1 Introduction

Refill friction stir spot welding (RFSSW) is solid-state joining technology which is characterized by reliability, safety and the fact that it is not very time-consuming. This process is a more recent application of the friction stir welding (FSW) process. RFSSW could be used for materials not recommended for fusion welding i.e. aluminium alloys (especially 2XXX and 7XXX alloy series) or titanium [1]. This technology along with other modern joining methods (e.g. electron beam welding, laser welded joint, riveting and hybrid joints: spot welding–adhesive) are of great technological interest [2–7].

In RFSSW, a specially designed rotating tool (Fig. 1) is used to create the weld spot. The tool is plunged into the workpieces to plasticize and mix the material. Heat is generated by frictional forces and due to deformation of the parent material [8].

Fig. 1
figure 1

Tool for RFSSW process: a during plunging and retraction steps, b after plunging into workpieces

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To introduce the tool design, select process parameters, predict void formation, and simulate material flow, FEM models could be used. The first approach of numerical analysis is the thermo-mechanical model. Most thermal analyses use a heat source distributed over the tool surface, with a heat flux per unit area. The heat is generated at the interface by friction or by viscous dissipation in a layer that is sufficiently thin. In a different approach, the heat input may be distributed over the probe volume. Such approximations lose significance as the distance from the heat source increases due to heat flow problems. The next assumption is usually to ignore tool tilt and the effect of metal flow on the distribution of heat generation. The source is treated as axisymmetric. The smooth circumferential distribution of heat is the consequence of the high rotational speed and convective heat flow by motion of the material [9, 10]. Computation of the thermo-mechanical fields during all the FSW phases (plunge, friction, retraction) without information about the process, only relying on accurate constitutive and friction models, is presented in [11, 12]. Based on the numerical and experimental investigations, the results of the model are found to be very sensitive to small variations of the friction coefficient. The study of the different process conditions shows that the main phenomena taking place during FSW can be simulated with the right sensitivities. Based on further analysis presented in [13], a valid model to determine the strength and temperature of the tool were constructed.

Another method for modelling structures welded by FSW is mechanical analysis. In [14] the analysis of stiffened panel structures with a friction stir weld was carried out. The base material and weld were modelled as 3D-solid elements. The difference of geometry after the welding process and properties of the materials were included. There is a high computational cost associated with full a 3D-solid model. Very finite meshes may need to be used and large strain shell problems can be complicated to solve [15].

For shorter modelling and computational times, 3D-shell elements are used. The three-dimensional continuum theory is shorter compared to a full three-dimensional analysis. It is important if many different configurations have to be analysed during the initial design phase of the structure. It is possible to model the RFSSW spot and heat affected zone (HAZ) as 3D-solid elements and the sheet base material as shell elements [16]. A comparison of three types of models was presented in [17]. A full 3D-solid model is the most exact, but it might be used only for small constructions. The restrictions are the long total solution time and computer requirements. The full shell model or 3D-shell model could be used for preliminary calculations to determine the weakest area in the structure or for large structures. Papers [18, 19] present the analysis of complex structures with 3D-solid elements for the weld spots and shell elements for the sheets.

2 Goal and scope of work

Determining crack locations by numerical and experimental analyzes of RFSSW joints during the tensile test is the goal of this paper. The structures were assessed regarding tensile strength, strains and deformations. 6061-T6 aluminium alloy sheets are welded as lap joints. Two types of geometry with four and five RFSSW spots are analysed—Figs. 2 and 3. Each sample is modelled as a full 3D-solid model. The numerical results are compared with the experimental investigation which was carried out using a non-contact system allowing for measuring displacements and strains in real time.

Fig. 2
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Geometry of sample with four RFSSW spots, mm

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Fig. 3
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Geometry of sample with five RFSSW spots, mm

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The surface area of spots in the sample with four and five RFSSW spots are respectively 208.23 and 271.85 mm2. The RFSSW process were made with following parameters: thickness of the spot of 2.2 mm, tool rotational speed of 2000 rpm, tool input speed of 0.7 s, tool output speed of 0.5 s.

3 Experimental investigation

Figure 4 shows the displacement–force diagram during the tensile test. The maximum force for the sample with four spots is 18.48 kN, while the maximum force for the sample with five spots is 21.19 kN. The displacements are respectively 1.94 and 2.27 mm. The shape of the curves is similar, especially for the displacement value of 1.5 mm. However, the tensile curve for the sample with five spots is longer due to the larger surface area of the spot group.

