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Experimental results Microstructure evolution

The ZK30s AA and ECAPed conditions of the inverse pole figures (IPF) coloring patterns and associated band contrast maps (BC) are shown in Fig.2. High-angle grain boundaries (HAGBs) were colored black, while Low-angle grain boundaries (LAGBs) were colored white for AA condition, and it was colored red for 1P and Bc, as shown in Fig.2. The grain size distribution and misorientation angle distribution of the AA and ECAPed ZK30 samples is shown in Fig.3. From Fig.2a, it was clear that the AA condition revealed a bimodal structure where almost equiaxed refined grains coexist with coarse grains and the grain size was ranged between 3.4 up to 76.7m (Fig.3a) with an average grain size of 26.69m. On the other hand, low fraction of LAGBs as depicted in Fig.3b. Accordingly, the GB map (Fig.2b) showed minimal LAGBs due to the recrystallization process resulting from the annealing process. ECAP processing through 1P exhibited an elongated grain alongside refined grains and the grain size was ranged between 1.13 and 38.1m with an average grain size of 3.24m which indicated that 1P resulted in a partial recrystallization, as shown in Fig.2c,d. As indicated in Fig.2b 1P processing experienced a refinement in the average grain size of 87.8% as compared with the AA condition. In addition, from Fig.2b it was clear that ECAP processing via 1P resulted a significant increase in the grain aspect ratio due to the uncomplete recrystallization process. In terms of the LAGBs distribution, the GB maps of 1P condition revealed a significant increase in the LAGBs fraction (Fig.2d). A significant increase in the LAGBs density of 225% after processing via 1P was depicted compared to the AA sample (Fig.2c). Accordingly, the UFG structure resulted from ECAP processing through 1P led to increase the fraction of LAGBs which agreed with previous study35,36. Shana et al.35 reported that during the early passes of ECAP a generation and multiplication of dislocation is occur which is followed by entanglement of the dislocation forming the LAGBs and hence, the density of LAGBs was increased after processing through 1P. The accumulation of the plastic strain up to 4Bc revealed an almost UFG, which indicated that 4Bc led to a complete dynamic recrystallization (DRX) process (Fig.2e). The grain size was ranged between 0.23 up to 11.7m with average grain size of 1.94m (the average grain size was decreased by 92.7% compared to the AA condition). On the other hand, 4Bc revealed a decrease in the LAGBs density by 25.4% compared to 1P condition due to the dynamic recovery process. The decrease in the LAGBs density after processing through 4Bc was coupled with an increase in the HAGBs by 4.4% compared to 1P condition (Figs.2f, 3b). Accordingly, the rise of the HAGBs after multiple passes can be referred to the transfer of LAGBs into HAGBs during the DRX process.

IPF coloring maps and their corresponding BC maps, superimposed for the ZK30 billets in its AA condition (a,b), and ECAP processed through (c,d) 1P, (e,f) 4Bc (with HAGBs in black lines and LAGBs in white lines (AA) and red lines (1P, 4Bc).

Relative frequency of (a) grain size and (b) misorientation angle of all ZK30 samples.

Similar findings were reported in previous studies. Dumitru et al.36 reported that ECAP processing resulted in the accumulation and re-arrangement of dislocations which resulted in forming a subgrains and equiaxed grains with an UFG structure and a fully homogenous and equiaxed grain structure for ZK30 alloy was attained after the third pass. Furthermore, they reported that the LAGBs is transferred into HAGBs during the multiple passes which leads to the decrease in the LAGBs density. Figueiredo et al.37 reported that the grains evolved during the early passes of ECAP into a bimodal structure while further processing passes resulted in the achievement of a homogenous UFG structure. Zhou et al.38 reported that by increasing the processing passes resulted in generation of new grain boundaries which resulted in increasing the misorientation to accommodate the deformation and the Geometrically Necessary Dislocations (GNDs) generated a part of the total dislocations with a HAGBs, thus develop misorientations between the neighbor grains. Tong et al.39 reported that the fraction of LAGBs is decreased during multiple passes for MgZnCa alloy.

