3.2.2. Effect of PW and PS on Elastic Strain Energy

Figure 12 shows the elastic strain energy (*Ees*) of the four kinds of center pillar (HPF, HPF + PW, HPF + PS, and HPF + PW + PS) during a side crash. For the HPF center pillar, the maximum *Ees* was 0.851 kJ at collision time (t) = 0.064 s and decreased to 0.30 kJ after the collision as a result of elastic recovery. When the PW was applied to the HPF center pillar, the maximum *Ees* increased to 0.928 kJ at t = 0.056 s. Because the rigidity of the HPF center pillar with PW increased, the absorption of elastic energy improved significantly. However, for the HPF center pillar with PS, the maximum *Ees* decreased to 0.655 kJ at t = 0.061 s. When the PS was applied to the bottom region of the HPF center pillar, because the stiffness of the HPF center pillar with PS decreased, the absorbed energy decreased in terms of elastic deformation.

**Figure 12.** Elastic strain energy (*Ees*) of the four kinds of the center pillar during a side crash.

Figure 13 shows the maximum *Ees* of the four types of center pillar for detailed evaluation of energy absorption of PW and PS. The *Ees* of the HPF center pillar with PW was 0.1 kJ, accounting for 10% of the total energy absorbed by the HPF center pillar with PW. The *Ees* of the HPF center pillar with PS decreased to 0.655~0.660, regardless of the inclusion of PW.

**Figure 13.** Maximum elastic strain energy (*Ees*) of the four types of center pillar.

3.2.3. Effect of PW and PS on Plastic Dissipated Energy

Figure 14 shows the plastic deformation energy (*Ep*) of the four kinds of the center pillar during a side crash. For the HPF center pillar, *Ep* increased to 4.538 kJ during deformation. The *Ep* was maintained after the collision, in contrast to the *Ees*, as a result of permanent deformation. For the HPF center pillar with PS, the *Ep* increased to 4.998 kJ at 0.1 s. The *Ep* of the HPF center pillar with PS was higher than that of the HPF center pillar. When PS was applied to the HPF center pillar, a large deformation occurred in the soft bottom region of the center pillar as a result of the ductility. As a result, the absorbed energy improved by 9.3%. However, there was no difference in absorbed energy between the HPF center pillar and the HPF center pillar with PW in terms of plastic deformation.

**Figure 14.** Plastic deformation energy (*Ep*) of the four kinds of the center pillar during side crash.

Figure 15 shows the maximum *Ep* of the four types of center pillar. For the HPF center pillar with PS and the HPF center pillar with PW and PS, 2.52~2.54 kJ of *Ep* was absorbed in the PS region, i.e., the bottom region of the center pillar. In terms of plastic deformation, the effect of PW was minimal, unlike elastic strain energy, whereas the *Ep* of the PS region accounted for 49.8~50.9% of the total plastic deformation energy between the HPF center pillar with PS and the HPF center pillar with PW and PS.

**Figure 15.** Maximum plastic deformation energy (*Ep*) of the four types of center pillar.

3.2.4. Effect of PW and PS on Internal Energy

Figure 16 shows the internal energy (*Ei*) of the four kinds of center pillar during a side crash. The total internal energy resulting from a collision consists of several energies and can be expressed by Equation (14):

$$E\_i = E\_{cs} + E\_p + E\_a + E\_{others} \tag{14}$$

where *Ei* is the internal energy; *Ees* is the elastic strain energy; *Ep* is the plastic deformation energy; *Ea* is the artificial strain energy; and *Eothers* is the energy dissipated by creep, viscoelasticity, and swelling.

**Figure 16.** Internal energy (*Ei*) of the four kinds of center pillar during a side crash.

Generally, *Ees* and *Ep* are the dominant factors affecting *Ei* during a collision, and the contributions of other energies are relatively small. Therefore, in this study, the internal energy was expressed as the sum of *Ees* and *Ep*, excluding other types of energy, such as viscoelasticity, friction, and creep energy. In terms of internal energy, when the PS technique was applied to the HPF center pillar, there was a slight difference in the absorbed energy. However, a synergistic effect occurred when PW and PS were applied to the HPF center pillar, and a large amount of energy was absorbed, as shown in Figure 16.

Figure 17a shows the maximum *Ei* for the four types of center pillar. As shown in Figure 17a, there is almost no difference in the plastic deformation energy between the HPF center pillars with and without PW. The PW was welded on the upper part of the HPF center pillar to increase the stiffness, but the impact region was applied from the middle to the bottom, as shown in Figure 17b. Therefore, small deformation occurred in the PW. Likewise, a comparison between the HPF center pillar with PS and the HPF center pillar with PW and PS revealed similar phenomenon with respect to the absorbed plastic deformation energy. Based on the above results, it is necessary to review whether PS technology should applied in light of the relationship between technical performance and manufacturing cost.

**Figure 17.** (**a**) Maximum internal energy (*Ei*) for the four types of center pillar. (**b**) Stress distribution of the center pillar during collision.

#### 3.2.5. Effect of PW and PS on the Intrusion Resistance

During a side crash, a large amount energy is absorbed. However, if the material is soft and a large amount of deformation occurs, the intrusion displacement increases, putting the passenger in danger. Therefore, it is important to evaluate intrusion displacement for passenger safety, as well as collision energy absorption.

As shown in Figure 18a, because both the center pillar and the MDB were deformed during the collision, the maximum intrusion displacement was calculated according to Equation (15).

$$d\_{\max,i} = d\_{\max,DMB}(t) - L\_b \tag{15}$$

where *dmax.DMB* is the maximum displacement of DBM, and *Lb* is the barrier length.

The evaluation method for the anti-intrusion resistance was introduced according to IIHS guidance. The primary performance of the center pillar is related to anti-intrusion resistance against side impact. According to the IIHS rating protocol, the center line of the vehicle's seat was generally in compliance with standard of the measured intrusion displacement, as shown in Figure 18b, with categories of good, acceptable, marginal, and poor [25]. In this study, multistructures, such as automobile seats, dummies, and windows were, not considered, so the maximum intrusion of the HPF center pillar with PW was used as the acceptable distance, achieving an acceptable level. As shown in Figure 18b, the maximum intrusion displacement of the HPF center pillar and the HPF center pillar with PW were −134.0 mm and −123.9 mm, respectively. When the stiffness of the upper part was strengthened with PW, the safety of the intrusion displacement was also improved by 7.5%. Likewise, in the case of the HPF center pillar with PS, the maximum intrusion displacement was −123.1 mm. A similar result was achieved with the HPF center pillar with PW. On the other hand, the maximum intrusion displacement of the HPF center pillar with PW and PS was −116.1 mm, representing an improvement of 13.4%. When the PW and PS were combined, a synergistic effect occurred.
