3.1 Factorial design of experiments:
3.1.1. Model fitting
The evaluation of effective process variables on the UBS (MPa) were performed based on the Composite Central design (CCD) matrix with two replicated points. The design points, experimental and predicted results of (UBS) are represented in the Table 5.
To minimize the effects of uncontrolled factors, the experiments were performed in a random sequence too. Present study have found that the relationship between Ultimate bending strength (UBS) of the friction welded samples joints is a function of the friction welding parameters such as a Rotational speed (X1), friction pressure (X2) and Friction time (X3) which can be expressed as [24]:
UBS = {X1;X2;X3} (1)
The second-order polynomial equation is used to represent the response surface Ultimate bending strength given by:
UBS= b0+ ∑biXi + ∑biiXi2 + ∑bijXiXj (2)
For three factors, the chosen polynomial model can be expressed as:
UBS = b0 + b1(X1) + b2(X2) + b3(X3) + b12(X1X2) + b13(X1X3) + b23(X2X3) + b11(X12) + b22(X22) + b33(X32) (3)
Where (b0) is the average of the responses and b1, b2, b3. . .b33 are regression coefficients [33] that depends on the respective linear, interactive, and squared terms of the factors. The significance of each coefficient is determined by ‘F’ and ‘p’ values, which are listed in Table 6.
Table 6 ANOVA analysis of UBS (MPa)
Source
|
Sum of squares
|
DF
|
Mean square
|
F-ration
|
p-value
|
Model
|
111129.13
|
9
|
12347.7
|
15.9716
|
0.0016*
|
Error
|
4638.62
|
6
|
773.1
|
|
|
C.Total
|
115767.75
|
15
|
|
|
|
*p˂0.05
The value of the coefficient is calculated using the Design Expert Software. The quadratic model proved to be adequate for predicting the response given by the following Equations:
UBS (MPa) = 1223.06+ 33.3* X1-24.8*X2+80.1*X3+ 4*(X1*X2)-42*(X1*X3)-4.25(X2*X3) + 55.39*X12-33.1*X22+31.39*X32 (4)
In Eq. (4) can show the interactions between variables. They have significant effects on the response; the results are therefore presented and discussed. The statistical significance of Eq. (4) is presented in Table 7. From Table 6, respectively the terms mean square, degree of freedom (DF) and sum of squares are defined as the variance estimation of the model, the number of model and total sum of squares for model. The ANOVA (F-test) shows that the second order model (quadratic polynomial) corresponds to the experimental data also. The p-value is a quantitative measure to report the result of a hypothesis test. This is the probability that the statistical test is at least as extreme as those observed since the null hypothesis is true. Based on the results of the Fig. 3, R2 it was equal to 0.96 indicating the model to satisfy well the response [24].
The degree of freedom (DF = 15) in Table 6 indicates the total number of model terms, including the intercept minus one. It is clearly that the model is highly significant, as suggested by the model F-value (15.9716) and a low probability value (p-value = 0.0016). If p-value is less than or equal to the chosen significance level alpha value of 0.05, the test suggests that the observed data are inconsistent with the null hypothesis. Therefore, it’s must be rejected and the factor effect is significant [34]. It appears from Table 7 the linear effects of rotation speed; friction pressure and time are significant. The same trend was observed for the interactions effects between these factors, which confirms that the model is highly significant with the p–value of 0.0016< 0.05 [35-37] and F-value of 15.9716 cited in ANOVA analysis in Table 6.
In current study have analyzed the results obtained which appear in the Table 7, it can be conclude that friction time (X3) is the most important parameter for the overall UBS (MPa) with a high t-ratio: 9.11, the parameter exerts a stronger influence on the response (UBS). Secondly, rotation speed can be the second important influencer parameter phenomenon with a t-ratio: 3.79. Friction pressure was the least significant parameter with a t-ratio: -2.82. The interactions of (X1 and X3) (with a high t-ratio: -4.27) was the most significant compared to the other combinations (X2 and X3) and (X1 and X2). The latter was the least significant (with a t-ratio: 0.41). The negative sign means that the factors and the response are inversely proportional.
