3.1. Evaluation of the Nil-Strength Temperature and Zero Strength Temperature
The experimentally determined nil-strength temperature corresponded to the highest value of the registered temperature at the moment of loss of material consistency (due to the combination of the action of the tensile force of 80 N and melting of grain boundaries), which was accompanied by the steep decline of the measured temperature (examples of data records are specified in
Figure 2). In the case of the steel A (with the lowest content of carbon), during its heating, in spite of the very small action of the tensile force, the testing rods were prolonged, and the resultant nil-strength temperatures were, in this case, burdened by a relatively significant dispersion. During the testing of other investigated steels, the testing rod was not prolonged, but after achieving the nil-strength temperature, brittle fracture occurred.
The average values of the measured nil-strength temperatures,
NST (°C), of the investigated steels and the corresponding standard deviations are presented in
Table 2.
Table 2 also includes the zero strength temperatures,
ZST (°C), which were determined in the IDS software via calculations considering the solidification of the investigated carbon steels under equilibrium conditions. The calculated zero strength temperatures of the steels A and B were obtained with the help of the IDS software, even though their chemical compositions—content of carbon in steel A and the content of sulfur and phosphorus in the steel B—were out of the range of the calculation module of this software (from 0.01 to 1.2 wt.% C, to 0.05 wt.% P and S). The zero strength temperatures of the steels A and B determined by the IDS software can, therefore, be burdened by a certain computing error. In
Table 2, there is also specified a difference between the measured nil-strength temperature and calculated zero strength temperature, Δ
T (°C), of the investigated steels:
For all the steels we investigated, the zero strength temperatures calculated by using the IDS software were higher than the experimentally determined nil-strength temperatures. The difference between the
ZST and
NST fluctuated from 43 to 85 °C depending on the carbon content of the investigated steels. Based on these results, it appears that the nil-strength temperature determined while heating is not the same as the zero strength temperature determined during solidification of the investigated steels. This fact can be explained by different definitions of nil-strength temperature during the heating of the material [
12,
17,
37] and definition of zero strength temperature during the solidification of the material [
14,
15,
16]. In both cases, however, the nil-strength and zero strength temperatures decline with the increasing carbon content in the investigated steels, as shown in
Figure 3.
The dependencies of the measured nil-strength temperature and calculated zero strength temperature on the carbon content of the investigated steels (except the free-cutting steel B) can be described with the simple linear equations:
High values of the determination coefficients—(R2) 0.9735 and 0.9921 for the Equations (6) and (7), respectively—prove the relatively good accuracy. With the help of Equations (6) and (7), it is thus possible to simply predicate the nil-strength temperature during heating and also zero strength temperature during solidification of the carbon non-alloy steels in the range from 0.008 to 0.885 wt.% C.
Using both methods, it was determined that a much higher content of sulfur in the steel B caused a significant decline of the measured nil-strength temperature and calculated zero strength temperature. This finding was surprising, especially in the case of determination of zero strength temperature when using the IDS software. The calculation module range of this software is in the case of sulfur lower by an order of magnitude than the content of sulfur in the steel B. In the case of the plastometric test, the decrease of the nil-strength temperature of the steel B can be influenced by so-called brittleness at glowing heat; this is when steel with a high content of sulfur expresses itself at temperatures above 1200 °C. The reason is the transition of sulfur to low-melting sulfides of FeS or FeS–MnS, which exude on the grain boundaries, and their melting point fluctuates around 1200 °C [
38]. This proposition, however, was not verified because plastometrically tested specimens from this steel were not subjected to the SEM analysis.
Based on the results, it was possible to determine the dependence of the experimentally measured nil-strength temperatures on the calculated zero strength temperatures of the investigated steels (as can be seen in
Figure 4). This relationship can be described by the simple equation:
3.3. The Dependence of the Nil-Strength Temperature and the Zero Strength Temperature on the Solidus Temperature of Investigated Steels
A regression analysis of the relation of the nil-strength and zero strength temperatures with the solidus temperature of the investigated carbon steels has been consequently performed. For these purposes, the solidus temperatures calculated only by using Equations (2) and (3) have been used, because by using these two equations, similar results were achieved. The paper [
1] experimentally verified the possibility of the use of Equation (3) for determining the solidus temperatures of steels with a wide range of chemical compositions. The solidus temperatures determined according to the Equations (1) and (4) were excluded from the consequential analyses because they showed the aforementioned inaccuracies already. The solidus temperatures determined with the use of the IDS software were also excluded from these analyses because the calculating module of this software does not use simple parametric equations (expressing an influence of the chemical composition) for the calculation of a solidus temperature, but uses thermodynamic equations, an equality of the chemical potentials, the inter-phase weight of the balance and Fick’s second law.
