Polyoptimisation of the refill friction stir spot welding parameters applied in joining 7075-T6 Alclad aluminium alloy sheets used in aircraft components

Aluminium alloys are an intensively investigated and widely used group of materials in the aircraft industry due to their high strength and low density. The 2xxx and 7xxx series aluminium alloys are commonly used to make up aircraft skins, cowls and other aircraft structures. The basic criterion governing the use of aluminium alloys for aircraft parts is the possibility of combining individual elements to ensure the greatest possible strength of the joint [1‐3]. The attractiveness of aluminium is that it is a lightweight metal and it is one of the most easily fabricated of the high-performance materials. Key features of aircraft structures are the lowest possible weight and a sufficiently low manufacturing cost [4].

The aluminium alloys used in the aircraft industry are mainly joined by bolting, riveting and bonding. Resistance spot welding (RSW) is a common method for the joining of thin-walled steel structures because of its advantages such as low-cost, reliability, high speed and ease of operation and automation. The RSW process typically involves placing two or more overlapping metal sheets between two electrodes and then applying pressure onto the electrodes in order to clamp the workpieces together [5, 6]. Then, electrical current is supplied to the sheets to be joined via the two electrodes for a specific period of time. This results in heat generation at the material and consequently a molten nugget is formed [5]. RSW of aluminium alloys is difficult due to low bulk resistance and high electrical and thermal conductivity. It requires pressure welding machines with high welding currents. The presence of an oxide layer on the surface of aluminium alloys, which is characterised by high contact resistance, causes rapid degradation of the electrode tip [7]. Another problem of RSW is the warpage deformation of the asymmetric sheet structures which results from the changed residual plastic strain due to thermal deformations [8, 9].

The friction stir spot welding (FSSW) technique has been widely studied by many authors. Descriptions of the method, including the relations between the process parameters and joint strength, were provided by, for example, Cao et al. [10], Chen [11] and Kubit et al. [12]. Refill friction stir spot welding (RFSSW) is a modern modification of the FSSW technique which has been extensively investigated over recent years. RFSSW is a solid-state joining technology which connects two similar or dissimilar materials together with minimal heat input or distortion.

The effect of the RFSSW process parameters on the joint microstructure and the load capacity of the joint has become a focus of the investigations of Shen et al. [13] who found that the overlap shear strength increases with increase in weld time and plunge depth due to increasing nugget diameter. Shen et al. [14] found that the void in the RFSSW weld played an important role in joint strength. Furthermore, it was also observed that the main feature affecting the mechanical properties of the joint is the Alclad between the upper and lower sheets. Oberembdt et al. [15] concluded that the most effective variable for controlling the joint strength was plunge depth. Tier et al. [16] studied the effect of tool rotational speed, plunge depth and welding time on the microstructure and shear strength of aluminium joints. It was found that the most significant variables influencing the mechanical performance of welds are tool rotational speed and plunge depth. In contrast volumetric defects have little influence on the shear strength of the joints. Verastegui et al. [17] applied the Taguchi statistical method to find out the set of parameters indicated to produce a joint with higher strength. He found that the galvanised layers of sheet to be joined do not cause any substantial effect on joint strength.

The state of knowledge concerning the phenomena occurring during the RFSSW process means that it is not fully understood in a satisfactory way, which results in difficulties in the selection of the optimal welding process for joining specific aluminium alloys [18‐20]. The welding of the Alclad covered aluminium alloy sheets commonly used in the aircraft industry, which are the test material in this paper, is difficult to conduct. The Alclad protects metal sheets against corrosion. It will, however, diminish the mechanical properties of the joints because it cannot stir together with the base materials. So, Alclad within the weld nugget causes heterogeneity in the structure of the weld. Alclad also makes the process of recrystallisation difficult. The welding of Alclad sheets requires special attention and precise welding procedures. Many authors used the trial and error method to select optimal process parameters, which makes it difficult to generalise the relationship between process parameters and joint quality. In addition, the Alclad sheets required for optimal joining conditions have different parameters than is the case with plates without the plating layer. The difference is largely due to the fact that Alclad, i.e. high-purity aluminium (99.9%), is characterised by a significantly higher value of thermal conductivity than the 7075-T6 aluminium alloy. Therefore, the heat generated in the welding process is non-uniformly distributed in the sheets to be joined due to the rapid dissipation of heat through the Alclad layer.

Methods commonly used to plan experiments, such as the Taguchi method, allow one to limit the research plan and determine the maximum value of the regression function, usually taking into account only one criterion, the load capacity of the joint. The results of previous RFSSW welding tests [12, 21] indicate that the parameters ensuring the maximum load capacity of the joint, however, result in a large scatter of results. Therefore, the aim of the investigations was to develop the methodology to determine optimal values of the welding parameters ensuring the maximum load capacity of the joint with the smallest possible variation in the results. Multi-criteria optimisation was used to achieve this goal. The method presented required experimental determination of the influence of RFSSW parameters on the load-bearing capacity of single lap joints of the 7075-T6 Alclad aluminium alloy sheets commonly used in aircraft applications.