Figure4a displays X-ray diffraction (XRD) patterns of the AA-ZK30 alloy, 1P, and 4Bc extruded samples, revealing peaks corresponding to primary -Mg Phase, Mg7Zn3, and MgZn2 phases in all extruded alloys, with an absence of diffraction peaks corresponding to oxide inclusions. Following 1P-ECAP, the -Mg peak intensity exhibits an initial increase, succeeded by a decrease and fluctuations, signaling texture alterations in the alternative Bc route. The identification of the MgZn2 phase is supported by the equilibrium MgZn binary phase diagram40. However, the weakened peak intensity detected for the MgZn2 phase after the 4BcECAP process indicates that a significant portion of the MgZn2 dissolved into the Mg matrix, attributed to their poor thermal stability. Furthermore, the atomic ratio of Mg/Zn for this phase is approximately 2.33, leading to the deduction that the second phase is the Mg7Zn3 compound. This finding aligns with recent research on MgZn alloys41. Additionally, diffraction patterns of ECAP-processed samples exhibit peak broadening and shifting, indicative of microstructural adjustments during plastic deformation. These alterations undergo analysis for crystallite size and micro-strain using the modified Williamson and Hall (WH) method42, as illustrated in Fig.4b. After a single pass of ECAP, there is a reduction in crystallite size and an escalation in induced micro-strain. Subsequent to four passes-Bc, further reductions in crystallite size and heightened micro-strain (36nm and 1.94103, respectively) are observed. Divergent shearing patterns among the four processing routes, stemming from disparities in sample rotation, result in distinct evolutions of subgrain boundaries. Route BC, characterized by the most extensive angular range of slip, generates subgrain bands on two shearing directions, expediting the transition of subgrain boundaries into high-angle grain boundaries43,44. Consequently, dislocation density and induced micro-strains reach their top in route BC, potentially influenced by texture modifications linked to orientation differences in processing routes. Hence, as the number of ECAP passes increases, an intensive level of deformation is observed, leading to the existence of dynamic recrystallization and grain refinement, particularly in the ECAP 4-pass. This enhanced deformation effectively impedes grain growth. Consequently, the number of passes in the ECAP process is intricately linked to the equivalent strain, inducing grain boundary pinning, and resulting in the formation of finer grains. The grain refinement process can be conceptualized as a repetitive sequence of dynamic recovery and recrystallization in each pass. In the case of the 4Bc ECAP process, dynamic recrystallization dominates, leading to a highly uniform grain reduction and, causing the grain boundaries to become less distinct45. Figure4b indicates that microstructural features vary with ECAP processing routes, aligning well with grain size and mechanical properties.

(a) XRD patterns for the AA ZK30 alloy and after 1P and 4Bc ECAP processing, (b) variations of crystallite size and lattice strain as a function of processing condition using the WilliamsonHall method.

Figure5 shows the volume loss (VL) and average coefficient of friction (COF) for the AA and ECAPed ZK30 alloy. The AA billets exhibited the highest VL at all wear parameters compared to the ECAPed billets as shown in Fig.5. From Fig.5a it revealed that performing the wear test at applied load of 1N exhibited the higher VL compared to the other applied forces. In addition, increasing the applied force up to 3 N revealed lower VL compared to 1 N counterpart at all wear speeds. Further increase in the applied load up to 5 N revealed a notable decrease in the VL. Similar behavior was attained for the ECAP-processed billets through 1P (Fig.5c) and 4Bc (Fig.5e). The VL was improved by increasing the applied load for all samples as shown in Fig.5 which indicated an enhancement in the wear resistance. Increasing the applied load increases the strain hardening of ZK30 alloy that are in contact as reported by Yasmin et al.46 and Kori et al.47. Accordingly, increasing the applied load resulted in increasing the friction force, which in turn hinder the dislocation motion and resulted in higher deformation, so that ZK30 experienced strain hardening and hence, the resistance to abrasion is increased, leading to improving the wear resistance48. Furthermore, increasing the applied load leads to increase the surface in contact with wear ball and hence, increases gripping action of asperities, which help to reduces the wear rate of ZK30 alloy as reported by Thuong et al.48. Out of contrary, increasing the wear speed revealed increasing the VL of the AA billets at all wear loads. For the ECAPed billet processed through 1P, the wear speed of 125mm/s revealed the lowest VL while the wear speed of 250mm/s showed the highest VL (Fig.5c). Similar behaviour was recorded for the 4Bc condition. In addition, from Fig.5c, it was clear that 1P condition showed higher VL compared to 4Bc (Fig.5e) at all wear parameters, indicating that processing via multiple passes resulted in significant grain size refinement (Fig.2). Hence, higher hardness and better wear behavior were attained which agreed with previous study7. In addition, from Fig.5, it was clear that increasing the wear speed increased the VL. For the AA billets tested at 1N load the VL was 1.52106 m3. ECAP processing via 1P significantly improved the wear behavior as the VL was reduced by 85% compared to the AA condition. While compared to the AA condition, the VL improved by 99.8% while straining through 4Bc, which is accounted for by the considerable refinement that 4Bc provides. A similar trend was observed for the ECAPed ZK30 samples tested at a load of 3 and 5 N (Fig.5). Accordingly, the significant grain refinement after ECAP processing (Fig.2) increased the grain boundaries area; hence, a thicker oxide protective layer can be formed, leading to improve the wear resistance of the ECAPed samples. It is worth to mentioning here that, the grain refinement coupled with refining the secondary phase particle and redistribution resulted from processing through ECAP processing through multiple passes resulted in improving the hardness, wear behavior and mechanical properties according to HallPetch equation7,13,49. Similar findings were noted for the ZK30 billets tested at 3 N load, processing through 1P and 4Bc exhibited decreasing the VL by 85%, 99.85%, respectively compared to the AA counterpart. Similar finding was recorded for the findings of ZK30 billets which tested at 5 N load.

