### 1. Introduction

^{1)}. There are many problems that occur during the fusion welding of aluminum and its alloys such as hot- cracking, porosity, oxidation and alloy segregation

^{2-4)}. Fusion welding of magnesium and its alloys also presents certain problems like complex thermal stress and severe distortion, porosity and crack in the weld zone, and excess eutectic formation

^{5)}. Friction Stir Welding (FSW), a solid state welding process, patented by The Welding Institute (TWI), eliminates most of these problems

^{6)}. In FSW, metallurgical bonding between similar or dissimilar materials can be created without melting as it is a solid-state welding process.

^{7)}. In this method, the main objective is to optimize the response surface that is influenced by various FSW process parameters. The steps involved in this method are: (i) designing a series of experimental condition based on the factor and its level, (ii) deriving a mathematical model using second order equation with best fit, (iii) finding the optimum process parameters that produces a maximum response value, and (iv) indicating the direct and interaction effect of the process parameters through two or three dimensional plots

^{8,9)}.

^{10)}investigated the effect of tempered conditions of base material (AA2014) on the joint strength and the optimized FSSW process. Karthikeyan et al

^{11)}optimized FSSW process parameters such as tool rotational speed, plunge rate, plunge depth and dwell time on AA2024 aluminum alloy using RSM, and found that the maximum TSFL was achieved at 9.39 kN under the welding conditions of tool rotational speed, plunge rate and plunge depth of 1000rpm, 13.56 mm/min, 5.178 mm, and 5.1 sec respectively. Ramanjaneyulu et al

^{12)}optimized the yield strength, tensile strength and ductility of friction stir welded AA2014-T6-jwj-34-3-23 aluminum alloy using RSM, and also found that AA 2014-T6-jwj-34-3-23 aluminum alloy welded with hexagonal tool pin profile had the highest tensile strength and elongation as compared to the conical, triangle, square, and pentagon pin profile, using a four factor five level central rotatable design matrix.

^{16)}, dissimilar Al alloys

^{17)}, and Mg alloys

^{18)}. However, no effort is yet made to perform this optimization on FSSW of AA6061 and AZ31B dissimilar joints using RSM. This investigation is focused on the optimization of the important FSSW process parameters such as tool rotational speed, plunge rate, dwell time, and tool diameter ratio to attain the maximum strength in dissimilar joints of AA6061 aluminum and AZ31B magnesium alloys.

### 2. Experimental Procedure

^{8-15)}, the independent process parameters affecting the strength of FSSW joints were identified as tool rotational speed(N), plunge rate(R), dwell time(T) and tool diameter ratio(D). The tool diameter ratio (D) is defined as the ratio between the tool shoulder diameter to the pin diameter. Feasible limits of each process parameter were chosen in such a way that the joint should be free from visible defects. The upper limit of the each process parameter was coded as +2 and lower limit as −2. The intermediate coded values were calculated from the following relationship.

##### Table 1

Alloy | Zn | Ti | Fe | Cu | Al | Mn | Si | Mg |
---|---|---|---|---|---|---|---|---|

AZ31B | 1.2 | - | 0.005 | 0.05 | 2.9 | 0.2 | 0.1 | Bal |

AA6061-T6-jwj-34-3-23 | 0.25 | 0.15 | 0.7 | 0.25 | 95.8 | 0.33 | 0..66 | 1.10 |

##### Table 2

Alloy | 0.2% Yield strength (MPa) | Ultimate Tensile strength (MPa) | Elongation in 50 mm gauge length (%) | Hardness@0.05Kg load (HV) |
---|---|---|---|---|

AZ31B | 234 | 254 | 15 | 164 |

AA 6061-T6-jwj-34-3-23 | 276 | 310 | 12 | 107 |

_{i}is the required coded value of a variable X; X is any value of the variable from X

_{min}to X

_{max}; X

_{min}is the lower limit of the variable and X

_{max}is the upper limit of the variable. The selected process parameters with limits are presented in Table 3.

##### Table 3

##### Table 4

### 3. Development of Empirical Relationship

_{0}is the average of responses and b

_{1}, b

_{2}… b

_{4}, b

_{11}, b

_{13}… b

_{44}are the coefficients that depend on the respective main and interaction effects of parameters. DESIGNEXPERT 9.1 software was used to calculate the values of these coefficients and presented in Table 5. After determining the coefficients, the empirical relationship to predict TSFL was developed. The developed empirical relationship in the coded form, is given below

##### Table 5

##### (4)

^{2}, R

^{2}, T

^{2}and D

^{2}are significant model terms. Values greater than 0.10 indicates that the model terms are not significant. The lack of fit F-value of 1.78 implies that the lack of fit is not significant relative to the pure error. The non-significant lack of fit is good. The co-efficient of determination R

^{2}values gives the goodness of fitness of the model. For a good model, R

^{2}valueshould be close to 1. In this model the calculated R

^{2}value is 0.99. This implies that 99% of the experimental data confirms the compatibility with the data predicted by the developed model. The value of the adjusted R

^{2}of 0.98 also indicates the high significance of the model. The predicted R

^{2}value is 0.96, which shows reasonable agreement with the adjusted R

^{2}of 0.98. Adequate precision measures the signal to noise ratio, and a ratio greater than 4 is desirable. The high value shows that this model can be used to navigate the design space. The observed values and predicted values of the responses are close to each other, which indicate an almost perfect fit of the developed empirical relationship (Table 7 & Fig. 6).

##### Table 6

### 4. Optimization of FSSW process parameters

^{19)}. Response surface graph and contour plots play a very important role in the study of a response surface. It is clear from Fig. 7(a-f) that the TSFL increases with the increase of tool rotational speed, plunge rate, and tool diameter ratio to a certain value and then decreases. It is also observed that the initial increase of dwell time increases the TSFL to a certain value and further increase of dwell time keeps the TSFL to remain constant.

^{20)}, re-dissolution and coarsening of strengthening precipitates at the nugget

^{21)}and lower dislocation density that decrease the TSFL value

^{22,23)}. The apex of each response graphs provides the optimal combination of parameters to attain maximum strength (TSFL). Similarly, the center of the contour plots provides the optimal combination of parameters to attain maximum strength (TSFL). Fig. 8 illustrates the perturbation plot for the response TSFL of FSSW joints. This plot provides silhouette view of the response surface and shows the change of TSFL while the parameter moves from the reference point, with all other parameters are held constant at the reference value. The perturbation plot indicates that deviation from the reference point is minimum at the maximum TSFL. It is also inferred that the TSFL varies significantly with change in tool rotational speed and plunge rate, whereas TSFL does not change significantly with variation in tool diameter ratio and dwell time. Fig. 9 shows the load displacement curves obtained during the tensile test for the typical joints.

### 5. Conclusions

1) An empirical relationship was developed to estimate the tensile shear fracture load (strength) of friction stir spot welded dissimilar joints of AA6061 aluminum and AZ31B magnesium alloys incorporating important parameters. This relationship can be effectively used to estimate TSFL at 95% confidence level.

2) The maximum TSFL value of 3.61 kN was exhibited by the joint fabricated using a tool rotational speed of 1000rpm, plunge rate of 16 mm/min, dwell time of 5 sec and tool diameter ratio of 2.5.

3) Of the four process parameters investigated, the tool plunge rate was found to have the greatest influence on tensile shear fracture load, followed by tool rotational speed, tool diameter ratio and dwell time (as per the F ratio).