Nonlinear Impact Force Reduction of Layered Polymers with the Damage-Trap Interface

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The proposed impact force reduction approach using a special material design can reduce the volumes and weights of protective materials such as a plastic phone case.

Abstract

In this paper, a damage-trap material interface design of polymeric materials was proposed. Towards that, baseline and layered Polymethyl methacrylate (PMMA) and Polycarbonate specimens were fabricated with a Loctite 5083 adhesive layer between the interfaces. Out-of-plane impact experiments were conducted and found that the maximum impact force was reduced in layered polymers with so-called “damage-trap material interfaces”. At the impact energy of 20 J, the maximum impact force of the layered PMMA specimens with the 5083 adhesive was reduced by 60% compared to the identical specimens without any adhesive bonding. For the layered Polycarbonate specimens with the 5083 adhesive bonding, the maximum impact force was reduced by 20% and energy absorption was increased by 130%. Simplified contact mechanics analysis showed that the low Young’s modulus of the 5083 adhesive layers was a key parameter in reducing impact force and damage. Therefore, a simple and effective way to design layered materials with improved impact resistance was proposed.

1. Introduction

In recent years, polymers and polymeric matrix composites in the forms of layered materials are widely used in automobile, aerospace, marine, electronic and medical industries [1,2,3]. Usually, their through-thickness impact resistance is a weakness, so how to improve impact resistance is an important topic for layered material designs [3,4,5,6,7,8,9,10]. On the impact experiments of layered polymers using high-speed photography [11,12,13], one of the authors found some interesting fundamental results. As shown in Figure 1, two brittle polymer Homalite specimens with different adhesive materials showed very different impact failure patterns. Surprisingly, a strong adhesive bonding (high bonding strengths) was not able to stop any impact damage or dynamic cracks, but dynamic cracks were trapped along a weak and thin interface (20 µm) that had Loctite 5083 adhesive, which is a kind of acetoxy silicone used mainly for potting, gasketing, or sealing. The exact reasons for the inability of these cracks to penetrate the weak bonding are complex. However, the pivotal role of the weak interface in triggering this behavior is clearly evident. A video of the whole impact failure process of the specimen shown in Figure 1b based on high-speed photography is provided as supplementary material (also next page). This phenomenon provides an efficient material design methodology to prevent the spread of impact damage. We call this efficient approach the “damage-trap material interface (DTMI)” design since minimal impact damage can be achieved at low costs by implanting thin interface/adhesive layers inside the base materials without other changes. However, fundamental failure mechanisms of crack trapping are not yet clear. For example, we do not know which parameter plays the major role in the crack arrest—the density, the high failure elongation of the 5083 adhesive, or the dynamic stress intensity factor reduction of the dynamic crack close to the interface? Obviously, answers to these questions will lead to better material system designs.

There is almost no paper on the same topic. However, Sheshkar et al. [14] studied the functional characterization of polymer composite where they used an energy-efficient approach to fabricate polymeric films. Alhareb et al. [15] improved the mechanical properties of nitrile butadiene rubber (NBR) with ceramic filler. Guo et al. [16] improved the impact resistance of polymer by using nanoscale interfacial structure. Singh et al. [17] studied the initiation and arrest of an initial interface crack subjected to stress wave loading, while our material systems have no initial cracks, and our cracks are not along the interfaces. However, our previous gas-gun impact experiments were two-dimensional section impact experiments, which represented simplified impact problems in order to use high-speed photography [12]. In this investigation, we conducted out-of-plane drop-weight impact experiments, which were very similar to an actual impact case. Moreover, the advantage of the drop-weight impact experiment was that the in-situ impact force could be measured from a test machine, which was not available in the gas-gun experiment. The major purpose of this investigation is to answer a simple question: whether the damage-trap material interface led to a reduction of the maximum impact force or not, because impact damage is directly related to the maximum impact force. If the answer is true, we could implement this simple but effective design to more engineering materials such as ceramics or composites to improve their impact resistance.

A video of the specimen’s failure process as shown in Figure 1b will be inserted here for final publication using the publisher’s multimedia. This video consists of 80 images from a high-speed camera, but the inter-frame time of these images was increased.

Click here to view this high-speed video as a YouTube video [18]. (or copy this URL: http://www.youtube.com/watch?v=5EDG2VZXaQ8&feature=plcp, (accessed on 7 April 2022).