Table 7 Estimated regression coefficients.
Parameter
|
Estimate
|
Standard Error
|
t-ratio
|
p-value
|
Intercept
|
1223.069
|
13.16365
|
92.91
|
˂.0001*
|
X1(V)
|
33.3
|
8.79
|
3.79
|
0.0091*
|
X2 (F)
|
-24.8
|
8.79
|
-2.82
|
0.0303*
|
X3 (T)
|
80.1
|
8.79
|
9.11
|
˂.0001*
|
X1*X2
|
4
|
9.83
|
0.41
|
0.6982
|
X1*X3
|
-42
|
9.83
|
-4.27
|
0.0052*
|
X2*X3
|
-4.25
|
9.83
|
-0.43
|
0.6806
|
X1* X1
|
55.39
|
17.12
|
3.23
|
0.0178*
|
X2* X2
|
-33.10
|
17.12
|
-1.93
|
0.1014
|
X3* X3
|
31.39
|
17.12
|
1.83
|
0.1164
|
On the other hand, the difference between experimental and predicted values is illustrated on UBS in Fig. 4. There are points below and above straight line called point of line zero; the positive values observed on the residual plot indicate a low predictive result. While, negative values imply that the prediction was high; a value of zero means that the prediction is accurate since there is a total superposition between experimental and predicted values. The residual plot for UBS following Eq (4) shows a random pattern. This indicates that the distribution of residuals for the response approximately follows the fitted normal distribution.
3.1.2. Interaction plots
Fig. 5 illustrates possible positive and negative effects of two variables interactions, respectively among the three parameters on UBS response. The non-parallel curves show the presence of interaction that can be estimated between rotation speed “X1”and friction time “X3” equal to 0.0052, which means that the higher values of rotation speed affects UBS capacity when friction time is high and equal to 9 s.
In addition, the effects of interactions such as rotation speed “X1” and friction pressure “X2”, friction pressure “X2” and friction time “X3” are negligible due to parallel curves, which indicate the friction pressure x2 is the least significant or non-significant in the presence of other parameters simultaneously. These results confirm the previous finding obtained from Table 7, related to each parameter of influence on UBS process. Consequently, and in order to better understand the relationship between the three variables studied and the response which can related to UBS, a cubic graph is presented in Fig. 6.
The cubic graph demonstrates that increasing rotation speed V from 2000 rpm to 3000 rpm and friction pressure from 20 MPa to 40 MPa considerably decreases UBS from 1288.51 MPa to 1145 MPa and 1288.51 MPa to 1255.41 MPa. The absence of parameter input of x2 (friction pressure) and speed of rotation of x1 on the weld joint could be explained in the survey. Consequences of an increase in two previously located parameters influence the increase in the welded joint resistance until it reaches its limit and then decreases again. The reason is increased plastic deformation resulting from the application of excessive pressure and rotational speed [7].
3.1.3. Response surface methodology (RSM)
To further illustrate and discuss the effect of each factor and the interactions between these factors we were referred to the 3D response surface plots which were drawn as three dimensional plots of two factors while the other factor was kept constant. The 3-dimentional response surface for UBS (MPa) is shown in Fig. 7.
Fig. 7a represents UBS for different values of rotation speed (X1) and friction pressure (X2) for a constant friction time (X3). It is clearly that the response (UBS) increases when friction pressure (X2) increase independently. Fig. 7b illustrates combined effect of rotation speed (X1) friction time (X3) for a constant value of friction pressure (X2) on UBS response. It can be seen that UBS increases as friction time (X3) decreases at friction pressure values. Therefore, Fig. 7c shows effect of friction pressure (X2) and friction time (X3) on UBS at constant value of rotation speed (X1). It can be seen that at high values of friction time t, UBS increases independently. As reported in previous work [15], with increasing friction time, hardness and tensile strength are increased. Those are influenced by augmentation of young’s modulus and impact of friction time on welded joint also recognized in the micro-structural observation. Fig. 7 indicates UBS optimization results which can be achieved at lower values of rotation speed (X1).
