**2. Materials and Methods**

#### *2.1. Mechanical Characterization*

The new proposed joining by forming process can easily assemble thin-walled crash boxes with individual panels made from dissimilar materials with different thicknesses. However, it was decided to select a single high-strength low alloy steel (HSLA 340) with 1 mm thickness and 7 μm thickness galvanized coating to ensure a fair comparison of the crashworthiness performance of the new crash boxes against those assembled by resistance spot-welding.

The mechanical characterization of the HSLA 340 steel was performed by means of stack compression tests [13] due to its capability to characterize the material stress response up to the large strains that were found in the compression of the flat-shaped surface heads of the tenons. The stack compression tests were carried out at room temperature in a hydraulic testing machine (Instron SATEC 1200 kN, Norwood, MA, USA) with a cross-head velocity of 10 mm/min and made use of multi-layer cylinder test specimens that were assembled by piling up 10 circular disks with 10 mm diameter cut out from the supplied sheets by wire-electro discharge machining (wire-EDM).

#### *2.2. Fabrication of the Crash Boxes*

The thin-walled crash boxes with double hat-shaped sections were made from two individual formed panels that were assembled by sheet-bulk compression with "mortise-and-tenon" joints placed every 40 mm along their flanges. Table 2 provides the geometry of the crash boxes and a schematic detail of the new proposed joining by forming process.

Conventional thin-walled crash boxes assembled by resistance spot welding were included in the experimental work plan for reference purposes. The welding parameters were selected by finite element modelling (refer to Section 3.2) and the joints consisted of around 5.4 mm diameter spots, positioned similarly along the flange as the "mortise-and-tenon" joints.


**Table 2.** Geometry and parameters of the thin-wall crash boxes assembled by sheet-bulk compression with "mortise-and-tenon" joints and by conventional resistance spot-welding.

#### *2.3. Axial Crush Tests*

The crash boxes were tested for quasi-static and dynamic axial crushing at room temperature. The quasi-static crush tests were performed in the hydraulic testing machine (Instron SATEC 1200 kN) that had been used in the mechanical characterization of the material. A cross-head velocity *v* = 10 mm/min was utilized, and the tests were stopped after reaching a prescribed crushing distance of 55 mm (approximately 1/3 of the initial length of the crash boxes).

The dynamic crush tests were performed in a drop weight testing machine that was designed and fabricated by the authors. The machine and its main components are schematically shown in Figure 2a. The mass *M* and drop height *H* of the falling ram can be adjusted up to maximum values of 250 kg and 5 m, respectively.

**Figure 2.** The drop weight testing machine: (**a**) schematic representation and identification of its main components; (**b**) photograph of the tool utilized in the crush tests.

The tool utilized in the quasi-static and dynamic crush tests is shown in Figure 2b. The crash boxes were placed centrally in the tool, without any further support and were subsequently compressed between the top and bottom flat platens. The tool was instrumented with a load cell based on traditional strain gauge technology in full wheatstone bridge with a capacity of 500 kN, a nominal sensitivity of 1 mV/V, and an accuracy class of 0.7. The load cell was connected to a signal amplifier unit (Vishay 2310B) and a personal computer data logging system based on a DAQ card (National Instruments, PCI-6115, Austin, TX, USA). The displacement transducer is a commercial linear variable differential transformer (Solartron LVDT AC15, Farnborough, UK). A special purpose LabView based software was designed to acquire and store the experimental data from both the load cell and the displacement transducer.

Table 3 gives a summary of the main operating conditions utilized in the quasi-static and the dynamic axial crush tests.