2. Out-of-Plane Impact Experiments

2.1. Materials

Unlike previous brittle polymer Homalite as shown in Figure 1, different polymers Polycarbonate and PMMA were selected in this investigation in order to obtain fundamental mechanics understanding which is independent of testing materials. These materials along with Polyurethane used in numerous applications in Army such as, Face shield and body shields, Helmet, Army ground vehicles, etc. [19]. In this study, we focused our attention on the dynamic failure of layered materials under impact loading. To bond the different layers, we have used Loctite 5083 adhesive which provides a weak bonding between the surfaces. The 5083 adhesives is considered a ductile adhesive since their elongation at failure (as measured by the manufacturer) in cured bulk form is 170% or two orders of magnitude higher than the other adhesives.

2.2. Specimen Preparation

Figure 2 shows a schematic diagram of the baseline and layered specimens. The length of the square impact specimen was 127 mm (maximum specimen size of our impact test machine), and was the same for the bonded and un-bonded baseline specimens. The specimen thickness was 12.7 mm for the baseline specimen and 13.2 mm for the layered specimen. For baseline, the specimens were cut from a PMMA or Polycarbonate sheets with a thickness of 12.7 mm, but the layered specimens were fabricated using two sheets with a thickness of 6.35 mm. The adhesive layer thickness of the bonded specimen was around 0.5 mm. For a layered/bonded specimen, after the 5083 adhesive was applied to the whole bonding area (specimen size), the pressure was applied in order to form a uniform adhesive layer without any visual bubbles. Figure 3 shows the side view of a typical bonded specimen with DTMI interface. The bonded specimens were cured with Ultraviolet (UV) light (intensity 225 mW/cm² and wavelength 365 nm) for 30 s as recommended by the manufacturer. After UV curing, the specimen was left for seven days in normal atmospheric conditions before impact tests.

2.3. Impact Test

Impact tests were carried out in a drop-weight impact machine. Figure 4a shows the drop-weight impact machine and Figure 4b shows the test section of the impact machine with a loaded specimen. The specimen was kept in a fixture that was attached to a fixed stand. The figure also shows the clamping device used to clamp the specimen over the fixture. This clamp applies a pressure of about 0.5 MPa to the top surface of the specimen to hold it tightly over the fixture. All the tests were carried out with a steel striker with a mass of 3.105 kg. The test machine automatically adjusted the initial height of the striker for the different energy levels. The specimens were fixed at all edges, and the impact experiments were carried out at different energy levels for the baseline polymer plates without any adhesive layer, and the bonded polymer specimens with the 5083 adhesive layers under the same impact energy levels.

3. Experimental Results

Figure 5 shows very different maximum impact forces measured directly from the test machine for two kinds of PMMA material systems with and without the 5083 adhesive layers. At the impact energy of 20 J, the maximum impact force of the layered PMMA specimen was reduced by 60% compared to the identical specimen without bonding as shown in

Table 1. Maximum impact force for baseline and layered PMMA specimens.

Impact Energy (J)	Max. Impact Force (kN)		Percentage Reduction
	Baseline	Layered PMMA
1.00	3.95 ± 0.64	2.30 ± 0.38	41.77
5.00	7.94 ± 0.81	3.87 ± 0.43	51.26
8.00	9.83 ± 1.37	-	-
11.00	11.39 ± 1.53	-	-
12.00	11.95 ± 1.24	4.54 ± 0.58	62.01
15.00	12.75 ± 1.49	4.50 ± 0.73	64.71
18.00	12.35 ± 1.23	-	-
20.00	12.51 ± 1.87	4.66 ± 0.96	62.75

. In the case of layered PMMA, 8 J, 11 J, and 18 J impact experiments were not performed as a significant difference was not observed from the impact energy reported in Table 1. For the layered Polycarbonate specimen with the 5083 adhesive, the maximum impact force was reduced by at least 20% even though the maximum impact energy was 120 J as shown in Figure 6.

Table 2. Maximum impact force for baseline and layered Polycarbonate sheets.