Volume loss of ZK30 alloy (a,c,e) and the average coefficient of friction (b,d,f) in its (a,b) AA, (c,d) 1P and (e,f) 4Bc conditions as a function of different wear parameters.

From Fig.5, it can be noticed that the COF curves revealed a notable fluctuation with implementing least square method to smoothing the data, confirming that the friction during the testing of ECAPed ZK30 alloy was not steady for such a time. The remarkable change in the COF can be attributed to the smaller applied load on the surface of the ZK30 samples. Furthermore, the results of Fig.5 revealed that ECAP processing reduced the COF, and hence, better wear behavior was attained. Furthermore, for all ZK30 samples, it was observed that the highest applied load (5 N) coupled with the lowest wear time (110s) exhibited better COF and better wear behavior was displayed. These findings agreed with Farhat et al.50, they reported that decreasing the grain size led to improve the COF and hence improve the wear behavior. Furthermore, they reported that a plastic deformation occurs due to the friction between contacted surface which resisted by the grain boundaries and fine secondary phases. In addition, the strain hardening resulted from ECAP processing leads to decrease the COF and improving the VL50. Sankuru et al.43 reported that ECAP processing foe pure Mg resulted in substantial grain refinement which was reflected in improving both microhardness and wear rate of the ECAPed billets. Furthermore, they found that increasing the number of passes up to 4Bc reduced the wear rate by 50% compared to the AA condition. Based on the applied load and wear velocity and distance, wear mechanism can be classified into mild wear and severe wear regimes49. Wear test parameters in the present study (load up to 5 N and speed up to 250mm/s) falls in the mild wear regime where the delamination wear and oxidation wear mechanisms would predominantly take place43,51.

The worn surface morphologies of the ZK30-AA billet and ECAPed billet processed through 4Bc are shown in Fig.6. From Fig.6 it can revealed that scores of wear grooves which aligned parallel to the wear direction have been degenerated on the worn surface in both AA (Fig.6a) and 4Bc (Fig.6b) conditions. Accordingly, the worn surface was included a combination of adhesion regions and a plastic deformation bands along the wear direction. Furthermore, it can be observed that the wear debris were adhered to the ZK30 worn surface which indicated that the abrasion wear mechanism had occur52. Lim et al.53 reported that hard particle between contacting surfaces scratches samples and resulted in removing small fragments and hence, wear process was occurred. In addition, from Fig.6a,b it can depicted that the wear grooves on the AA billet were much wider than the counterpart of the 4Bc sample and which confirmed the effectiveness of ECAP processing in improving the wear behavior of the ZK30 alloy. Based on the aforementioned findings it can be concluded that ECAP-processed billets exhibited enhanced wear behavior which can be attributed to the obtained UFG structure52.

SEM micrograph of the worn surface after the wear test: (ac) AA alloy; (b) ECAP-processed through 4Bc.

