*2.2. Results*

The impact striker geometry assessment on the composite panels' destruction was made on the basis of microscopic tests. The tests allowed the authors of this article to measure the diameter of the panel damages after impact. Because of the plastic character of aramid fiber destruction, the damages in the panel reflected the striker geometry, and the depth of the penetration could be calculated based on the cavity diameter and the geometry of the used striker. The results are shown in Table 3.


**Table 3.** Average experimental results, depending on striker geometry.

The microscope images of the damage in composite panels presented in Figure 4 show the significant influence of the striker geometry. During the same impact, the same values of impact kinetic energy and destruction level in composite panels were limited from the matrix cracking in the blunt striker case to the almost complete penetration in the conical striker case. For the blunt striker, fibers absorbed almost all impact energy—there was no fiber damage. The cracked matrix is only one visible sign after impact in this case. That fact proved the high resistance of fiber reinforced composites on the impact of blunt elements. Cross sections of the samples after impact of the strikers are presented in Figure A2.

(**c**)

(**a**)

> (**d**)

(**b**)

**Figure 4.** Selected samples after impact of the striker: (**a**) conical, (**b**) hemispherical, (**c**) blunt, (**d**) ogival.

The destruction caused by a hemispherical striker was characterized by a high amount of compressed fibers. Around a newly created cavity, the characteristic bulge was formed. Fibers that were initially in the first layer of the impact area (in the center of panel) were then ripped out from the matrix. The broken and compressed fibers in this formed cavity were also visible. However, their amount was low, which proved that only fibers from the first layers were damaged, and fibers in the next layers were in good shape. There were no carbon fibers in the cavity, which suggests that the panel penetration is limited to the first four layers of the reinforced material. This was also confirmed by the calculated depth of penetration. It was circa 1.5 mm, which corresponds to the thickness of approximately of three layers of used aramid fabric. The cross section of the sample (Figure A2) also confirms that the penetration of the composite stops before the reinforcing layer made from carbon fibers was damaged.

The destruction caused by an ogival striker suggests much more sensitivity of the hybrid composite to the impact of such elements. The penetration depth was much higher compared with the penetration depth in the case of a hemispherical striker. The analysis of the microscopic images shows a lot of broken fibers in the created cavity. The broken fibers were visible as sticking out parts of the reinforcing fabric directed towards to the cavity. These fibers were also compressed at the boundary of the cavity. Like in the previous case, the first layer damage around the impact zone was also visible. The penetration

depth in this case was 4.5 mm, which corresponds to the depth of the second reinforcing layer made from carbon fibers. At the bottom of the created cavity, there were no carbon fibers, which suggests that the second carbon reinforced layer was not penetrated. The cross section of the formed damage presented in Figure A2 also confirms that the second reinforcing layer made from the carbon fibers was not damaged.

The conical striker caused the largest destruction in the tested material. In this case, both the cavity diameter and its penetration depth were the largest. The destruction mechanism was the same as in the case of the ogival striker. Inside the formed cavity, it was possible to observe the parts of broken fibers. In the case of this striker, fibers' deformation was also visible at the first layer around the impact area. This fact suggests that the conical geometry of the striker caused pushing fibers sideways of the creating cavity. The considered striker did not have enough energy to break fibers, so it stuck between them and pushed them sideways. The weave and weight of an applied reinforced fabric could have a critical meaning in strength aspect. As mentioned, fibers in the first layers were deformed, which confirm this fact. This also explained why damage caused by a conical and an ogival striker was largest compared with that of other strikers used.