Impact Energy (J)	Max. Impact Force (kN)		Percentage Reduction
	Baseline	Layered Polycarbonate
7.00	7.03 ± 0.68	3.75 ± 1.12	46.66
10.00	8.16 ± 1.26	4.50 ± 0.95	44.85
20.00	10.60 ± 1.74	6.19 ± 1.08	41.60
30.00	12.17 ± 1.16	7.58 ± 1.20	37.72
40.00	13.20 ± 1.92	8.68 ± 1.22	34.24
50.00	14.06 ± 1.11	9.90 ± 1.31	29.59
60.00	14.90 ± 2.46	10.97 ± 1.19	26.38
70.00	15.64 ± 1.10	12.04 ± 1.67	23.02
80.00	16.45 ± 2.02	12.10 ± 1.84	26.44
90.00	16.89 ± 1.95	13.91 ± 1.56	17.64
100.00	17.46 ± 1.89	14.65 ± 1.81	16.09
120.00	18.22 ± 1.76	16.18 ± 1.45	11.20

shows the maximum impact force measured from the test machine as a function of impact energy. If we define an allowable impact force of 12 kN for the Polycarbonate plate according to our experimental records, the allowable impact energy of the baseline Polycarbonate plate should not exceed 30 J. But the allowable impact energy of the layered Polycarbonate plate with the damage-trap material interface could reach 70 J without any final failure, or 133% increase in terms of the allowable impact energy for the same allowable maximum impact force. Therefore, this simple material design could yield significant energy absorption.

Therefore, we find at least one mechanism of the damage-trap material interface, i.e., it reduces the maximum impact force acting on the layered polymers. As a result, impact damage is reduced. However, the above result was based on experimental observation. In order to find the relationship between the failure mechanisms and material properties, we present a simplified model. For a projectile impact test, the first stage is elastic indentation/contact, and the second stage is a complicated failure process. It should be noted that the impact failure of layered materials with highly mismatched properties requires three-dimensional numerical simulations to obtain a complete understanding [20,21]. In this experimental paper, we only employ a simplified elastic model in order to understand some mechanics insight for our experimental studies, which will be helpful for new material designs.

4. Simplified Dynamic Contact Mechanics Analysis

The low-speed impact problem could be treated as a contact/indentation mechanics problem [22]. For example, Kistler and Waas [23] employed Hertz’s indentation model to analyze the low-speed impact mechanisms of composite laminates. The impact or indentation load P of a spherical indenter or projectile with a radius R is a function of the indentation depth h:

$$P=\frac{4}{3}\sqrt{R}{E}_r{h}^{\frac{3}{2}}=C h^{\frac{3}{2}}$$

(1)

where C is the contact stiffness, and E_r is the reduced modulus [24]. Andrews et al. [25] found that the maximum impact force is achieved at the zero relative speed of the projectile respect to the target (no penetration), and is simply determined by impact energy W of the projectile, and the contact stiffness:

$$P_{max}=1.73\sqrt[5]{W^3{C}^2}$$

(2)

Therefore, at a fixed impact energy, decreasing the contact stiffness (proportional to E_r) will decrease the maximum impact force acting on the target (also projectile). The reduced modulus E_r is determined by the Young’s modulus E and the Poisson’s ratio ν of the indenter/projectile material (subscript i) and the target (subscript t):

$$\frac{1}{E_r}=\frac{1-{\nu }_i^2}{E_i}+\frac{1-{\nu }_t^2}{E_t}$$

(3)

Because decreasing the contact stiffness is equivalent to decreasing the reduced modulus as shown in Equation (1), the through-thickness Young’s modulus along the impact direction of the target E_t should decrease according to Equation (3), especially E_i (for steel projectile, 200 GPa) >> E_t (for PMMA, 3.79 GPa). We find that the only factor to reduce E_t is the addition of the soft 5083 adhesive layer. After the soft silicon layers are embedded inside polymers, a series rule-of-mixture model [26] could be used to predict the effective through-thickness modulus E_t in terms of polymer volume percent V_p and its Young’s modulus E_p, and the Young’s modulus of the added silicon layer E_add as shown in Equation (4):

$$\frac{1}{E_t}= \frac{ V_p}{E_p}+\frac{1-V_p}{E_{add}}$$

(4)

The reason to employ a series model rather than a parallel model is that impact load acts on the polymer part first, and then transfers to the adhesive layer, i.e., the same applied load assumption for a series model in mechanics of composite materials ([26]). Since V_p > 90% and E_p >> E_add (less than 0.001 GPa of the silicon layer based on the adhesive company’s data), or V_p/E_p is very small, E_t ≈ E_add/(1 − V_p) in Equation (4). Because the added adhesive layer has a very low Young’s modulus, the reduced modulus and the contact stiffness decre. Therefore, the low Young’s modulus of the adhesive layer is identified as a major material parameter in order to reduce the maximum impact force and damage.

