Optimization of Thermal Processes Applied to Hypoeutectic White Cast Iron containing 25% Cr Aimed at Increasing Erosive Wear Resistance

: Hypoeutectic white cast irons containing 25% Cr are used in very demanding environments that require high resistance to erosive wear, for instance, the crushing and processing of minerals or the manufacture of cement. This high percentage in Cr, in turn, favors corrosion resistance. The application of a Design of Experiments (DoE) allows the analysis of the effects of modifying certain factors related to the heat treatments applied to these alloys. Among these factors, the influence of prior softening treatment to facilitate the machining of these cast irons and the influence of the factors related to the destabilization of austenite, during both quenching and tempering, were analyzed. The precipitated phases were identified by X-ray diffraction (XRD), while the Rietveld structural refinement method was used to determine their percentages by weight. Erosive wear resistance was calculated using the ASTM G76 standard test method. It is concluded that the thermal softening treatment, consisting of 2 h at 1000 ◦ C and 24 h at 700 ◦ C, does not result in additional softening of the material compared to its as-cast state. Furthermore, it is observed that not only eutectic carbides influence wear resistance, but that the influence of the matrix constituent is also significant. It is also verified that the tempering treatment plays a decisive role in wear resistance. Temperatures of 500 ◦ C and tempering times of 6 h increase the wear resistance and hardness of the aforementioned matrix constituent. Tempering temperatures of 200 ◦ C lead to an increase in retained austenite content and the presence of M 3 C carbides versus mixed M 7 C 3 and M 23 C 6 carbides. The quench cooling medium is not found to have a significant influence on the hardness or wear resistance.


Introduction
High-Cr white cast irons are widely used to withstand abrasive and erosive wear in applications such as the crushing and processing of minerals, cement manufacturing, and the pumping of sludge generated in these industries [1,2]. These alloys usually contain between 15 and 30% Cr [1]. Wear resistance increases as the percentage of chromium increases [3]. The type and distribution of eutectic or secondary carbides depend on the composition of the alloy and the heat treatments it is subjected to [1]. To enhance the wear resistance of these cast irons, it is advisable to carry out a treatment to destabilize the austenite [4]. The destabilization of austenite requires long dwell times at the austenitization temperature, due to the high concentration of alloy elements in the austenite crystalline cell, which hinders the diffusion of carbon. With increasing dwell time at the destabilization temperature, two kinetics simultaneously compete with one another: On the one hand, the dissolution of eutectic

Materials and Methods
Via the application of a DoE, the aim is to modify certain manufacturing parameters in a deliberate and controlled manner so as to analyze the variations produced in the properties of the material. In this case, the aim is to analyze the variations in the erosive wear resistance and microstructure of the material so as to subsequently correlate in-service performance with these microstructural changes. Statistical analysis of the variations in the responses of the material enables us to determine which of the analyzed factors has a significant effect on its wear resistance. Table 2 shows the analyzed factors and the levels of analysis in each of these factors. Among the factors listed in Table 2, the meaning of factor C needs clarifying. This is a softening treatment aimed at facilitating the machining of this material before the hardening treatment [20]. This heat treatment consisted of 2 h at 1000 • C and 24 h at 700 • C. The goals of this treatment would be to destabilize the retained austenite and to seek a majority presence of perlite, thus facilitating hypothetical machining should it be necessary for the manufacture of industrial components using this material. The proposed dwell times at the destabilization temperature of austenite in the quenching process, Factor B, are higher than usual.