3.1.4. Optimal design conditions using the desirability method
The main object of this study was to find the optimal conditions in which UBS will be maximized, that desirability function was well used by Suich and Derringer in 1980 to solve the problems related to the optimization of industry-related multiple responses which have been applied in many studies [38-40]. Fig. 8 illustrates the prediction profiler function of studied parameter, it can be concluded that optimized conditions were rotation speed of 2000 rpm, friction pressure of 24.77 MPa and friction time of 13 s for a predicted response UBS of 1406.892 MPa with a desirability value of 0.991859.
3.2 Experimental results:
3.2.1 Micrographic and metallographic analysis:
Fig. 9 shows an optical micrograph of welded joint for different zones, thermal affected zones (TAZ) and thermo-mechanical affected zones (TMAZ). As can be seen in Fig. 9, the welded joints were perfectly bonded; no cracks, low pores and no defect are observed. The grains are different in each affected zone, mainly resulting from the variation in temperature and pressure distribution. The grains are not uniform, elongated in the TAZ as shown in Fig. 9a & 9c, and refined in TMAZ as shown in Fig. 9d & 9f, cause of pressure application and heat due to thermo-mechanical action [41]. Furthermore, a reduction in ferrite and pearlite rate in each of steels is observed in compared to the base metals [24]. Ferrite/pearlite ratio remained the same in both steels after welding, i.e., the proportion of ferrite is predominant in C45 and conversely the rate of pearlite is higher in 16NiCr6.
Two flows are observed in the vicinity of the welded joint Fig. 9b & 9e; the connection line of two steels plays role of an inverse axis of symmetry. Noticed also, that the absence of interface is enrolled by existence of continuity; within a good junction between the samples, the grain size has decreased significantly compared to TMAZ, which is a direct consequence of a dynamic recrystallization (DRZ) of the grains [42-43]. Indeed, the welding zone consists of equiaxed grains as a reason of sufficient DRZ is occurred [44].
Fig.10 represents SEM and EDX analysis performed at the central region of bonding interface and also at the ends of welded joint. The results are similar, with little variation in diffusion layer between the main chemical elements of C45 and 16NiCr6 steel. Fig. 10a reveals most relevant advantages of friction welding can be easily deduced. In fact, a significant reduction in the number of pores compared to base metals can be seen, probably a consequence of high plastic deformation [45]. Fig. 10b shows inter-diffusion between Ni, Cr, Si and Mn characterizing the diffusion as the main bonding mechanism in the rotary friction welding process. The analysis records clearly diffusion of Cr and Ni through the interface from 16NiCr6 to C45. As a result of the diffusion, a gradual reduction of Cr and Ni in 16NiCr6 side adjacent to the interface and increasing of Cr and Ni in C45 side. Conversely is occurred for Si and Mn while these two last elements decrease in C45 interface side and increase in 16NiCr6 side, this result is in adequacy with references [7].
Fig. 11 shows EBSD map of welded joint of two samples S3(00-1) and S11(00+1). The maps show red, green and blue colour present 001, 011 and 111 planes respectively. It can be seen that the green colour dominates in the EBSD map for S3 welding parameters with low friction time and blue colour for S11 in high friction time, Fig. 11a & 11b respectively, which indicates that the grain orientation mainly concentrates in the normal direction of crystallographic plane {101} for S3 and {111} for S11.
For low parameters the grain size is not uniform than for high parameters, no special high-density orientation distribution. The statistical result of grain indicates that the proportion of average diameter grain size is 3.32 um in parameters with low friction time (00-1) and 2.15 um for parameter with high friction time (00+1). The origin of finer grains in the high friction time input joint can be attributed to micro-structural evolution during RFW.
