of 20 µm the oxides are a mixture of magnetite and hematite Fe2O3. This structure of the oxide layer indicates that increasing the grinding depth caused increasingly higher temperatures to which the surface heated during grinding. However, the temperature increase in no case exceeded the temperature of transformation of perlite to austenite, which for C45 steel is 728°C. The absence of wustite (FeO) also indicates that grinding to depth of 2 µm does not increase the temperature of the ground surface above 570°C. The most favorable microstructure in Zone I appears to occur after grinding to a depth of 2 µm because the oxide layer is the thinnest, does not peel, adheres well to the substrate, and is the most compact. To assess the size of the crystallites in the ferrite sub-grains in second zone, the W-H analysis of the XRD patterns was performed. As the peaks of the ferrite and cementite overlapped, their deconvolution was performed before calculating the peak broadening. Figure 5 shows an example of a deconvolution analysis performed with the Gaussian function.
Figure 6 presents plots of Bcosθ vs. sinθ for raw ferrite and for ferrite grains after their grinding on different depths. The slope of the lines in Fig. 6 allows determining the strain (ε) of the crystal lattice and their intersection with the ordinate axis to determine the size of the crystallites (L). Table 1 summarizes the information obtained based on the lines Bcosθ vs sinθ, and Fig. 7 shows the change in residual stresses and the size of crystallites depending on the grinding depth. As can be seen from Fig. 7, grinding increases both the size of the crystallites in the ferrite and causes the generation of residual compressive stresses in the ferrite grains.
|
4ε (%)
|
as·λ/L
|
L (nm)
|
E (GPa)
|
σR (MPa)
|
Table 1
Microstrain, crystallite size, and residual stress in raw ferrite and after grinding to different depth
raw ferrite
|
0.0056
|
0.0021
|
73
|
180
|
154
|
2 µm depth
|
0.0125
|
0.0025
|
154
|
180
|
333
|
8 µm depth
|
0.0051
|
0.0039
|
96
|
180
|
414
|
14 µm depth
|
0.0156
|
0.0019
|
81
|
180
|
702
|
20 µm depth
|
0.0103
|
0.0007
|
220
|
180
|
464
|
However, these changes are not monotonic. In the case of residual stresses, their constant increase is observed up to a grinding depth of 14 µm. Grinding to a depth of 20 µm causes a decrease in residual stresses, but they are still greater than after grinding to a depth of 2 and 8 µm. In turn, in the case of the size of the crystallites in zone II, grinding to a depth of 2 µm increases their size. Further increasing the grinding depth to 8 and 14 µm reduces their size, but they remain larger than for raw ferrite. On the other hand, grinding to a depth of 20 µm again increases the size of the crystallites. The size of the crystallites is the result of the deformation of the ferrite grains, with different degrees of crush, and the formation of a new dislocation structure, resulting in the formation of new crystallites.
To calculate the dislocations density in the ferrite, a nanoindentation test was performed in which the displacement of the indenter h was determined (see Fig. 8 and Table 2). It is worth noting that the load-displacement curves between 0 nm and about 50 nm follow a different pattern than for displacements greater than 50 nm. This is due to the difference in the residual stresses of type I and II. W-H analysis allowed calculating the stresses of II type, while the residual stresses of I type, covering the area of crystallites, may reach different values and even have different character. Based on Eq. (13), the GND density was calculated, and the SSD density was determined based on Eq. (14). The proportion of screw and edge dislocations in the dislocation structure of ferrite was then calculated. Figure 9 shows an example of an XRD pattern, for a workpiece before grinding, used in a MW-M analysis. To calculate the share of edge and screw dislocations, graphs (∆K-α)2/K2 as a function of H2 were prepared (see Eqs. 5 and 6). The parameter q, which describes the share of edge and screw dislocations, was determined as the reciprocal of the value of the intersection of the straight lines with the abscissa, as shown in Fig. 10. Figure 11 shows the percentage change in the share of screw and edge dislocations caused by grinding ferrite to a different depth. As can be seen in Fig. 11, grinding increases the share of edge dislocations. In the annealed ferrite, 90% of screw dislocations and 10% of edge dislocations occur. Grinding causes an inversion in this proportion. The highest share of edge dislocations occurs after grinding to a depth of 20 µm (90.5%) and the lowest after grinding to a depth of 14 µm (68.6%).