Fig. 4
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Displacement–force diagram

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The strain distribution for the analysed samples are presented in Fig. 5. The distributions are symmetrical with respect to the vertical axis (Z-axis). In each sample, the area of maximum value concentration is located on the edge of the spot group and base material, where the sample fractures are Fig. 6.

Fig. 5
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Samples during tensile test: a strain distribution for four RFSSW spots, b strain distribution for five RFSSW spots

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Fig. 6
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Samples after the tensile test: a four RFSSW spots, a five RFSSW spots

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4 Computational models

The numerical studies were carried out with the ADINA System based on the FEM. The boundary conditions and type of load are the same for each sample: all the degrees of freedom on the first external edge of the sample are fixed, the second external edge of the sample has one free degree of freedom (X-translation) and that edge is loaded by displacement. The load values are equivalent to the displacements which were reached during the experiments. Plastic orthotropic material with following parameters: modulus of elasticity 68.9 GPa, yield strength 276 MPa, Poisson’s ratio 0.33 and density 2700 kg/m3, are used for each model. The meshes of the samples are shown in Figs. 7 and 8.

Fig. 7
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Mesh of sample with four spots: a whole model view, b RFSSW spots view

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Fig. 8
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Mesh of sample with five spots: a whole model view, b RFSSW spots view

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The sheets and spots are modelled as 8-node 3D-solid elements. Between the 3D element surfaces of the sheets, the contact conditions are assumed. The sheet and spot elements are connected in nodes. The boundary conditions and load are added to the surfaces. The model with four RFSSW spots is comprised of 27,851 3-D solid elements, which is equivalent to 22,176 nodes. The model with five spots is comprised of 34,272 finite elements, which is equivalent to 32,735 nodes. The calculations are performed in 100 time steps.

5 Results

The total solution time for the sample with four RFSSW spots was 1794.40 s. The total memory used by the program for that model was 525.3 mb. However, the total solution time for the sample with five RFSSW spots was 2488.85 s and total memory used by the program for that model was 640.4 mb.

The effective plastic strains for the samples with four and five spots are presented in Figs. 9 and 10 respectively.

Fig. 9
figure 9

Effective plastic strains for sample with four spots: a X–Z view, b X–Y view, mag. ×5

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Fig. 10
figure 10

Effective plastic strains for sample with five spots: a X–Z view, b axonometric view, mag. ×5

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In both samples, the plastic effective strains distributions are symmetrical with respect to the X-axis and similar in both sheets. In each kind of sample, the strain maximum is located on the inner side of the sheet surrounding the RFSSW spots, on the part which is fixed. The extreme values are concentrated on the inner sides of the spots, which is difficult to specifically identify. The minimum is also located on the inner side of the sheet surrounding the RFSSW spots, but on the part which is free.

The Y-displacement and deformations for the samples with four and five spots are presented in Figs. 11 and 12.

Fig. 11
figure 11

Y-displacement (mm) and deformations for the sample with four spots, mag. ×5

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Fig. 12
figure 12

Y-displacement (mm) and deformations for the sample with five spots, mag. ×5

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The free parts of the sheets are deformed. The direction of the deflection is consistent with respect to the Y-axis. The deflection for one sheet of the samples with four and five spots are 4.5 and 4.7 mm. Furthermore, the deformation is near the welded area.

6 Discussion

The higher strength of the sample with five RFSSW spots than the sample with four spots is caused by the larger surface area of the spots group. The shape of the tensile curve is similar for both samples. It proves the similar behaviour of the structures. In each of the analysed cases, the fracture is on the edge of the spots and base material. In accordance with articles [20–22] the spot welds in the groups are not separated from each other, nor from the sheets, as in the case of welding by a single spot joint.

The experimental and numerical analyses prove that regardless of the joint geometry, the strains concentration is in the area of the base material near the RFSSW spots. It indicates the places of fracture initiation.

The deformations of sheets parts are the result of non-fixed edges with respect to the Y-axis. The deformation of the welded area is caused by the strength of the joints and deflections of the sheets.

7 Conclusion

The analysis of RFSSW joints with different numbers and spot arrangement of are investigated. The following conclusions were made:

  • It is possible to model those joints as 3D-solid elements. Good agreement is observed with the specimens compared to the experimental results.

  • The strength of the sample with five RFSSW spots is higher than the sample with four RFSSW spots.

  • In the each sample, the strains concentration is observed on the outer edge of the spots, between the inner surfaces of the sheets.

  • In each case, the fracture is on the edge of the spots and base material. The spot welds in the groups are not separated from each other, nor from the sheets.

  • The free parts of sheets are deflected with respect to the Y-axis.