## **3. Numerical Research**

#### *3.1. Preparation of Numerical Model*

The numerical research was carried out using the finite element method and commercially available LS-PrePost/LS-Dyna (LSTC, Livermore, CA, USA) software. The multilayered composite could be modeled in a few scales. The modeling scale is related to the homogenization of the composite strength properties. In the case of modeling the composite as a one part, homogenization of the mechanical properties should be performed for the whole composite. Modeling in this scale makes it impossible to observe some processes occurring inside the composite material, for example, delamination, which, as mentioned in the introduction, is an energy absorbing process. A di fferent approach is to model the composite with respect to the division on the reinforcing layers. In this approach, the strength properties should be homogenized in the level of the reinforced layer (used reinforcing fabric and the matrix). This modelling scale allows observing the delamination between the reinforcing layers. There is also the possibility to observe the movement between the adjacent reinforcing layers and the consideration of the friction between them. Woven composites could also be modeled with respect to the reinforcing fiber geometry. The mechanical properties of the fiber and the matrix are defined individually. Observation of the delamination process is also possible. Moreover, modelling in that scale allows to observe the deformation of each fiber and the friction between the fibers. If the modeling scale is more accurate, the physical model takes into account more energy absorbing phenomena. Therefore, the choice of the modeling scale and level of homogenization of strength properties has an impact on the obtained result. The selection of the modeling scale is related to use of the simplifications. Each simplification will be associated with the omission of some energy absorbing phenomenon. However, it should be remembered that, if the physical model is more advanced, the computational cost will be greater. Modeling of the composite with respect to the division on the reinforcing layers (homogenization of the strength properties in the reinforcing layer level) gives satisfactory results, which are in accordance with experimental research [51]. It was decided to model the composite material in a macro scale. It means that each reinforced layer was modeled as an individual part. This approach is widely used [51–54] in the case of impact analysis. A flat surface with dimensions of 50 × 100 mm (height × width) was created, and then it was discretized into the finite elements. The surface was divided into Belytschko–Tsay type shell elements with "hourglass" control based on sti ffness. A total of 5000 Belytschko–Tsay shell elements were created in this way. It was assumed that the thickness of each layer, regardless of the reinforced material, was 0.5 mm, which allowed the physical model to achieve the overall thickness of the composite used in the experiment (7 mm). On the basis of this assumption, 13 subsequent surfaces were created, spaced 0.5 mm from

the previous layer along the axis perpendicular to the surface of the layers. The composite model created in this way consists of 70,000 shell elements. As a composite material model, the MAT58 \*MAT\_LAMINATED\_COMPOSITE\_FABRIC [55] was used. This model requires the definition of homogeneous strength properties of the used materials. Taking into account the destruction of the physical model, the finite elements are controlled by the ERODS parameter. The ERODS parameter is calculated based on the deformation in defined fiber directions in the reinforced plane and on the shear deformation. In this material, model stress increases nonlinearly until the maximum strength is reached (XT). When the maximum strength is reached, the stress is reduced by the SLIMx factor and held until material reaches the strain specified by the ERODS parameter. When strain reaches the value defined as an ERODS, the finite element is deleted [56]. The typical stress–strain curve for the selected MAT58 composite material model is shown in Figure 5.

**Figure 5.** Typical stress—strain curve for the selected MAT58 composite material model.

On the basis of the research [56], ERODS = 0.4 was adopted. Because the values of SLIMx coefficients do not have their physical interpretation [57], their value was adopted in accordance with the recommendations [55]. The impact of individual factor values on the convergence with an experimental solution is presented, among others, in the work of [56]. The used material properties of epoxy composites with carbon and aramid reinforcement (in two directions) are shown in Table 4.