|
|
h
(nm)
|
ρGND x 1014
(m− 2)
|
HISE
(GPa)
|
ρSSD x1015
(m− 2)
|
H0
(GPa)
|
Table 2
GND and SSD densities calculated on the base of nanoindentation test and the hardness of ferrite after grinding to various depths
raw ferrite
|
460*
|
4.6
|
2.01
|
0.062
|
0.850601
|
2 µm depth
|
260
|
8.22
|
11.4
|
11.61
|
11.02416
|
8 µm depth
|
365
|
5.74
|
6.7
|
3.72
|
6.235907
|
14 µm depth
|
340
|
5.52
|
6.3
|
3.25
|
5.765856
|
20 µm depth
|
324
|
6.55
|
7.4
|
4.58
|
6.927975
|
* For the load 10 mN |
Figure 11 also shows the changes in the dislocations density in the ferrite caused by grinding it with different depths. As shown in Fig. 11, grinding caused a strong increase in SSD density in ferrite, with the highest increase in dislocations density observed for grinding to a depth of 2 µm. SSD density in ferrite after grinding to a depth of 2 µm is over 186 times higher than in raw ferrite. This in turn implies a large increase in hardness after grinding, as shown in Table 2. Further increasing the grinding depth to 14 µm causes a decrease in the dislocations density in the ferrite grains, and grinding to a depth of 20 µm causes a slight increase. However, each depth of grinding generates in ferrite at least a 54-fold increase in dislocations density compared to raw ferrite.
The dislocations mobility in ferrite grains, after grinding to different depths, was determined based on the course of indenter displacement changes during the dwell time. Figure 12 shows the change in relative strain (indenter displacement) as a function of time. The period during which the strain rate is constant has been approximated by a linear function, as shown in Fig. 12. The differentiation of the linear function over time allowed to determine the strain rate of the ferrite during its flow (see Fig. 13). As can be seen from Fig. 13, raw ferrite grains have the lowest relative strain rate. Grinding causes an increase in the strain rate, while the highest strain rate was recorded for ferrite grains after grinding to a depth of 2 µm. Figure 13 also shows the mobility of the dislocations in ferrite grains, calculated on the base of Eq. (16). As can be seen in Fig. 14, the mobility of dislocations in ferrite grains after grinding to a depth of 2 µm is two orders of magnitude lower than in annealed ferrite. According to the theory of Taylor and Orowan, the material strengthening will be greater, the higher the dislocation density (Taylor) and the lower their mobility (Orowan). Hence, the hardening can be characterized by the hardening factor expressed as the quotient of these two quantities. Figure 14 shows the change in the strain hardening factor of ferrite after grinding it to a different depth. For comparison, the same figure also shows the change in ferrite hardness after grinding with different depths. As shown in Fig. 14, the course of changes in hardness and the strain hardening factor is similar.
3.1. Mechanism of strain hardening of ferrite
During grinding, the flow stress depends on the temperature and the strain rate applied. It can be assumed that the rate of ferrite strain while grinding it to a different depth, was constant. Furthermore, the deformation behavior of ferrite is also a function of the crystal orientation following Schmid’s law [18]. Since the microstructure of the sample is changed during the grinding as a result of dislocations production and annihilation, the deformation behavior depends on the degree of the sample deformation i.e. grinding depth. In this work, only the influence of grinding depth will be considered. In crystalline materials, plastic deformation usually occurs by a glide on slip planes along with certain slip directions. Twinning is another mechanism of plastic deformation, however, in BCC metals, this mechanism occurs only at reduced temperatures or at high strain rates.
Since there are no such circumstances during grinding, this deformation mechanism will also not be considered. Yet another mechanism for the movement of dislocations is their climbing. Because climb requires diffusion, it occurs only when the temperature is higher than 0.3 Tm, where Tm is the melting point or where stresses are very high. Therefore except for special cases, the glide is the dominant mechanism of motion.
In BCC metals, the activation of edge dislocation slip begins in the slip system with the lowest value of the critical tangential stress. Starting a slip in a given system causes an increase in the dislocation density, which reduces the mobility of dislocations and blocks their further slip. Further gliding of edge dislocations is possible in planes with lower atomic density, provided that the load is increased to exceed the critical stresses for other gliding systems. In BCC metals, there are 48 of such slip systems: 12 {110} <111 > systems; 12 systems {211} <111>; and 24 {321} <111 > systems. Unlike edge dislocations, screw dislocations do not have slip systems and can move along any plane and in any direction. During a slide, dislocations encounter two types of obstacles on their way, i.e. barriers with short-range interactions and barriers with long-range interactions. Thermal activation of dislocation makes it possible to overcome the short-range interactions, while the long-range interaction cannot be overcome by thermal activation. The flow stresses are therefore the sum of two components: the thermal component ε ̇ and the athermal component εi which can be written ε = ε ̇+ εi. The thermal component is described by the Orowan equation (see Eq. 16) and the athermal component εi is described by Taylor theory according to which the contribution of interactions between parallel dislocations to the flow stress can be written as:
$${\epsilon }_{i}=\alpha \bullet G\bullet b\sqrt{{\rho }_{SSD}}$$
17
Two dislocations can pass with each other when the stress εi exceeds the value of interaction between them.