3.2.2 Mechanical behaviour
RSM study shows that the most significant parameter influencing UBS is the friction time. In this perspective present work studied the mechanical behaviour of welded joint at the parameters of (0.0.-1) (0.0.0) and (0.0.+1), to demonstrate the contribution of friction time to weld joint behaviour. Valuable information’s on mechanical behaviour are provided using the measurements of hardness, wear and nano-indentation at different stages of the friction time.
Vickers micro-hardness distributions in specimens previously selected are shown in Fig. 12a. The measurements were carried out from C45 side to 16NiCr6 side. As expected, the micro-hardness reaches maximum values close to the interface and decreases very rapidly from TMZA until base metal. Fig. 12a shows a comparison between welded specimens with high, low and medium friction time, as observed from this figure can recognize an increase of micro-hardness from t: 9 s Hv 360 ± 10 to t: 11 s Hv 430 ± 10 and then decrease in t: 13 s to achieve Hv350 ± 10 where the base metal on both C45 and 16NiCr6 were approximately Hv 200 ±10 for C45 and Hv 220 ± 10 for 16NiCr6 , this increasing may have caused by micro-structural evaluations around the interface, diffusion of elements on the sides, work hardening, dislocation and refinement of grains.
The literature demonstrates a similar hardness profile for dissimilar material couples [46]. Microhardness at t: 13 s friction pressure, represent approximately 65% up than microhardness of the base metals which is very low compared to other fusion welding process, [24]. The decrease in hardness at t: 13 s which can be attributed to the decrease in temperature generated. In fact, after the plastic deformation, a reduction in friction is generally observed. The same behaviour has seen in Fig. 12c. The nano-indentation applied on the same samples shows a similar behaviour where the displacement into surface at t: 11 s is less than those at t: 9 s and 13 s, which leads us to suppose that the hardness at 9 and 11 s friction time is similar.
Nevertheless, Fig. 12d shows better understand the impact by increasing of welding time on the mechanical behaviour. Noticed there is a clear increasing of young’s modulus of 260 GPa compared to the lower friction times, t: 11 s is 210 GPa and t: 9 s is 230 GPa. Fig. 12b illustrates three different scratch profiles. It can be seen at the interface with substrate various coefficient of friction with change of welding time, also observed a deep fluctuations in both C45 and 16NiCr6 sides that may be related to presence of pores in that areas and can easily notice the decrease in these fluctuations at the weld interface, which maybe equates to decrease in that pores and confirms with Fig. 10a. Thus, close to the interface, a low deformation is observed due to the presence of TAZ, which reveals a high microhardness and that for all welded samples.
Regarding to the behaviour as a function of friction time variation, noticed that the friction coefficient decreases in the welded zone, which can be explained by high grains refinement. On the other hand, the variation of friction coefficient shows an increase at t: 11 s, which leads us to suppose that the grains have coalesced, this coefficient relapses at t: 13 s, due to grain disintegration formed after t: 11 s.
Bending fracture surface micrographs by SEM were performed on specimen S11 (0.0.1) and S7 (1.1.-1). As presented in Fig. 13, bending specimen S11 shows that the fracture mostly takes place at rotary part (C45 side), with elongated grain structure at fracture zone, the SEM observation indicates a river like pattern that commonly attributed to the brittle fracture [47]. The elongated structure at some region shows ductile fracture [48]. Fig. 13a shows detailed view of the fracture surface in which the structure is elongated and dislocated, which’s remarkable from one zone to another. Fig. 13b and 13c illustrate fracture surface for steels are with half bubbles or cups, the latter are characteristic of a ductile fracture and are formed by growth of cavities in the material. Ductile fracture is preceded by significant plastic deformation, often resulting in cups linked to decohesion around inclusions that act as initiation of fracture. Fracture surfaces show the presence of several cups of sizes between 5 to 10 μm. These cups extend in the tensile direction. These cavities gather and coalesce in order to accelerate the fracture.