The differences between the experimentally determined nil-strength temperature, calculated zero strength temperature and the solidus temperature (Equations (2) and (3)) of the investigated steels are presented in
Table 4. As it is also clear from
Table 4, the measured nil-strength temperatures are lower than the solidus temperatures, while calculated zero strength temperatures are almost always higher than the solidus temperatures of the investigated steels. The nil-strength temperature determined experimentally during steel heating corresponds to the moment of grain boundary melting, and should thus be lower than the solidus temperature, which corresponds to the statement in [
5,
6]. On the contrary, the zero strength temperature determined by calculation in the IDS software, in the case of the low-alloy steels A, C and D, was almost equal with the solidus temperature of the investigated steels. In the case of steels with higher contents of carbon (i.e., from 0.384 wt.%), the difference between the zero strength temperature determined by calculation in the IDS software and the solidus temperature was increasing. It supports the statement in [
14,
15] that the zero strength temperature determined during solidification of steel should be higher than the solidus temperature because at the moment of its achieving, 20–35% of material should remain in the molten state.
Because of a lower standard deviation in the relation between the measured nil-strength temperatures or calculated zero strength temperatures and solidus temperatures determined according to Equation (2) (as can be seen in
Table 4), only this equation was applied for the consequential analysis. Using regression analysis, a linear dependence of the measured nil-strength temperature and calculated zero strength temperature on the solidus temperature of the investigated steels determined according to Equation (2) was determined (as can be seen in
Figure 6). These linear dependencies can be described by simple equations that enable easy prediction of the nil-strength temperature and zero strength temperature of non-alloy carbon steels with carbon contents from 0.008 to 0.885 wt.%, including the free-cutting steel B based on knowing the solidus temperature (calculated using Equation (2)):
High accuracy of the above-mentioned equations is documented by the high values of the determination coefficients,
R2 = 0.9738 in the case of the
NST and
R2 = 0.9965 in the case of the
ZST. The main benefit of Equations (9) and (10) is an inclusion of a more significant influence of the chemical composition of steel through the calculation of the solidus temperature (see Equation (2)). Equations (9) and (10), in comparison to Equations (6) and (7), also react to the decline of the nil-strength and zero strength temperatures due to the increased content of sulfur in the free-cutting steel B (as can be seen in
Table 5 and
Table 6). The results obtained from Equations (9) and (10) in comparison with the results obtained from Equations (6) and (7) showed a lower standard deviation of the relative error of the backward calculation of the nil-strength and zero strength temperature and higher correlation coefficients (as can be seen in
Table 5 and
Table 6).
In the paper [
39], results of similarly focused experiments leading to the determination of the linear dependence between solidus temperature and zero strength temperature of unalloyed steels with 0.003–1.60 wt.% C were published. The difference for these results in comparison to Equations (9) and (10) is mainly due to the choice of the alloys tested, the fundamentally different methodology of the experiment and the method of determining the solidus temperature. The investigated steels contained a minimized content of other elements (e.g., no more than 0.49% Mn; 0.004% P and 0.004% S). This made it possible to determine the
TS values as equilibrium solidus temperature in Fe-C binary alloys. Alloys characterized in
Table 1 are the common carbon steels with up to 1.13% Mn, 0.055% P, 0.311% S (in the case of free-cutting steel) and 0.27% Cr. Their solidus temperatures were not determined experimentally, but by more complex and still more efficient parametric equations. The mathematical determination of
TS values subsequently enables, with high accuracy, a simple prediction of the
NST and
ZST values considering the chemical compositions of the investigated steels. Zero strength temperature was determined in [
39] on specimens which were in-situ melted, solidified and tensile tested at the specified temperature upon subsequent cooling. Hot ductility was determined by the reduction of area, not by elongation to rupture. In most cases, the
ZST values are determined virtually identically to the values of nil ductility temperature
NDT (°C) and embody the temperature at which dendritic solid phases are connected with each other and plastic deformation can start after a considerable progress of solidification (with approximately 10% of residual liquid). In contrast, the
NST value determined by the much simpler methodology described above is not associated with any partial or full melting of the specimen during heating. In addition, this
NST value is always higher than the
NDT value (according to the authors of the paper [
5,
6,
11] on average by 35 °C with a tolerance of ± 20 °C).
Support for these claims can be found in
Figure 7 which graphically compares the
ZST or
NST values determined by various authors. Only the indisputable
ZST values were located by digitizing the previously published graphs [
39,
40,
41,
42]. In this case,
TS value corresponds to the equilibrium solidus temperature in the Fe-C binary diagram and thus does not reflect the influences of other chemical elements. This was reflected in the less accurate linear dependence
NST = f(
TS)—compare in
Figure 6. The values of
ZST determined by using of IDS software and the values of
ZST determined in [
40] were practically the same. All datasets exhibits a linear dependency, but with different slopes and intercepts. The key is that for comparable carbon and solidus temperatures, relationship
ZST >
NST is valid. Therefore, the values
ZST and
NST must be considered to be fundamentally dissimilar, which is mainly due to the different methodology of their determination. Moreover, these material characteristics may be affected by the rate of temperature change during the test [
43].