The redissolution of any possible cementite carbides precipitated during the softening treatment is, thus sought, thereby favoring the precipitation of Cr-rich secondary carbides and an increase in the Ms temperature so as to avoid the presence of retained austenite as far as possible after quenching [20]. The effect of a factor is defined as the variation in certain property of the material as a result of the variation of said factor. The property of the material may be the wearing resistance, hardness, the volume fraction of retained austenite, et cetera. This type of effect is called the main effect. Sometimes, the effect of one factor depends on the value that another takes. When this occurs, these factors are said to interact. The influence of the main effects on the variations in the response of the material is greater than that of the two-factor interactions. In turn, the influence of the two-factor interactions is greater than that of the three-factor interactions, and so on successively. In industrial practice, it is sufficient to take into account the main effects and two-factors interactions. This simplification allows for reducing the number of experiments. In this study, the effect of six factors with eight experiments has been analyzed. If the aim were to analyze all the possible interactions, it would be necessary to perform 64 experiments (2 6 = 64). In the case in hand, however, only eight effects (2 6−3 ) have been estimated, which means a 1/8 (64/8 = 8) fractional factorial design. Table 3 shows the array of experiments thus generated to carry out a DoE with six factors, two levels for each factor, and eight experiments. Columns D, E, and F have been, respectively, constructed from the product of columns A × B, A × C, and B × C. The "Restricted Confounding Pattern" column indicates only the main effects and those 2-factor interactions whose effects are confounded with the main effects. The main effects and interactions may be associated with the terms of a Taylor series of the response function. Hence, by excluding third-order interactions, the third-order terms of the Taylor series would likewise be excluded. This allows performing fractional DOEs, reducing the number of experiments, but assuming a possible error resulting from excluding interactions between factors. The confounding pattern should include all the effects confounded with each other. However, Table 3 shows a restricted confounding pattern in which only the main effects and the two-factor interactions are represented. The aim of using a fractional approach is not to achieve a good fit, but to try to determine which factors have a significant effect on the response variable.
The effects are linear combinations of the analyzed responses. Hence, applying the central limit theorem (CLT), they will follow a normal law. If we represent the distribution function of the N Metals 2020, 10, 359 4 of 17 (0,σ) law on the normal probability plot scale, it will take the form of a straight line. This line must necessarily pass through the coordinate point (0.50). If any calculated effect followed a different normal law, e.g., N (µ,σ'), it would not appear aligned along this line. Those effects that deviate from the straight line towards the ends on the normal probability plot are considered significant. For example, if an effect deviates to the left, this would indicate that the factor associated with this effect at its −1 level would increase the value of the response. Similarly, if an effect deviates to the right of the straight line, this would indicate that the factor associated with this effect at its +1 level would increase the value of the response. The statistical analysis was carried out with the help of the Statagraphics Centurion XVI program, version 16.1.18.
The wear resistance, hardness, and hardness of the matrix constituent were analyzed via the eight experiments listed in Table 3. The aim of the last analysis was to test whether the wear resistance of the material might have some kind of relationship with the hardness of the matrix constituent. Moreover, the possible relationship between the microstructure obtained in these experiments and the wear resistance of the material was likewise analyzed. The analyzed responses were: • Vickers hardness of the material. The applied load was 300 N, while the hardness value was the average value obtained from 10 indentations.

•
The Vickers hardness of the constituent matrix. In this case, the applied load was 0.5 N, while the hardness value was calculated as the average value obtained from 10 indentations.

•
Erosive wear resistance. This test was carried out as per ASTM G76 [21] by means of compressed air blasting with corundum particles, applying a pressure of 2 bar, a flow rate of 250 g/min and a 30 • angle of incidence on the sample surface. The times employed in each experiment were 2, 4, and 6 min. Three repetitions were performed per test. The weight loss per unit time (mg/min) was determined from the average values obtained at each test time. As noted in the aforementioned standard, the results are shown in mm 3 of material loss per gram of abrasive (mm 3 /g). The microstructural variables were determined by X-ray diffraction on a SEIFERT XRD 3000 T/T diffractometer (Baker Hughes, Celle, Germany). The radiation was emitted via a fine-focus Mo tube at a working power of 40 kV × 40 mA and monochromatized to the Kα doublet: λ 1 = 0.7093616 Å and λ 2 = 0.713607 Å. The diffracted intensity was determined in a 2θ range from 7 to 57 • with an angular step and counting time of approximately 0.03 • and 22 s, respectively. To calibrate the equipment, the