**Table 3.** Summary of the quasi-static and dynamic axial crush testing conditions.

#### *2.4. Finite Element Modelling*

The assembly of the individual panels of the thin-walled crash boxes by means of sheet-bulk compression with "mortise-and-tenon" joints was simulated with the finite element computer program I-form. The computer program was developed by the authors and is based on the irreducible finite element formulation,

$$
\Pi = \int\_{V} \overline{\sigma} \dot{\overline{\varepsilon}} dV + \frac{1}{2} K \int\_{V} \dot{\overline{\varepsilon}}\_{V}^{2} dV - \int\_{S\_{T}} T\_{i} u\_{i} dS + \int\_{\tilde{S}\_{f}} \left( \int\_{0}^{|u\_{r}|} \pi\_{f} du\_{r} \right) dS,\tag{1}
$$

where, the symbol *<sup>σ</sup>* is the effective stress, . *<sup>ε</sup>* is the effective strain rate, . *ε<sup>V</sup>* is the volumetric strain rate, *K* is a large positive constant imposing the incompressibility of volume *V*, *S* is the surface under consideration, *Ti* and *ui* are the surface tractions and velocities on surface *ST*, *τ<sup>f</sup>* and *ur* are the friction shear stress and the relative velocity on the contact interface *Sf* between the material and tooling. Further details on the computer program with special emphasis to contact and frictional sliding between rigid and deformable objects are available in Reference [14].

The numerical simulation made use of two-dimensional plane strain deformation models and the cross section of the tenons and mortises were discretized by means of approximately 1000 quadrilateral elements. The tools were modelled as rigid objects and their geometries were discretized by means of linear contact-friction elements.

The assembly of the individual panels of the thin-walled crash boxes by means of resistance spot-welding was simulated with the commercial finite element computer program SORPAS [15], which is based on an electro-thermo-mechanical formulation as described in details in [14]. The mechanical formulation follows Equation (1). Solution of the electrical potential Φ is based on integration of Laplace's equation, which in variational form can be written as

$$\int\_{V} \Phi\_{,i} \delta \Phi\_{,i} dV = 0,\tag{2}$$

where subscripts indicate spatial derivatives. The current density, calculated from the derivative of the potential and electrical resistivity, is used in the calculation of Joule heating during the welding process. The following variational equation governs the thermal solution for the temperature field *T*,

$$\int\_{V} k T\_{,i} \delta T\_{,i} dV + \int\_{V} \rho c \dot{T} \delta T dV - \int\_{V} \dot{q} \delta T dV - \int\_{S} k T\_{,n} dS = 0 \tag{3}$$

The first term is related to heat conduction through the conductivity *k*, and the second term is related to the temperature rate . *T* with material properties being mass density *ρ* and heat capacity *c*. Joule heating and heating from plastic work are included in the heat generation rate per volume . *q* in the third term. Finally, the last term includes heat generation and loss along surfaces stemming from frictional heating, convection and radiation. The subscript in the last term refers to spatial derivative along a surface normal. Further details like treatment of contact conditions are available in Reference [14].

#### **3. Results**

#### *3.1. Mechanical Characterization*

The stress-strain curve of the HSLA 340 steel obtained from the stack compression tests is shown in Figure 3. The enclosed photograph shows the multi-layer cylinder test specimens that were assembled by piling up 10 circular disks before and after compression. The stress-strain curve is utilized in the finite element simulation of the assembly of thin-walled crash boxes by sheet-bulk compression with "mortise-and-tenon" joints.

**Figure 3.** Stress-strain curve of the high-strength low alloy (HSLA) 340 steel obtained from stack compression tests.

#### *3.2. Finite Element Modelling and Experimentation of the Fabrication Process*

The reference joining process was simulated by the commercial software SORPAS [15]. The simulation result is shown in Figure 4 in terms of process peak temperature and identification of weld nugget. The simulation was based on the parameters given in Table 2. The simulation reveals a weld nugget with a diameter of 5.4 mm across the interface and a proper penetration into both of the two HSLA 340 sheets.

**Figure 4.** Distribution of simulated peak temperature in resistance spot-welding together with identification of the weld nugget.

The assembly of the thin-walled crash boxes by the novel sheet-bulk compression process with "mortise-and-tenon" joints required the tenons to be cut and bent out of the panels by lancing (Figure 1a), and subsequently compressed in the direction perpendicular to thickness (Figure 1c,d). Figure 5a,b show the finite element computed distribution of effective strain in the tenons at the end of the first sheet-bulk compression stage. Two different process operating conditions (Table 2) are shown: a tenon with a free length *h* = 4.5 mm that is successfully compressed by a tapered heading punch (Figure 5a) and a tenon with a free length *h* = 6 mm that fails by buckling (Figure 5b).