**Table 4.** Mechanical properties of epoxy composites reinforced by carbon and aramid fibers [58].

The delamination is an important energy absorption mechanism in the case of low velocity impact [51]. In case of the modeling approach used in research, the connection between successive layers of reinforcing material can be modeled in several ways [52,59–61]. Modeling of the bonding connection between adjacent reinforcing layers could be realized using cohesive elements [54,62]. This approach involves inserting additional cohesive elements between elements of adjacent reinforcing layers. In the initial phase, these elements may have zero thickness. The behavior of the cohesive elements can be described, for example, using a bilinear curve. These curves describe the dependence between the cohesive element stresses from its deformation [54,59,60,62]. If the cohesive element is not damaged, its sti ffness is constant. However, if an element is damaged, its sti ffness decreases as deformation increases [62]. The use of cohesive elements requires high computational costs [52]. A broader description of this type of connection has been described, among others, in the literature [54,59,60,62]. The second approach of modeling the bonding connection between the adjacent reinforcing layers is the use of the bilateral constraints (tiebreak contact type). This contact allows for the simplification of crack propagation based on the cohesive element [51]. After reaching normal and shear stresses, damage is a linear function of the distance between points that were initially in contact. After reaching the defined critical crack opening, the bonding connection is broken and further contact behaves like unilateral constraints. This approach does not require the use of additional elements and, shown in the work of [51], this bonding connection modelling method give results in accordance with experimental research. In the conducted research, it was decided to use the bilateral constraint contact with strength criterion (\*AUTOMATIC\_SURFACE\_TO\_SURFACE\_TIEBREAK [63]). This contact type behaves like a bonded connection before the strength criterion is exceeded. After exceeding the strength criterion, this contact behaves like a unilateral constraint contact without a bonded connection. There are several possibilities to define the bonded connection using the selected contact type. In the case of shell elements, the definition OPTION = 8 is most commonly used [59]. This option requires to define the critical normal and shear stresses in a bonding connection. The critical normal stress assumed in the physical model equals Sn = 75 MPa [49] and the critical shear stress equals Ss = 44 MPa [59], respectively. The friction coe fficient between reinforced layers was defined as 0.18 [52,64,65].

Additionally, one more part created in the presented model was a polyethylene base plate, to which the tested samples were glued. The plate was discretized using eight node solid elements with one integration point. The edge length of each element was 1 mm. The base plate model consisted of 50,000 solid elements. It was decided to choose the linear elastic material model (\*MAT\_ELASTIC [55]). The applied mechanical properties of polyethylene [66] are shown in Table 5. The contact between the last layer of the composite and the polyethylene base plate was modeled using the unilateral constraint contact (\*AUTOMATIC\_SURFACA\_TO\_SURFACE). The value of 0.29 was adopted as a friction coe fficient [66].


**Table 5.** Mechanical properties of polyethylene.

During the experiment, four di fferent types of strikers were used (Figure 2). Their geometries were made in CAD software (Autodesk Inventor Professional 2019), and then they were imported and discretized using eight nodal solid elements. These elements were given mechanical properties corresponding to the steel and treated as non-deformable using the \*MAT\_RIGID [55] material model. The strikers were placed opposite to the first layer of the laminate. An initial velocity of the striker V0 = 31 m/s was set. The boundary condition assigned to the model blocked all degrees of freedom (translational and rotational) for all nodes of a polyethylene base plate at the side opposite to the side of contact with the composite. The contact between the non-deformable striker and the composite layers was defined as \*AUTOMATIC\_SURFACE\_TO\_SURFACE (unilateral constraint). The values of static and dynamic friction coe fficients between the striker and the reinforcing layers were set as 0.18 [52,64,65]. The schematic diagram of the created model is shown in Figure 6a. The prepared model is shown in Figure 6b.

**Figure 6.** Numerical research: (**a**) schematic diagram, (**b**) physical model.

## *3.2. Numerical Results*

Damage caused by the strikers with various geometries at different instances of the simulation (up to reach the maximum depth of the penetration) is shown in Figures A3–A6. Each reinforcing layer is marked by a different color. The cross sections of damaged areas owing to the impact of various strikers are shown in Figure 7. The direction of the impact is marked using a white arrow.

**Figure 7.** Cross sections of damaged areas caused by (**a**) conical striker, (**b**) hemispherical striker, (**c**) blunt striker, and (**d**) ogival striker.