position of the reflections and the profiles of the associated Bragg peaks were calibrated with the National Institute of Standards and Technology (NIST) Si (640C) standard and LaB6 (660a) standard, respectively. The Rietveld structural refinement method was used to determine the percentage of the crystalline phases via fitting of the diffractograms. To this end, following the recording of the diffraction figures, a structural refinement was carried out using the crystallographic information files present in the Inorganic Crystal Structure Database (ICSD), FIZ Karlsruhe, Germany. The program employed for this purpose was FullProf.2k, version 6.20 (2018). The increase in width observed in the peaks of the majority phases were modeled using Stephens' formulation [22], which is implemented in the aforementioned analysis program. Figure 1 shows the microstructure of these cast irons in the as-cast state following solidification in a sand mold. This microstructure is mainly made up of eutectic carbides of the K 2 type, retained austenite and pearlite. The proeutectic austenite presents a dendritic growth model. The presence of One of the analyzed factors was the effect of a possible softening treatment designed to facilitate machining of this material with chip removal [20]. Figure 2 shows the microstructure obtained following this treatment. Coalescence and thickening of the secondary carbides precipitated during the destabilization of austenite, prior to the isothermal dwell time at 700 °C, can be observed [20,23]. However, the measured hardness in this state reached an average value of 360 HV, which was greater than of the as-cast state. This reason for this could be the high volume fraction of retained austenite that these cast irons present in said as-cast state [24]. From all the above, it follows that if the aim were to machine this material before its hardening by heat treatment, it would not be necessary to perform a prior softening treatment, contrary to what was concluded in a previous study on white cast irons containing 18% Cr. One of the analyzed factors was the effect of a possible softening treatment designed to facilitate machining of this material with chip removal [20]. Figure 2 shows the microstructure obtained following this treatment. Coalescence and thickening of the secondary carbides precipitated during the destabilization of austenite, prior to the isothermal dwell time at 700 • C, can be observed [20,23]. However, the measured hardness in this state reached an average value of 360 HV, which was greater than of the as-cast state. This reason for this could be the high volume fraction of retained austenite that these cast irons present in said as-cast state [24]. From all the above, it follows that if the aim were to machine this material before its hardening by heat treatment, it would not be necessary to perform a prior softening treatment, contrary to what was concluded in a previous study on white cast irons containing 18% Cr. Table 4 shows the results obtained from the analysis of:

Results
• the overall hardness of the material • the hardness of the constituent matrix, whose microstructure is a consequence of the destabilization of austenite and its transformation • the weight loss in the erosive wear test.  Table 4 shows the results obtained from the analysis of: • the overall hardness of the material • the hardness of the constituent matrix, whose microstructure is a consequence of the destabilization of austenite and its transformation • the weight loss in the erosive wear test. Figure 3 shows the representation of these effects on a normal probabilistic plot, highlighting those that have a significant influence on the analyzed responses. Figure 3a shows that factors A and E (destabilization temperature of austenite and tempering temperature) have a significant effect on the hardness of the material. Placing these two factors at their +1 level (1100 °C and 500 °C, respectively) would result in an increase in hardness. It can further be seen that some of the AE and BF interactions would have a significant effect on hardness. Table 5 shows the results of the analysis of these interactions. It can be seen that the interaction that produces a greater increase in hardness is AE when both factors are placed at their +1 level. Figure 3b shows that E (tempering temperature) and F (tempering time) are the factors that have a significant effect on the hardness of the matrix constituent. An increase in this hardness would be achieved by placing these two factors at their +1 level (500 °C and 6 h, respectively). From these results, it may be deduced that a high tempering temperature and long tempering times favor a second destabilization of the retained austenite. The significant effect of interactions AF and BE can also be appreciated. Table 6 shows the results of the analysis of these two interactions. It follows that the effect of factor F is favored when factor A (destabilization temperature of austenite) is placed at its +1 level (1100 °C). Similarly, it follows that the effect of factor E is favored when factor B (dwell time at the destabilization temperature) is placed at its +1 level (8 h). Figure 3c shows that factors E (tempering temperature) and F (tempering time) have a significant effect on erosive wear resistance. Placing both factors at their +1 level (500 °C and 6 h, respectively) would result in an increase in wear resistance. It should be noted that these same factors are those that have a significant influence on the hardness of the matrix constituent, thus corroborating the importance of this constituent with respect to the wear resistance.