The selection of the optimal parameters of the welding process requires the determination of an adequate mathematical model in the form of the regression function W(x). Regression analysis was carried out using the least squares method with the following criterion assessing the quality of the approximation:

where the value of the function R is a certain measure of the deviation of the approximation function W(x) from the approximated function f(x), i = 1, ... and N, number of experiments.

During the approximation, the most frequently selected basic functions are monomials according to Weierstrass’ theorem. This theorem defines that for every function f(x) specified and continuous on a closed and limited interval [a, b] there exists a polynomial W = b₀ + b₁x₁ + b_mx^m, that approximates monotonously the function f(x) on the interval [a, b]. During the analysis, however, it was not possible to obtain such a polynomial with a rational m level which could be considered adequate. Therefore, the m-degree algebraic polynomial was adopted for the definition of the interactions between the RFSSW process parameters:

In Eq. (3), there exists L-number of unknown coefficients \( {b}_0,{b}_i^{(1)},{b}_{ij}^{(1)},{b}_{ij\dots \mathit{\ln}}^{(1)},{b}_{ij}^{(2)},{b}_{ii\dots m}^{(m)} \) while i, j, ..., n = 1, ..., S variables of a polynomial (3).

The assessment of the significance of the coefficients in the regression equation was performed by comparing their values with the critical value determined on the basis of the formula:

where: t_{(α, f)} = t_kr is the test value of the coefficient t determined based on the basis of the t-Student distribution table, r is the number of repetitions.

The Fisher-Senecor test was used to assess the adequacy of the regression equation with the test results. At the first stage of the analysis, the adequacy of the variance was determined, according to the following formula:

where \( \overline{y_i} \), average value of measurement results in the i-th experiment; \( \overline{\overline{y_i}} \), value calculated from the regression equation for the levels of input and output factors in i-th experiment; k, a number of terms in the regression equation (without a free term) after rejection of the insignificant terms; N, the total number of experiments.

was compared with the critical value determined from the Fisher-Snedecor distribution table. This allowed an adequate regression equation to be obtained describing the influence of the RFSSW process parameters on the load capacity of joints, with the following form:

The values of coefficients for the regression function describing the load capacity of the joint W_F(x) and standard deviation of the process W_σ(x) are given in Table 2.

Figure 9 shows a graph of the regression function for a constant value of duration of welding equal to x₃ = 1.5 s. The maximum error value of the regression function did not exceed 6.11%, while the mean square error between the experimental and mathematical modelling results was equal to 2.55%. The graph shows a clear increase in the load capacity of the joint with an increase in tool rotational speed and a local maximum of the regression function at a tool plunge depth of 1.5 mm. The shape of the function obtained can explain the large standard deviation values obtained with regard to the load capacity of joints for a tool plunge depth of x₂ = 1.5 mm and tool rotational speed x₁ = 2800 rpm. A regression function, after reaching the maximum, rapidly falls both towards the larger and smaller values of tool plunge depth. It is very difficult to set the tool at the appropriate plunge depth due to the high plasticity of the material (the sticking of the sheet material to the tool surface). Even a small error in the tool plunge depth can significantly affect the load capacity of the joint, which is manifested by a large variance of results.

At a tool plunge depth of x₂ = 1.5 mm (Fig. 10), an increase in tool rotational speed results in an increase in the load capacity of the joint. This is observed for durations of welding ranging from 1.5 to 2.5 s. A further increase in the duration of welding results in a sudden decrease in the load capacity of the joint.

The regression function describing the variation of process W_σ(x) that meets the Fisher-Snedecor adequacy criterion has a much simpler form (Table 2). The maximum error of the regression function in this case did not exceed 14.51%, while the mean square error was 14.59%. Figure 11 shows the influence of tool rotational speed and tool plunge depth on the process stability (standard deviation). Analysis of the chart indicates that the increase in tool rotational speed causes an increase in the value of the standard deviation. Therefore, the use of a tool rotational speed of 2800 rpm in order to assure maximum load capacity of the joint may not be justified. In a real structure consisting of a large number of joints, only some will be able to transfer the maximum load, which may contribute to reducing its reliability.

A similar tendency to reduce process stability can be observed by analysing the graph of the influence of the tool rotational speed and the duration of welding on the standard deviation of the load capacity of the joints (Fig. 12). An increase in the duration of welding also leads to a reduction in process stability.

In order to replace classic resistance welding by the RFSSW technique, thus ensuring a better quality of welds, it is necessary to select optimal welding parameters. This selection must guarantee not only a high load capacity of the joints produced, but also high process stability, characterised by the lowest possible value of the variance of the results obtained. This requires multi-criteria optimisation of the process and finding a compromise solution that meets the abovementioned mathematical model.