Several regression transformations approach and associations among variables that are independent have been investigated in order to model the wear output responses. The association between the supplied parameters and the resulting responses was modeled using quadratic regression. The models created in the course of the experiment are considered statistically significant and can be used to forecast the response parameters in relation to the input control parameters when the highest possible coefficient of regression of prediction (R2) is closer to 1. The regression Eqs.(9)(14) represent the predicted non-linear model of volume loss (VL) and coefficient and friction (COF) at different passes as a function of velocity (V) and applied load (P), with their associated determination and adjusted coefficients. The current studys adjusted R2 and correlation coefficient R2 values fluctuated between 95.67 and 99.97%, which is extremely near to unity.

$${text{AA }}left{ {begin{array}{*{20}l} {VL = + 1.52067 times 10^{ - 6} - 1.89340 times 10^{ - 9} P - 4.81212 times 10^{ - 11} V + 8.37361 times 10^{ - 12} P * V} hfill & {} hfill \ { - 2.91667E - 10 {text{P}}^{2} - 2.39989E - 14 {text{V}}^{2} } hfill & {(9)} hfill \ {frac{1}{{{text{COF}}}} = + 2.72098 + 0.278289P - 0.029873V - 0.000208 P times V + 0.047980 {text{P}}^{2} } hfill & {} hfill \ { + 0.000111 {text{V}}^{2} - 0.000622 {text{P}}^{2} times V + 6.39031 times 10^{ - 6} P times {text{V}}^{2} } hfill & {(10)} hfill \ end{array} } right.$$

$$1{text{ Pass }}left{ {begin{array}{*{20}l} {VL = + 2.27635 times 10^{ - 7} + 7.22884 times 10^{ - 10} P - 2.46145 times 10^{ - 11} V - 1.03868 times 10^{ - 11} P times V} hfill & {} hfill \ { - 1.82621 times 10^{ - 10} {text{P}}^{2} + 6.10694 times 10^{ - 14} {text{V}}^{2} } hfill & {} hfill \ { + 8.76819 times 10^{ - 13} P^{2} times V + 2.48691 times 10^{ - 14} P times V^{2} } hfill & {(11)} hfill \ {frac{1}{{{text{COF}}}} = - 0.383965 + 1.53600P + 0.013973V - 0.002899 P times V} hfill & {} hfill \ { - 0.104246 P^{2} - 0.000028 V^{2} } hfill & {(12)} hfill \ end{array} } right.$$

$$4{text{ Pass}}left{ {begin{array}{*{20}l} {VL = + 2.29909 times 10^{ - 8} - 2.29012 times 10^{ - 10} P + 2.46146 times 10^{ - 11} V - 6.98269 times 10^{ - 12} P times V } hfill & {} hfill \ { - 1.98249 times 10^{ - 11} {text{P}}^{2} - 7.08320 times 10^{ - 14} {text{V}}^{2} } hfill & {} hfill \ { + 3.23037 times 10^{ - 13} P^{2} * V + 1.70252 times 10^{ - 14} P times V^{2} } hfill & {(13)} hfill \ {frac{1}{{{text{COF}}}} = + 2.77408 - 0.010065P - 0.020097V - 0.003659 P times V} hfill & {} hfill \ { + 0.146561 P^{2} + 0.000099 V^{2} } hfill & {(14)} hfill \ end{array} } right.$$

The experimental data are plotted in Fig.7 as a function of the corresponding predicted values for VL and COF for zero pass, one pass, and four passes. The minimal output value is indicated by blue dots, which gradually change to the maximum output value indicated by red points. The effectiveness of the produced regression models was supported by the analysis of these maps, which showed that the practical and projected values matched remarkably well and that the majority of their intersection locations were rather close to the median line.

Comparison between VL and COF of experimental and predicted values of ZK30 at AA, 1P, and 4Bc.

As a consequence of wear characteristics (P and V), Fig.8 displays 3D response plots created using regression models to assess changes in VL and COF at various ECAP passes. For VL, the volume loss and applied load exhibit an inverse proportionality at various ECAP passes, which is apparent in Fig.8ac. It was observed that increasing the applied load in the wear process will minimize VL. So, the optimal amount of VL was obtained at an applied load of 5N. There is an inverse relation between V of the wear process and VL at different ECAP passes. There is a clear need to change wear speeds for bullets with varying numbers of passes. As a result, the increased number of passes will need a lower wear speed to minimize VL. The minimal VL at zero pass is 1.50085E06 m3 obtained at 5N and 250mm/s. Also, at a single pass, the optimal VL is 2.2266028E07 m3 obtained at 5 N and 148mm/s. Finally, the minimum VL at four passes is 2.07783E08 m3 at 5N and 64.5mm/s.

Three-dimensional plot of VL (ac) and COF (df) of ZK30 at AA, 1P, and 4Bc.