The numerical results have shown that the largest damages (Figure 7a) occurred when a conical striker was used. The smallest damage occurred in the case of a blunt striker (Figure 7c), which corresponds to the experimental results. The area of damage for each striker geometry is di fferent. The damage caused by impact of the striker with a conical end (Figure 7a) is characterized by the formation of a narrowing taper. In each subsequent damaged layer, the number of degraded elements decreased to form a characteristic cone. These damages are the largest among the analyzed cases. The sharp end of the conical striker penetrating successive layers of material caused rapid damage to the individual elements in subsequent reinforcing layers, which contributed to the weakening of the entire structure.

The damage caused by the hemispherical striker (Figure 7b) was less extensive compared with the damage caused by the conical striker. The resulting damage does not form a characteristic cone. The largest damages were observed in the first four layers of reinforcement. The elements that were not deleted are arranged in a chaotic manner. It can be observed that the elements in the second layer of reinforcement in the impact area are not completely destroyed, which can be interpreted as the fiber compression inside the formed crater (as mentioned in the chapter about experimental research). The other two damaged layers (5 and 6) were minimally damaged—individual elements were deleted. The blunt striker did not cause any visible damage in the reinforcement material (Figure 7c). The ogival striker caused the most damage (Figure 7d) in the first two layers of the material. Penetration of subsequent layers was characterized by the removal of the same number of finite elements until the striker energy was too low to damage the next layer. The last of the damaged layers degraded in the form of individual elements.

The colored map of Tresca stress presented in Figure 8 showed that the primary yarns (at the direction defined as a fiber direction—X and Y axis) carried the largest load. The secondary yarns were much less loaded. This conclusion was confirmed in the work of [16]. In addition to the analysis of destruction, which was performed based on the Figure 7c, the value of Tresca stresses shown in Figure 8 suggests that the matrix could be damaged. As shown in Table 2, the tensile strength of the matrix is 75–85 MPa. Tresca stress at the edge of impacting striker (on the first layer of reinforcement) was much higher (92.5–110 MPa). This analysis suggests that the matrix could be damaged, as in the case of the experimental research (matrix cracking). The average diameter of this area was 7.5 mm.

**Figure 8.** Colored map of Tresca equivalent stress on the first layer of reinforcement in case of blunt striker impact.

Table 6 shows the diameters of the cavities and depth of the penetration of the damages created by the impact of strikers with di fferent geometries. The measurement of cavity diameters was done between the nodes of the elements at the first layer, which were not deleted after impact. The biggest damage in the first layer of reinforcing material was observed for the case in which the conical striker hits the composite. The second largest diameter of the damaged area was observed for the case in which a hemispherical striker was used. The diameter of the damaged area in this case was slightly larger than in the case of the impact of the ogival striker. The depth of penetration was based on the number of damaged reinforced layers—0.5 mm of damage for each damaged layer.


**Table 6.** Numerical results, depending on striker geometry.

The largest depth of penetration was observed for the case in which the composite panel was hit by a conical striker. As a result of its impact, 12 layers of reinforcing material were damaged. The impact with an ogival striker resulted in damage to eight layers of reinforcing material. In the case of a hemispherical striker, six layers of reinforcing material were damaged. However, these damages were di fferent. The damage created did not resemble a cone geometry. As it was mentioned, the individual elements were deleted from 5 and 6 damaged layer (damage area was smaller than used striker). Due to that, this two layers were not considered in depth of penetration calculation. For the impact on the composite material with a blunt striker, no damage was observed in the reinforcing material, but small deformation was observed.