**Figure 5.** Assembling the individual formed panels of the thin-walled crash boxes: (**a**) effective strain distribution at the end of the first stage of the sheet-bulk compression of a tenon with a free length *h* = 4.5 mm; (**b**) effective strain distribution at the end of the first stage of the sheet-bulk compression of a tenon with a free length *h* = 6 mm.

Successfully compressed tenons are needed for the second stage of the sheet-bulk compression, during which a flat heading punch assembles the crash boxes by mechanically locking the individual formed panels to each other.

Figure 6 shows finite element deformed meshes at different instants of the crash box assembly by means of sheet-bulk compression with "mortise-and-tenon" joints. The case included in the figure consists of a bent tenon with a free length *h* = 4.5 mm and corresponds to the working conditions that were utilized to fabricate all the crash boxes with "mortise-and-tenon" joints that were subjected to the axial crush tests.

As seen in Figure 6a,b, the tapered heading punch prevents the collapse by buckling at the early stages of deformation. The flat heading punch (Figure 6c,d) produces the flat-shaped surface heads (Figure 6e) that will lock the panels to each other and assemble the crash box.

Figure 7 shows the experimental and finite element computed evolution of the force with displacement for the first and second stages of the sheet-bulk compression with "mortise-and-tenon" joints. The agreement is good and allows estimating the energy required to perform the first and second stages of the new proposed joining by forming process.

**Figure 6.** Fabrication of the crash boxes by sheet-bulk compression with "mortise-and-tenon" joints (*h* = 4.5 mm): (**a**) finite element mesh at the beginning of the first stage; (**b**) computed finite element mesh at the end of the first stage; (**c**) computed finite element mesh at the beginning of the second stage; (**d**) computed finite element mesh at the end of the second stage; (**e**) crash box with a detail showing the flat-shaped surface head of a compressed tenon.

**Figure 7.** Experimental and numerical evolution of the force with displacement for the first and second stages of the sheet-bulk compression of tenons with *h* = 4.5 mm.

#### *3.3. Axial Crush Tests*

Figure 8a shows the force-displacement curves for the quasi-static axial crush tests of the thin-walled crash boxes with double-hat section assembled by sheet-bulk compression with "mortise-and-tenon" joints and by resistance spot-welding. As seen, the force increases steeply up to a peak value where the first fold is formed (initiation of collapse). Then, the force decreases and the subsequent folds, corresponding to the oscillations of the force-displacement curve, are triggered for smaller local force peaks.

Figure 8b shows the force-displacement curves for the dynamic axial crush tests of the two types of crash boxes. The tests were performed in the drop weight testing machine (Figure 2), which converts the potential energy *Ep* at the beginning of the fall,

$$E\_p = M \text{g} \, H,\tag{4}$$

into an axial crush velocity *vi* at the impact by conservation of linear momentum between the mass *M* of the falling ram and the mass *Mt* of the upper tool part containing the compression platen,

$$
v\_i = \eta M \sqrt{2gH}/M\_{t\prime} \tag{5}$$

In the above equation, *g* is the gravity acceleration and *η* is the efficiency, which accounts for the air resistance, friction sliding along the columns and type of collision between the falling ram and the upper tool part (Figure 2a). The mass *M* and the drop height *H* of the falling ram were adjusted to deform the crash boxes by approximately 1/3 of their initial length with an impact velocity *vi* 16 m/s. Finally, it is worth noting that the impact velocity *vi* is progressively reduced to zero by the absorption of energy.

As seen, the overall trend of the dynamic force-displacement curves is similar to that of the quasi-static tests (Figure 8a) but the peak force to trigger collapse increases from 89 kN to 115 kN, in case of the crash boxes assembled with "mortise-and-tenon" joints. Similar increase in the peak force is obtained for the resistance spot-welding joints.

**Figure 8.** *Cont*.

**Figure 8.** Experimental evolution of the force 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.