Figure8df presents the effect of wear parameters P and V on the COF for ECAPed ZK30 billets at zero, one, and four passes. There is an inverse proportionate between the applied load in the wear process and the coefficient of friction. As a result, the minimum optimum value of COF of the ZK30 billet at different process passes was obtained at 5 N. On the other hand, the speed used in the wear process decreased with the number of billet passes. The wear test rates for billets at zero, one, and four passes are 250, 64.5, and 64.5mm/s, respectively. The minimum COF at zero pass is 0.380134639, obtained at 5N and 250mm/s. At 5N and 64.5mm/s, the lowest COF at one pass is 0.220277466. Finally, the minimum COF at four passes is 0.23130154 at 5N and 64.5mm/s.

The previously mentioned modern ML algorithms have been used here to provide a solid foundation for analyzing the obtained data and gaining significant insights. The following section will give the results acquired by employing these approaches and thoroughly discuss the findings.

The correlation plots and correlation coefficients (Fig.9) between the input variables, force, and speed, and the six output variables (VL_P0, VL_P1, VL_P4, COF_P0, COF_P1, and COF_P4) for data preprocessing of ML models give valuable insights into the interactions between these variables. Correlation charts help to investigate the strength and direction of a linear relationship between model input and output variables. We can initially observe if there is a positive, negative, or no correlation between each two variables by inspecting the scatterplots. This knowledge aids in comprehending how changes in one variable effect changes in the other. In contrast, the correlation coefficient offers a numerical assessment of the strength and direction of the linear relationship. It ranges from 1 to 1, with near 1 indicating a strong negative correlation, close to 1 indicating a strong positive correlation, and close to 0 indicating no or weak association. It is critical to examine the size and importance of the correlation coefficients when examining the correlation between the force and speed input variables and the six output variables (VL_P0, VL_P1, VL_P4, COF_P0, COF_P1, and COF_P4). A high positive correlation coefficient implies that a rise in one variable is connected with an increase in the other. In contrast, a high negative correlation coefficient indicates that an increase in one variable is associated with an increase in the other. From Fig.9 it was clear that for all ZK30 billets, the both VL and COP were reversely proportional with the applied (in the range of 1-up to- 5N). Regarding the wear speed, the VL of both the AA and 1P conditions exhibited an inversed proportional with the wear speed while 4Bc exhibited a direct proportional with the wear speed (in the range of 64.5- up to- 250mm/s) despite of the COP for all samples revealed an inversed proportional with the wear speed. The VL of AA condition (P0) revealed strong negative correlation coefficient of 0.82 with the applied load while it displayed intermediate negative coefficient of 0.49 with the wear speed. For 1P condition, VL showed a strong negative correlation of 0.74 with the applied load whereas it showed a very weak negative correlation coefficient of 0.13 with the speed. Furthermore, the VL of 4Bc condition displayed a strong negative correlation of 0.99 with the applied load while it displayed a wear positive correlation coefficient of 0.08 with the speed. Similar trend was observed for the COF, the AA, 1P and 4Bc samples displayed intermediate negative coefficient of 0.047, 0.65 and 0.61, respectively with the applied load while it showed a weak negative coefficient of 0.4, 0.05 and 0.22, respectively with wear speed.

Correlation plots of input and output variables showcasing the strength and direction of relationships between each inputoutput variable using correlation coefficients.

Figure10 shows the predicted train and test VL values compared to the original data, indicating that the VL prediction model performed well utilizing the LR (Linear Regression) technique. The R2-score is a popular statistic for assessing the goodness of fit of a regression model. It runs from 0 to 1, with higher values indicating better performance. In this scenario, the R2-scores for both the training and test datasets range from 0.55 to 0.99, indicating that the ML model has established a significant correlation between the projected VL values and the actual data. This shows that the model can account for a considerable percentage of the variability in VL values.

Predicted train and predicted test VL versus actual data computed for different applied loads and number of passes of (a) 0P (AA), (b) 1P, and (c) 4Bc: evaluating the performance of the VL prediction best model achieved using LR algorithm.