The graph representing kinetic energy of the striker depending on its geometry is shown in Figure 9. The fastest braking of the striker occurred with a blunted one. This striker was rebounded from the composite panel, obtaining the kinetic energy of about 16 J. This testified that a small amount of energy was absorbed by the composite panel. The hemispherical striker was rebounded from the panel, obtaining a value of the kinetic energy of about 8.5 J. The braking of the striker before it was rebounded proceeded with the same intensity as in the case of a blunt striker, despite the damage caused in the reinforcing layers. A smaller value of the rebounded kinetic energy of the striker is associated with a greater amount of energy absorbed by the composite. Conical and ogival strikers had the lowest kinetic energy after rebounded (approximately 2 J). Despite the di fferences in the strikers' braking intensity, they were stopped at the same time and had similar kinetic energy after being rebounded. The curve depicting the kinetic energy value of the ogival striker has a distinctive area of braking corresponding to the level of material penetration. The first change in the angle of inclination of this curve at the time t ≈ 0.1 ms is associated with the first damage to the material. Another angle change in the time t ≈ 0.2 ms is associated with the end of damaging of the reinforcement layers. In the next phase, material was deformed without damaging and striker was inhibited and rebounded. Braking of the conical striker was the gentlest, which was probably because of the fact that its pointed end easily damaged the elements in the subsequent layers of the composite. It is interesting that the conical and ogival strikers, despite large di fferences in the damage caused, were characterized by the same value of the kinetic energy after rebound.

**Figure 9.** Kinetic energy of strikers during impact depending on their geometry.

#### *3.3. Comparison of Experimental and Numerical Research*

The results of the conducted experimental and numerical research were compared based on the diameters and depth of penetration of cavities formed after impact of the strikers. Figure 10 shows the comparison of the diameters of the cavities formed after the impact.

**Figure 10.** Comparison of cavity diameter formed after impact.

The damage caused by the blunt striker in the experiment (Figure 4c) is limited to the matrix cracking. The diameter of the resulted crack corresponds to the diameter of the edge of the impacting striker. The resulting damage did not damage the reinforcing layer in any way. Performing numerical research in the selected scale makes it impossible to capture phenomena like matrix cracking, but proper analysis of the stress map could bring valuable conclusions. As discussed in the numerical research results, the obtained Tresca stress value suggests that the matrix was damaged, as in the case of the experimental research. The measured diameter of damaged area was almost the same as in the case of the experimental research. Another discrepancy between the experimental and numerical research is in the case of hitting the composite by the conical striker. During the experimental research, the pointed tip of the cone stuck between the individual fibers, pushing them sideways. Fibers pushed sideways constituted resistance for the striker, and tightened on it, thus reducing damage caused in subsequent layers. In the case of numerical research, individual fibers were not considered. Each reinforcing layer was modeled as a single part with directionally assigned properties. The indicated directions corresponded to the directions of the fibers in the used reinforcing fabric, however, the modeling of the reinforcement in this way makes it impossible to imitate the mechanism of deformation of individual fibers. Finite elements hit directly by the tip of the cone were quickly removed. When an element was removed, it stopped absorbing the energy, so material did not resist as much energy as in the case of the experiment. This fact could have an e ffect for the larger amount of destruction in the case of the numerical research. The same remark applies to the discrepancy between the results obtained for the ogival striker.

Figure 11 shows the comparison of the depths of penetration obtained as a result of the provided experimental and numerical research. For conical and hemispherical strikers, the depths of penetration obtained as a result of numerical research were larger than in the experimental research. In the case of the experimental research, depths were determined indirectly based on the diameter of the formed cavity and the striker geometry. This method could be subject to a large error, resulting from the lack of information about the damaged fibers under the visible layer of damaged reinforcement. Additionally, in the case of the numerical research, elements removed during calculations do not constitute any resistance for the strikers' movement at a later stage. In real conditions, the damaged fibers were still in the forming cavity, clamping on the striker, or accumulating in front of its forehead, thus a ffecting the formation of further damage. Figure 12 shows the percentage variation between the results obtained from the experimental and numerical research.

**Figure 11.** Comparison of depth of penetration after impact.

**Figure 12.** Percentage variation between the results obtained from experimental and numerical research.