It should also be noted that the quench cooling medium is not found to have a significant influence either on the hardness or wear resistance of the material.    Figure 3 shows the representation of these effects on a normal probabilistic plot, highlighting those that have a significant influence on the analyzed responses. Figure 3a shows that factors A and E (destabilization temperature of austenite and tempering temperature) have a significant effect on the hardness of the material. Placing these two factors at their +1 level (1100 • C and 500 • C, respectively) would result in an increase in hardness. It can further be seen that some of the AE and BF interactions would have a significant effect on hardness. Table 5 shows the results of the analysis of these interactions. It can be seen that the interaction that produces a greater increase in hardness is AE when both factors are placed at their +1 level.  Figure 3b shows that E (tempering temperature) and F (tempering time) are the factors that have a significant effect on the hardness of the matrix constituent. An increase in this hardness would be achieved by placing these two factors at their +1 level (500 • C and 6 h, respectively). From these results, it may be deduced that a high tempering temperature and long tempering times favor a second destabilization of the retained austenite. The significant effect of interactions AF and BE can also be appreciated. Table 6 shows the results of the analysis of these two interactions. It follows that the effect of factor F is favored when factor A (destabilization temperature of austenite) is placed at its +1 level (1100 • C). Similarly, it follows that the effect of factor E is favored when factor B (dwell time at the destabilization temperature) is placed at its +1 level (8 h).  Figure 3c shows that factors E (tempering temperature) and F (tempering time) have a significant effect on erosive wear resistance. Placing both factors at their +1 level (500 • C and 6 h, respectively) would result in an increase in wear resistance. It should be noted that these same factors are those that have a significant influence on the hardness of the matrix constituent, thus corroborating the importance of this constituent with respect to the wear resistance.
It should also be noted that the quench cooling medium is not found to have a significant influence either on the hardness or wear resistance of the material. Figure 4 shows the diffractograms obtained in the eight experiments, highlighting the main identified phases. Figure 5 shows the overall fittings using the Rietveld method. The red marks indicate the observed intensities; the black line, the intensity calculated according to the Rietveld structural model; the blue line, the difference between the two, while the vertical segments indicate the angular positions of the different identified phases.           Table 7 shows the percentages by weight and the mesh parameters of the main crystalline phases detected by XRD. The goodness-of-fit is defined by factor Rwp, index Rexp, and the ratio of their squares, Chi 2 = (Rwp/Rexp) 2 .  Table 8 shows the average values obtained in each experiment, together with the effects corresponding to the restricted confounding pattern specified in the array of experiments. The row corresponding to the average shows the average value obtained for each of the analyzed responses. Figure 6 shows the representation of these effects on a normal probability plot, highlighting those that have a significant effect on these responses.    Table 7 shows the percentages by weight and the mesh parameters of the main crystalline phases detected by XRD. The goodness-of-fit is defined by factor Rwp, index Rexp, and the ratio of their squares, Chi 2 = (Rwp/Rexp) 2 .     Figure 6a shows that factor E (tempering temperature) has a significant influence on the percentage of tempered martensite. If the aim were to increase this content, this factor should be placed at its +1 level (500 °C). Figure 6b shows that factors A (destabilization of austenite temperature) and E (tempering temperature) have a significant effect on the percentage of retained austenite. An  Figure 6a shows that factor E (tempering temperature) has a significant influence on the percentage of tempered martensite. If the aim were to increase this content, this factor should be placed at its +1 level (500 • C). Figure 6b shows that factors A (destabilization of austenite temperature) and E (tempering temperature) have a significant effect on the percentage of retained austenite. An increase in this phase would be obtained by placing factor A at its +1 level (1100 • C) and factor E at its −1 level (200 • C). Interactions AE+BF are also found to have a significant influence. Table 9 shows the results of their analysis. It can be seen that the effect of factors A and E increase when these factors are respectively placed at their +1 and −1 level. From the XRD analysis, it is concluded that retained austenite is only observed in Experiments 2 and 4. These are the experiments in which a low tempering temperature (200 • C) was employed. This finding is consistent with the results shown in Figure 6b and Table 9. However, a softening treatment was also employed in these experiments. Hence, it follows that the austenitization temperature at 1100 • C is high enough to dissolve precipitated carbides during this softening treatment, thereby favoring an increase in retained austenite after cooling [25]. This austenite would be destabilized when tempering at 500 • C, but not when tempering at 200 • C. Figure 7 shows the microstructure obtained after the reported softening treatment, followed by austenitization at 1100 • C for 8 h and oil cooling. It can be seen that the precipitated carbides were considerably reduced during the softening treatment compared to Figure 2. Subsequent tempering at 500 • C would remove this retained austenite.    