The R2-scores for training and testing three distinct ML models for the output variables VL_P0, VL_P1, and VL_P4 are summarized in Fig.11. The R2-score, also known as the coefficient of determination, is a number ranging from 0 to 1 that indicates how well the model fits the data. For VL_P0, R2 for testing is 0.69, and that for training is 0.96, indicating that the ML model predicts the VL_P0 variable with reasonable accuracy on unknown data. On the other hand, the R2 value of 0.96 for training suggests that the model fits the training data rather well. In summary, the performance of the ML models changes depending on the output variables. With R2 values of 0.98 for both training and testing, the model predicts 'VL_P4' with great accuracy. However, the models performance for 'VL_P0' is reasonable, with an R2 score of 0.69 for testing and a high R2 score of 0.96 for training. The models performance for 'VL_P1' is relatively poor, with R2 values of 0.55 for testing and 0.57 for training. Additional assessment measures must be considered to understand the models' prediction capabilities well. Therefore, as presented in the following section, we did no-linear polynomial fitting with extracted equations that accurately link the output and input variables.

Result summary of ML train and test sets displaying R2-score for each model.

Furthermore, the data was subjected to polynomial fitting with first- and second-degree models (Fig.12). The fitting accuracy of the data was assessed using the R2-score, which ranged from 0.92 to 0.98, indicating a good fit. The following equations (Eqs.15 to 17) were extracted from fitting the experimental dataset of the volume loss at different conditions of applied load (P) and the speed (V) as follows:

$${text{VL}}_{text{P}}0 = 1.519e - 06{ } + { } - 2.417e - 09{text{ * P }} + { } - 3.077e - 11{ * }V$$

(15)

$$VL_{text{P}}1 = 2.299e - 07 - 5.446e - 10 * {text{P}} - 5.431e - 11 * V - 5.417e - 11 * {text{P}}^{2} + 2.921e - 12 * {text{P}} V + 1.357e - 13 * V^{2}$$

(16)

$$VL_{text{P}}4 = 2.433e - 08 - 6.200e - 10 * {text{P}} + 1.042e - 12 * V$$

(17)

Predicted versus actual (a) VL_P0 fitted to Eq.15 with R2-score of 0.92, (b) VL_P1 fitted to Eq.16 with R2-score of 0.96, (c) VL_P4 fitted to Eq.17 with R2-score of 0.98.

Figure13 depicts the predicted train and test coefficients of friction (COF) values placed against the actual data. The figure seeks to assess the performance of the best models obtained using the SVM (Support Vector Machine) and GPR (Gaussian Process Regression) algorithms for various applied loads and number of passes (0, 1P, and 4P). The figure assesses the accuracy and efficacy of the COF prediction models by showing the predicted train and test COF values alongside the actual data. By comparing projected and actual data points, we may see how closely the models match the true values. The ML models trained and evaluated on the output variables 'COF_P0', 'COF_P1', and 'COF_P4' using SVM and GPR algorithms show great accuracy and performance, as summarized in Fig.13. The R2 ratings for testing vary from 0.97 to 0.99, showing that the models efficiently capture the predicted variables' variability efficiently. Furthermore, the training R2 scores are consistently high at 0.99, demonstrating a solid fit to the training data. These findings imply that the ML models can accurately predict the values of 'COF_P0', 'COF_P1', and 'COF_P4' and generalize well to new unseen data.

Predicted train and predicted test COF versus actual data computed for different applied loads and number of passes of (a) 0P (AA), (b) 1P, and (c) 4Bc: evaluating the performance of the COF prediction best model achieved using SVM and GPR algorithms.

Figure14 presents a summary of the results obtained through machine learning modeling. The R2 values achieved for COF modeling using SVM and GPR are 0.99 for the training set and range from 0.97 to 0.99 for the testing dataset. These values indicate that the models have successfully captured and accurately represented the trends in the dataset.

Result summary of ML train and test sets displaying R2-score for each model.

The results of the RSM optimization carried out on the volume loss and coefficient of friction at zero pass (AA), along with the relevant variables, are shown in Appendix A-1. The red and blue dots represented the wear circumstance (P and V) and responses (VL and COF) for each of the ensuing optimization findings. The volume loss and coefficient of friction optimization objective were formed to in range, using minimize as the solution target, and the expected result of the desirability function was in the format of smaller-is-better attributes. The values of (A) P=5 N and (B) V=250mm/s were the optimal conditions for volume loss. Appendix A-1(a) shows that this resulted in the lowest volume loss value attainable of 1.50127E-6 m3. Also, the optimal friction coefficient conditions were (A) P=2.911 N and (B) V=250mm/s. This led to the lowest coefficient of friction value possible, which was 0.324575, as shown in Appendix A-1(b).

