Joining Sheets to Tubular Profiles by Tube Forming RESULTS AND DISCUSSION Compression Beading The first stage of the proposed joining process consists of compression beading of thin-walled tubes and is based on a local buckling collapse mechanism that drives material to flow outward and, eventually, inward. In fact, by varying the ratio between the initial gap height and the reference radius of the tube l gap /r 0 it is possible to categorize material flow into two different groups; for small values of l gap /r 0 (say, l gap /r 0 1) tube beads develop predominantly outward whereas for increasing values of l gap /r 0 , tube beads are shaped under a combination of outward and inward material flow. The later gives rise to a defect (geometrical depression) on the surface of the tube located at the vicinity of the bead as shown in the rightmost tubular specimen pictured in Figure 6a (please refer to the oval mark). The width of the beads is also influence by the ratio l gap /r 0 and can be made slightly larger or smaller by changing the initial gap height l gap within the aforementioned process formability window. Figure 6b shows the experimental load- displacement evolution during the first stage of the joining process for cases 1 to 4 of Table 1. Two different trends are observed; for specimens with l gap /r 0 >0.31 it is possible to identify a local peak followed by a subsequent decrease in the compressive load, whereas for l gap /r 0 =0.31 the compressive load increases monotonically without showing a local peak. The differences between the two types of load-displacement curves are caused by the fact that for l gap /r 0 >0.31 the tubular specimens will always experience collapse under local buckling. In this context, it is worth notice that although the trend of the experimental load-displacement evolution registered for l gap /r 0 =1.25 has been included in the first category it shows peculiar characteristics related to the formation of a small secondary load pick caused by changes from inward to outward material flow at the last stage of the process. The insets included in Figure 6b, obtained from finite element modelling, present an insight into the aforementioned surface depres- sion that develops at the vicinity of the bead for l gap /r 0 =1.25. The following section of the chapter provides comprehensive results of finite element model- ling supported with experimental data for joining applications involving compression beading and external inversion. The deformation mechanics of joining sheets to tubular profiles by means of two-stage compression beading will not be ad- dressed because the process feasibility window of the second stage is identical to that of the single stage compression beading. Joining by Compression Beading and External Inversion Figure 7 shows the experimental and finite ele- ment predicted evolution of the load­displacement curves for a test case in which joining was suc- cessfully accomplished (case 2 plus 6 of Table 1). Two different stages are distinguished: (i) shaping the tube beads by compression (Figure 7a) and (ii) clamping the sheet to the tube by means of external inversion (Figure 7b). In case of external inversion two different numerical predictions are provided as a result of numerical modeling being performed with rigid or plastically deformable sheet panels (see Figure 5). The numerical and experimental load-displace- ment curves compare well and the insets, showing details of the finite element simulation at various stages of deformation, provide a good insight on material flow behaviour during the joining process. As mentioned in the previous section, the evolution of the load-displacement curve during the first stage of the joining process (compression beading) is dependent on the ratio l gap /r 0 being ap- propriate for developing plastic instability modes after attaining the critical instability load. 329