Equations (16) and (17) show that an increase in dislocation density may contribute to either weakening of the ferrite (Orowan's theory) or its strengthening (Taylor's theory). In the case of high mobility of dislocation, ferrite weakening will occur, and when their mobility is low, the strengthening will increase. In BCC metals, deformation is strongly temperature-dependent and controlled by the low mobility of screw dislocations, whose velocity is much lower than that of edge dislocations [18], [11], [19]. At 0 K, dislocation can be completely straight, but at higher temperatures, due to temperature fluctuations, dislocation contains kinks. These kinks mean that the dislocation does not overcome the Peierl’s barrier at the same time along its entire line. Two kinks of an opposite sign may appear on the dislocation line, creating short dislocation segments with the kink height h (see Fig. 15). Such kinks may be subject to diffusion drift under the influence of slight stresses, which contributes to the sliding motion of the entire dislocation. The velocity of movement of a kink in a screw dislocation can be written:
where Dk is the diffusion coefficient of the kinks, k is the Boltzman constant and T is temperature.
The kinks concentration ck is:
In Eq. (19), d denotes the shortest repetition distance along the dislocation line, while ΔFk is the kink formation energy. The velocity of all positive and negative kinks drifting in opposite directions gives the resultant velocity of the entire screw dislocation which can be written as follows:
At low temperatures, below the critical temperature TK being 350 K for α-Fe (TK is of 0.2 melting temperature Tm), the movement of screw dislocations occurs by kink pair formation and propagation of kinks in opposite direction, which practically immobilizes the dislocation segment towards the kink (see Fig. 15) [19]. Furthermore, atomistic simulations have shown that in BCC metals the core of a screw dislocation splits into several fractional dislocations [20]. These splits increase Peierl’s barrier which consequently strongly suppresses the movement of screw dislocations. Above temperature TK the yield strength becomes independent of temperature and screw and edge dislocations have equal mobilities [21]. At these temperatures, kink motion occurs rapidly in comparison to kink-pair nucleation [22]. As can be seen in Fig. 13, the lowest dislocation mobility occurs after grinding to a depth of 2 µm. Increasing the grinding depth increases the mobility of dislocations in the range from 216 to 284%. Therefore, it can be assumed that the temperature of the surface layer during grinding to a depth of 2 µm did not exceed TK. This observation is also supported by the fact that no wustite was found in Zone I for this grinding depth.
On the other hand, as shown in Fig. 11, the largest share of screw dislocations in the dislocation structure of ferrite occurs after grinding to a depth of 14 µm. At the same time, for this grinding depth, ferrite shows the greatest mobility of dislocations and the lowest work hardening factor (see Figs. 13 and 14). From this, it can be concluded that when grinding to a depth of 14 µm, the temperature reached by surface layer exceeded TK, and mobility of screw and edge dislocations was the same. Additionally, in BCC metals it has been also observed that the mobility of screw dislocations can be enhanced in the vicinity of the free surface sample [19]. Matsui and Kimura [23] developed a model of surface-enhanced screw mobility due to bent screw dislocations. In their model, kinks are formed on the screw dislocations near the surface, move inside the workpiece, and interact and form dislocation sources. Because grinding is a surface treatment, the deformation mechanism associated with the movement of screw dislocations can play a significant role.
Additionally, as shown by diffractogram analysis, grinding increases the residual compressive stress which leads to a decrease in the distance between dislocations. Reducing the distance between dislocations results in the formation of pile-ups between dislocations and defects or grains bounduary, which implies dislocation short-circuiting and consequently a decrease in their mobility [24]. W-H analysis also showed that grinding increases the crystallite size in ferrite grains. According to the Hall-Petch relationship, as well as the pile ups model, grain boundaries are a barrier to dislocation slip transfer between adjacent grains, which is due to both elastic interaction of dislocations with grain boundaries and absorption of dislocations by grain boundaries. These phenomena explain the increase in yield strength of metals with decreasing grain size. However, grinding does not change the size of the ferrite grain but only its shape and the size of the crystallites that make up the grain. Therefore, no correlation was found between crystallite size and the degree of strengthening of the grinded surface layer.
During the deformation of ferrite due to its grinding, the dislocation density increases (see Fig. 11), giving rise to an increase in the athermal component of the flow stress. The increase of the flow stress gives strain-hardening, as can be seen in Fig. 14. Since grinding causes the ferrite to heat simultaneously, thermal diffusional rearrangement of crystal defects occurs in the ferrite. It seems obvious that grinding to a depth of 20 µm introduces the most heat into the material. This caused some residual stress present in a crystal was released as can be seen in Fig. 7. Additionally, a rearrangement may also result in dislocation migration and annihilation leading to energetically favorable dislocation arrays like subgrain boundaries, with the subsequent growth of the subgrains. As can be seen from Fig. 7, grinding to a depth of 20 µm produces the largest crystallites in the ferrite grains, which proves the ongoing polygonization process [25]. Figure 2d shows the ferrite subgrains resulting from grinding to a depth of 20 µm. Apart from the poligonization, the decrease of the work hardening (Fig. 14) is also associated with the mutual annihilation of dislocations, as can be seen in Fig. 11.