Appendix A-2 displays the outcomes of the RSM optimization performed on the volume loss and coefficient of friction at one pass, together with the appropriate variables. The volume loss and coefficient of friction optimization objectives were designed to be "in range," with "minimize" as the solution objective. It was anticipated that the intended function would provide "smaller-is-better" traits. The ideal conditions for volume loss were (A) P=4.95 N and (B) V=136.381mm/s. This yielded the lowest volume loss value feasible of 2.22725E-7 m3, as seen in Appendix A-2 (a). The optimal P and V values for the coefficient of friction were found to be (A) P=5 N and (B) V=64.5mm/s. As demonstrated in Appendix A-2 (b), this resulted in the lowest coefficient of friction value achievable, which was 0.220198.

Similarly, Appendix A-3 displays the outcomes of the RSM optimization performed on the volume loss and coefficient of friction at four passes, together with the appropriate variables. The volume loss and coefficient of friction optimization objectives were designed to be "in range," with "minimize" as the solution objective. The desired functions expected result would provide of "smaller-is-better" characteristics. The optimal conditions for volume loss were (A) P=5 N and (B) V=77.6915mm/s. This yielded the lowest volume loss value feasible of 2.12638E-8 m3, as seen in Appendix A-1 (a). The optimal P and V values for the coefficient of friction were found to be (A) P=4.95612 N and (B) V=64.9861mm/s. As seen in Appendix A-1(b), this resulted in the lowest coefficient of friction value achievable, which was 0.235109.

The most appropriate combination of wear-independent factors that contribute to the minimal feasible volume loss and coefficient of friction was determined using a genetic algorithm (GA). Based on genetic algorithm technique, the goal function for each response was determined by taking Eqs.(9)(14) and subjecting them to the wear boundary conditions, P and V. The following expression applies to the recommended functions for objective: Minimize (VL, COF), subjected to ranges of wear conditions: 1P5 (N), 64.5V250 (mm/s).

Figures15 and 16 show the GA optimization techniques performance in terms of fitness value and the running solver view, which were derived from MATLAB, together with the related wear requirements for the lowest VL and COF at zero pass. VL and COF were suggested to be minimized by Eqs.(9) and (10), which were then used as the function of fitness and exposed to the wear boundary limit. According to Fig.15a, the lowest value of VL that GA could find was 1.50085E6 m3 at P=5N and V=249.993mm/s. Furthermore, the GA yielded a minimum COF value of 0.322531 at P=2.91 N and V=250mm/s (Fig.15b).

Optimum VL (a) and COF (b) by GA at AA condition.

Optimum VL (a) and COF (b) by hybrid DOE-GA at AA condition.

The DOEGA hybrid analysis was carried out to enhance the GA outcomes. Wear optimal conditions of VL and COF at zero pass are used to determine the initial populations of hybrid DOEGA. The hybrid DOEGA yielded a minimum VL value of 1.50085E-6 m3 at a speed of 249.993mm/s and a load of 5N (Fig.16a). Similarly, at a 2.91 N and 250mm/s speed load, the hybrid DOEGA yielded a minimum COF (Fig.16b) of 0.322531.

The fitness function, as defined by Eqs.11 and 12, was the depreciation of VL and COF at a 1P, subject to the wear boundary condition. Figure17a,b display the optimal values of VL and COF by GA, which were 2.2266E7 m3 and 0.220278, respectively. The lowest VL measured at 147.313mm/s and 5 N. In comparison, 5 N and 64.5mm/s were the optimum wear conditions of COF as determined by GA. Hybrid DOEGA results of minimum VL and COF at a single pass were 2.2266 E-7 m3 and 0.220278, respectively, obtained at 147.313mm/s and 5 N for VL as shown in Fig.18a and 5 N and 64.5mm/s for COF as shown in Fig.18b.

Optimum VL (a) and COF (b) by GA at 1P condition.

Optimum VL (a) and COF (b) by hybrid DOE-GA at 1P condition.

Subject to the wear boundary condition, the fitness function was the minimization of VL and COF at four passes, as defined by Eqs.13 and 14. The optimum values of VL and COF via GA shown in Fig.19a,b were 2.12638E8 m3 and 0.231302, respectively. The lowest reported VL was 5 N and 77.762mm/s. However, GA found that the optimal wear conditions for COF were 5 N and 64.5mm/s. In Fig.20a,b, the hybrid DOEGA findings for the minimum VL and COF at four passes were 2.12638E8 m3 and 0.231302, respectively. These results were achieved at 77.762mm/s and 5 N for VL and 5 N and 64.5mm/s for COF.

Optimum VL (a) and COF (b) by GA at 4Bc condition.

