*3.4. Alignment of the "Mortise-And-Tenon" Joints*

The crashworthiness performance of the new crash boxes with "mortise-and-tenon" joints raises the question of the alignment of the protrusions of the flat-shaped surface heads of the tenons above the adjacent sheet panel, after compression. Should the flat-shaped surface heads be collinear or perpendicular to the longitudinal axis of the crash box?

Experiments performed by the authors revealed that the flat-shaped surface heads must be perpendicular to the longitudinal axis of the crash boxes because if they are collinear, they are easily pulled-out during axial crushing, diminishing the overall performance of the crash box (Figure 9).

**Figure 9.** *Cont*.

**Figure 9.** Thin-walled crash boxes with double-hat section assembled by sheet-bulk compression with "mortise-and-tenon" joints after axial crushing: The flat-shaped surface heads of the tenons are (**a**) collinear (front view), (**b**) collinear (side view), (**c**) perpendicular (front view), and (**d**) perpendicular (side view) to the longitudinal axis of the crash box.

#### **4. Discussion**

The evolution of the force with displacement for the quasi-static and dynamic axial crush tests performed with the two different types of crash boxes allow concluding that the new proposed "mortise-and-tenon" joints can successfully replace resistance spot-welds. In fact, Figure 8 shows that the overall trend of the force-displacement curves is similar with peak forces to trigger collapse being higher in the dynamic crush tests. In case of the crash boxes assembled with "mortise-and-tenon" joints, for example, the peak values increase from 89 kN to 115 kN when dynamic conditions are applied.

The energy *E* absorbed by the crash boxes during the axial crush tests are obtained from the areas below the experimental force-displacement curves of Figure 8,

$$E = \int\_0^{\delta\_{\text{max}}} F d\delta\_\prime \tag{6}$$

where *δ*max = 55 mm is the maximum specified testing distance (refer to Figure 8).

The results are shown in Figure 10 and allow concluding that the new type of crash box can absorb an overall level of energy similar to that of the resistance spot-welded crash boxes.

The maximum absorbed energy in the dynamic tests, is approximately 30% higher than in the quasi-static tests. This increase of crashworthiness performance with velocity is attributed to the strain-rate sensitivity of the HSLA 340 steel [16]. However, it is worth noting that the maximum absorbed energy in the dynamic tests is approximately 25% smaller than the total energy provided by the drop weight machine (3.2 kJ) because part of this energy is lost in the conversion of linear momentum between the mass *M* of the falling ram and the mass *Mt* of the tool, in the elastic deformation of the tool and of the drop weight testing machine, and in the vibration of its different components.

Another result that is relevant from a manufacturing point of view is the total energy required to fabricate a "mortise-and-tenon" joint and a resistance spot-welded joint. From the experimental and numerical evolution of the force with displacement for the first and second stages of the sheet-bulk compression of the tenons it may be concluded that approximately 7 J and 10 J will be needed to accomplish both stages. Thus, by considering these values of energy as well as that required to perform the lancing operation, it is concluded that the total amount of energy to fabricate a "mortise-and-tenon" joint is a very small fraction of that required by a resistance spot-welded joint (Figure 11). This is an important advantage of the new proposed type of crash boxes regarding environmental friendliness.

**Figure 10.** Experimental evolution of the absorbed energy with displacement for the axial crush tests of thin-walled crash boxes with double-hat section assembled by sheet-bulk compression with "mortise-and-tenon" joints and by resistance spot-welding: (**a**) quasi-static tests; (**b**) dynamic tests.

**Figure 11.** Energy required to produce "mortise-and-tenon" and resistance spot-weld joints. The energy required by the mortise-and-tenon joint is referred to the vertical left axis whereas that of the resistance spot-welded joint is referred to the vertical right axis.

#### **5. Conclusions**

The fabrication of crash boxes by sheet-bulk compression with "mortise-and-tenon" joints can successfully replace conventional production processes based on resistance spot-welding. The crash boxes with "mortise-and-tenon" joints can absorb the same amount of energy as those with resistance spot-welding joints in quasi-static and dynamic axial crush tests. They can also avoid the problems caused by residual stresses in the resistance spot-welding of panels made from dissimilar materials with different thicknesses.

The greater applicability of the new crash boxes comes with a disadvantage regarding productivity due to the multi-stage characteristics of the proposed joining by forming process. However, this disadvantage can be offset by the environmental friendliness resulting from the total required energy to assemble a crash box by sheet-bulk compression with "mortise-and-tenon" joints being a very small fraction (1.3%) of that required by resistance spot-welding.

**Author Contributions:** D.F.M.S., C.M.A.S., and I.M.F.B. designed and fabricated the crash boxes with "mortise-and-tenon" joints. C.V.N. and C.M.A.S. designed and fabricated the crash boxes with resistance spot-welded joints. D.F.M.S., C.M.A.S., and I.M.F.B. performed the quasi-static and dynamic axial crush tests. D.F.M.S. and C.V.N. performed the finite element simulations. C.M.A.S. and I.M.F.B. analyzed the results. L.M.A. and P.A.F.M. contributed as advisors and proposed the subject. P.A.F.M. supervised the overall research work and wrote the article with the collaboration of all the other authors.

**Funding:** This research was funded by Fundação para a Ciência e a Tecnologia of Portugal under LAETA— UID/EMS/50022/2013 and PDTC/EMS-TEC/0626/2014.

**Acknowledgments:** The authors would like the technical support of Mahsa Seyyedian Choobi in the resistance spot-welding experiments.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, and in the decision to publish the results.