For the writing of the multi-criteria problem, the following designations have been adopted:

The problem of multi-criteria optimisation of the selection of process parameters can be written in the form of:

The one-criteria problem:

is an i-th partial problem, where the vector z^io ∈ D in which the i-th objective function reaches the extremum searched. The vector:

is a vector called the ideal (utopian) solution in the space of evaluations, while:

is the ideal solution for the function (8). Usually the ideal solution of function (8) is not available, which means that in the set of permissible solutions D there is no vector z^o, for which all objective functions reach the extremum searched. Therefore, effective solutions were searched for during the solution of the problem presented.

The set of effective solutions usually contains many solutions. Therefore, the goal of the problem presented was to select one compromise (optimal) solution from a set of effective solutions. For this purpose, function (8) has been reduced to a single-criterion form, with the scalarisation function s: R^k → R in the form:

Scalarisation of the function was carried out using the method of weighting the grades. Values of weights u_i > 0 of particular criteria f_i (fulfilling the condition u₁ + u₂ = 1) were assumed, and then the optimal solution of the problem was determined (13):

It is only possible to create a function \( \varphi (z)=\sum \limits_{i=1}^k{u}_i{f}_i(z) \) if all the values of objective functions are expressed in the same units and scales. Since the objective functions in this case were expressed in different scales of values, they were transformed into a dimensionless form:

Objective functions \( {f}_i^u \) take values for z ∈ D from the interval [0, 1] and they are dimensionless. The function describing the load capacity of the joint W_F(x) reaches the maximum value of 7801.3 N at a speed x₁ = 2800 rpm, tool plunge depth x₂ = 1.55 mm, and duration of welding x₃ = 1.5 s, and minimum value of 5613.5 N at x₁ = 2000 rpm, x₂ = 1.9 mm, and x₃ = 1.5 s. The maximum and minimum values obtained correspond to the extreme setting of parameters of the welding process at which the tests were carried out.

After transformation, the function describing the load capacity of the joint, which is a partial problem of the function (8), takes the following form:

The second function describing the standard deviation of the dispersion of results takes the highest value (380.87 N) at a tool rotational speed x₁ = 2800 rpm, tool plunge depth x₂ = 1.46 mm, and duration of welding x₃ = 3.5 s, while the minimum value (16.85 N) is at x₁ = 2226.55 rpm, x₂ = 1.9 mm, and x₃ = 1.81 s. Because both functions are to be maximised in the method of weighting the grades, the second function will take the form:

After the unitarisation, an optimal solution of the problem is determined according to:

The optimal solution of the function (17) is an effective solution to the multi-criteria problem. The form of the solution depends on the weight values u_i adopted. If during the calculations, it is assumed that the load capacity of the joint is the most important parameter determining the quality of the joint (u₁ = 1, u₂ = 0), then the solution obtained coincides with the optimal solution of the partial problem (Eq. 15) (point P1 in Fig. 13).

In the case of adopting equal values of the weights (u_i = 0.5), the function (17) achieves the maximum for a tool rotational speed x₁ = 2229 rpm, tool plunge depth x₂ = 1.60 mm, and duration of welding x₃ = 2.02 s. This corresponds to the load capacity of the joint equalling 7071.5 N and a standard deviation of the dispersion of results of 86.22 N. If, on the other hand, different weight values are adopted during the optimisation process, then another compromise solution can be obtained. Assuming that the load capacity of the joint is more important than the process variance (u₁ = 0.6, u₂ = 0.4), the optimal solution moves to the point corresponding to the rotational speed x₁ = 2256.05 rpm, tool plunge depth x₂ = 1.55 mm, and duration of welding x₃ = 3.4 s (point P2 in Fig. 13). The application of the given process for setting parameters provides the opportunity to obtain a joint load capacity of 7462.37 N with a standard deviation of the dispersion of results of 142.09 N. In order to verify the results obtained, 6 welds were made with parameters corresponding to the point P2 in Fig. 13, and then tensile/shear tests were performed. The average value of the load capacity of the joint was 7511 N, which is 0.6% more than the value obtained as a result of optimisation with a standard deviation of 102.3 N.

Welds fabricated with optimal parameters were characterised by a lack of visible incomplete refill between the weld side and the upper sheet, a lack of voids on the outer edge of the weld and the lack of a clear structural notch (Fig. 14). The Alclad swirl existing in the bottom part of the weld results from insufficient stirring of the Alclad with the base materials. It is a basic defect of joining clad coated sheets [12, 13, 21, 23]. The cross section of the RFSSW joint thus formed reveals four regions in terms of the microstructural characteristics of the joint in the sequence from the SZ towards the BM (see example in Fig. 14). The visible HAZ has a small width and depth. This is due to the presence of the Alclad, which has a higher thermal conductivity (229 W/mK) than the BM (134 W/mK) and very rapidly transfers the heat out of the joint.

In this paper, a method of optimisation of the RFSSW process parameters, i.e. rotational speed, tool plunge depth, and welding time, was presented that assures the maximum load capacity of the RFSSW joint. The main conclusions drawn are as follows:

RFSSW is one of the most modern methods of joining aluminium alloys. The research conducted has shown that this method can be successfully used in the aircraft industry, due to the possibility of ensuring high strength joints while reducing the labour consumption in the process of the assembly of welded structures.