Optimum VL (a) and COF (b) by hybrid DOE-GA at 4Bc condition.

A mathematical model whose input process parameters influence the quality of the output replies was solved using the multi-objective genetic algorithm (MOGA) technique54. In the current study, the multi-objective optimization using genetic algorithm (MOGA) as the objective function, regression models, was implemented using the GA Toolbox in MATLAB 2020 and the P and V are input wear parameter values served as the top and lower bounds, and the number of parameters was set to three. After that, the following MOGA parameters were selected: There were fifty individuals in the initial population, 300 generations in the generation, 20 migration intervals, 0.2 migration fractions, and 0.35 Pareto fractions. Constraint-dependent mutation and intermediary crossover with a coefficient of chance of 0.8 were used for optimization. The Pareto optimum, also known as a non-dominated solution, is the outcome of MOGA. It is a group of solutions that consider all of the objectives without sacrificing any of them55.

By addressing both as multi-objective functions was utilized to identify the lowest possible values of the volume loss and coefficient of friction at zero pass. Equations(9) and (10) were the fitness functions for volume loss and coefficient of friction at zero pass for ZK30. The Pareto front values for the volume loss and coefficient of friction at zero pass, as determined by MOGA, are listed in Table 2. The volume loss (Objective 1) and coefficient of friction (Objective 2) Pareto chart points at zero pass are shown in Fig.21. A friction coefficient reduction due to excessive volume loss was observed. As a result, giving up a decrease in the coefficient of friction can increase volume loss. For zero pass, the best volume loss was 1.50096E06 m3 with a sacrifice coefficient of friction of 0.402941. However, the worst volume loss was 1.50541E06 m3, with the best coefficient of friction being 0.341073.

The genetic algorithm was used for the multi-objective functions of minimal volume loss and coefficient of friction. The fitness functions for volume loss and coefficient of friction at one pass were represented by Eqs.(11) and (12), respectively. Table 3 displays the Pareto front points of volume loss and coefficient of friction at one pass. Figure22 presents the volume loss (Objective 1) and coefficient of friction (Objective 2) Pareto chart points for a single pass. It was discovered that the coefficient of friction decreases as the volume loss increases. As a result, the volume loss can be reduced at the expense of a higher coefficient of friction. The best volume loss for a single pass was 2.22699E07 m3, with the worst maximum coefficient of friction being 0.242371 and the best minimum coefficient of friction being 0.224776 at a volume loss of 2.23405E07 m3.

The multi-objective functions of minimal volume loss and coefficient of friction were handled by Eqs.(13) and (14), respectively, served as the fitness functions for volume loss and coefficient of friction at four passes. The Pareto front points of volume loss and coefficient of friction at four passes are shown in Table 4. The Pareto chart points for the volume loss (Objective 1) and coefficient of friction (Objective 2) for four passes are shown in Fig.23. It was shown that when the volume loss increases, the coefficient of friction lowers. The volume loss can be decreased as a result, however, at the expense of an increased coefficient of friction. The best minimum coefficient of friction was 0.2313046 at a volume loss of 2.12663E08 m3, and the best minimum volume loss was 2.126397E08 m3 at a coefficient of friction of 0.245145 for four passes. In addition, Table 5 compares wear response values at DOE, RSM, GA, hybrid RSM-GA, and MOGA.

This section proposed the optimal wear parameters of different responses, namely VL and COF of ZK30. The presented optimal wear parameters, such as P and V, are based on previous studies of ZK30 that recommended the applied load from one to 30 N and speed from 64.5 to 1000mm/s. Table 6 presents the optimal condition of the wear process of different responses by genetic algorithm (GA).

Table 7 displays the validity of wears regression model for VL under several circumstances. The wear models' validation was achieved under various load and speed conditions. The volume loss response models had the lowest error % between the practical and regression models and were the most accurate, based on the validation data. Table 7 indicates that the data unambiguously shows that the predictive molding performance has been validated, as shown by the reasonably high accuracy obtained, ranging from 69.7 to 99.9%.

Equations(15 to 17) provide insights into the relationship that links the volume loss with applied load and speed, allowing us to understand how changes in these factors affect the volume loss in the given system. The validity of this modeling was further examined using a new unseen dataset by which the prediction error and accuracy were calculated, as shown in Table 8. Table 8 shows that the data clearly demonstrates that the predictive molding performance has been validated, as evidenced by the obtained accuracy ranging from 69.7 to 99.9%, which is reasonably high.

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