Table 2) have a significant effect on the percentage of K2 or K1 carbides. However, Figure  6e shows that factor E (tempering temperature) does have a significant effect on the percentage of Fe3C. An increase in this phase would be achieved by placing this factor at its −1 level (200 °C). Lower temperatures are required for Fe3C to precipitate during the tempering of the martensite, as it is only the C atoms, dissolved in a solid insert solution, which have to diffuse until reaching the crystalline defects of the cubic martensite (tempered martensite). However, the precipitation of K1 and K2 carbides requires a) the diffusion of Cr atoms, dissolved in a solid replacement solution, and b) the prior redissolution of Fe3C to provide C atoms in the precipitation of these carbides. Higher temperatures are necessary for these processes to take place. In the case of the precipitation of K1 and K2 carbides, it is necessary to reach a temperature of 500 °C. In turn, the transformation of retained austenite into martensite is also achieved by high tempering temperatures, as evidenced by the results shown in Figure 6b. This figure also shows that high austenitization temperatures seem to favor the presence of retained austenite, as it is found alloyed with C and Cr. This could explain why the combination of a high austenitization and low tempering temperatures favored the presence of retained austenite. Figure 8 shows a representative micrograph of each experiment that allows us to appreciate the general microstructure of these cast irons, consisting mainly of eutectic carbides of type K1, secondary carbides of type K1, K2, and Fe3C (this last carbide when tempering at low temperatures, 200 °C),   Table 2) have a significant effect on the percentage of K 2 or K 1 carbides. However, Figure 6e shows that factor E (tempering temperature) does have a significant effect on the percentage of Fe 3 C. An increase in this phase would be achieved by placing this factor at its −1 level (200 • C). Lower temperatures are required for Fe 3 C to precipitate during the tempering of the martensite, as it is only the C atoms, dissolved in a solid insert solution, which have to diffuse until reaching the crystalline defects of the cubic martensite (tempered martensite). However, the precipitation of K 1 and K 2 carbides requires a) the diffusion of Cr atoms, dissolved in a solid replacement solution, and b) the prior redissolution of Fe 3 C to provide C atoms in the precipitation of these carbides. Higher temperatures are necessary for these processes to take place. In the case of the precipitation of K 1 and K 2 carbides, it is necessary to reach a temperature of 500 • C. In turn, the transformation of retained austenite into martensite is also achieved by high tempering temperatures, as evidenced by the results shown in Figure 6b. This figure also shows that high austenitization temperatures seem to favor the presence of retained austenite, as it is found alloyed with C and Cr. This could explain why the combination of a high austenitization and low tempering temperatures favored the presence of retained austenite. Figure 8 shows a representative micrograph of each experiment that allows us to appreciate the general microstructure of these cast irons, consisting mainly of eutectic carbides of type K1, secondary carbides of type K 1 , K 2 , and Fe 3 C (this last carbide when tempering at low temperatures, 200 • C), tempered martensite and the possible existence of retained austenite if the tempering takes place at low temperatures (200 • C).
austenite into martensite is also achieved by high tempering temperatures, as evidenced by the results shown in Figure 6b. This figure also shows that high austenitization temperatures seem to favor the presence of retained austenite, as it is found alloyed with C and Cr. This could explain why the combination of a high austenitization and low tempering temperatures favored the presence of retained austenite. Figure 8 shows a representative micrograph of each experiment that allows us to appreciate the general microstructure of these cast irons, consisting mainly of eutectic carbides of type K1, secondary carbides of type K1, K2, and Fe3C (this last carbide when tempering at low temperatures, 200 °C), tempered martensite and the possible existence of retained austenite if the tempering takes place at low temperatures (200 °C). Figure 9 shows, as a representative example, one of the tracks resulting from the wear test. In this case, the micrograph corresponds to one of the samples from Experiment 1 after 6 min of testing.   Figure 9 shows, as a representative example, one of the tracks resulting from the wear test. In this case, the micrograph corresponds to one of the samples from Experiment 1 after 6 min of testing.

Conclusions
The application of a Design of Experiments (DoE) allowed the analysis of the effects of modifying a variety of factors related to the heat treatments applied to hypoeutectic white cast iron