5. Discussion

According to Equation (2), we find that the maximum impact force is a nonlinear function of impact energy. Figure 5 and Figure 6 exactly show this trend of experimental data (mainly the first 70% impact energy ranges). Due to the contact stiffness difference between two kinds of polymers with and without the 5083 bonding, their maximum impact force is quite different as we expected. However, we lack enough material properties to provide a rough prediction using Equation (2). Usually, the adhesive manufacturers only provide very limited material data, because measuring the properties of pure adhesives in the form of thin and soft layers is always difficult [27,28]. In Figure 5, we notice that the maximum impact force increases very slowly after impact energy exceeds 15 J. Therefore, for specific materials/structural designs such as impact resistance designs of new cell phones or cell phone cases, if their performance against low-speed or low-energy impact is satisfied, their further performance against high-energy impact would require much fewer efforts after a critical impact energy (15 J in this case). Of course, the above estimation needs detailed stress and deformation analysis of all potential impact energy ranges for the service requirements (i.e., cell phones’ drop locations and heights).

Figure 7 shows the baseline PMMA specimen after the impact of 12 J energy, and the specimen cracked throughout its thickness. On the other hand, at the same impact energy level, cracks were observed only on the top layer of the layered specimen as shown in Figure 8. Debonding was found on the adhesive layer of the layered specimen. By comparing Figure 7 and Figure 8, it is noticed that for the baseline specimen, impact energy dissipation was polymer damage only, while for the layered specimen, impact energy dissipation included polymer damage and adhesion damage. To support this statement, we have also conducted impact experiments on the specimens without the adhesive layer, i.e., two PMMA layers were simply stacked together at the test section of the drop-weight impact machine. The clamping force applied by the clamp during testing keeps both the layers in place as mentioned in Section 2.3. Figure 9 shows the layered specimen without adhesion after impact, and we observed that both the top and bottom layers cracked after impact. Therefore, based on the three polymer designs as seen in Figure 7, Figure 8 and Figure 9, we conclude that the adhesive layer dissipated some impact energy, reduced the maximum impact force, and saved the bottom layer from being damaged.

Figure 10 and Figure 11 show photos of the baseline and layered Polycarbonate specimens at the same impact energy of 120 J. No crack was noticed on the Polycarbonate specimens, but permanent plastic deformation was observed, and this was expected because Polycarbonate is much more ductile than PMMA. Figure 11 shows that debonding occurred around the impact site as additional energy dissipation.

Obviously, the reduction of the maximum impact force leads to less damage to the target [29,30]. On the other hand, it also causes less damage to the projectile. For some applications, this feature would be a win-win case. For example, failure of composite turbine blades is often caused by bird/bat strikes, and debris/hail impact [31]. Replacing or repairing these large wind blades is a very expensive and time-consuming task. The bird strike is becoming a key issue for major wind energy companies, because they not only have to repair or replace the damaged components sooner than economically feasible, but they are also being pursued to pay heavy fines for causing wildlife fatalities to the government. The above damage-trap material interface could yield more resilient wind blades by limiting the maximum impact force through material designs, which will incidentally provide the striking birds a higher chance to survive.

With the fast development of additive manufacturing [32,33], our basic research work can be easily used for practical applications. For example, during a multi-material 3D printing process, several polymer layers are printed first, then a DTMI layer is printed before more polymer layers are printed above the DTMI layer. Also, this approach can be extended to 3D printing for composite materials to improve their damage tolerance.

6. Conclusions

Extensive impact experiments showed that the maximum impact force was reduced by about 60% and 20% for layered PMMA and Polycarbonate specimens by using the DTMI design. Besides, the energy absorption for layered Polycarbonate was increased by 130% for a particular maximum impact force. Failure analysis of the damaged specimens revealed that the adhesive layer is capable of absorbing some impact energy to reduce the impact damage. Simplified contact mechanics analysis showed that the low Young’s modulus of the added adhesive layer is one of the key parameters to reducing the maximum impact force in layered polymers, which leads to dynamic crack arrest at interfaces. Therefore, an efficient material design principle was proposed to develop future material systems with improved impact resistance at low costs.