Research on the penetration resistance of particle ceramic/polyurethane composite materials

Abstract

This study designed and fabricated polyurethane-based granular ceramic/polyurethane composites. The dynamic mechanical properties and anti-penetration performance of different composites were systematically investigated by varying the hardness of the polyurethane matrix and the material composition of ceramic spheres. Penetration experiments revealed that composites with higher polyurethane matrix hardness exhibited larger damage areas on the rear elastic surface while maintaining favorable anti-penetration performance. Among various ceramic spheres tested, alumina ceramic beads demonstrated superior ballistic resistance. Finite element simulations were employed to reconstruct the penetration failure modes of the composites with enhanced precision. The simulation results indicate that high-hardness ceramic spheres serve as the primary factor contributing to both the excellent anti-penetration characteristics and the extensive damage area observed in post-impact composite structures.

Keywords

polyurethane elastomer composite structure penetration

Introduction

The emergence of high-kinetic-energy armor-piercing projectiles and shaped charge warheads has disrupted the offense-defense equilibrium, posing severe challenges to traditional monolithic steel plate armor configurations due to their inadequate protective efficacy at equivalent areal density and prohibitively high economic costs.^1–4 Consequently, the pursuit of innovative materials or structural configurations has become pivotal for achieving breakthroughs in armor protection technology.^5–8

Polyurethane (PU), a polymer synthesized via condensation reactions between isocyanates and polyols, exhibits exceptional mechanical properties and processability.^9,10 Liu et al.¹¹ synthesized PU elastomers using phthalic anhydride-modified polyester polyols and polymeric methylene diphenyl diisocyanate (PMDI) as raw materials. Building upon this formulation, porous nano-silica was incorporated to develop modified PU composites through synergistic interactions between silica and graphene oxide. Qiao et al.¹² demonstrated that the addition of nano-silica significantly enhances the wear resistance and thermal conductivity of PU composites. Zhong et al.¹³ embedded nanospheres into a PU polymer matrix, where optimized interfacial interactions between the nanospheres and matrix endowed the composite with superior dynamic mechanical performance. S. K. Mishra et al.¹⁴ fabricated functionally graded materials by incorporating nano-sized alumina ceramic particles into an epoxy resin matrix, which exhibited excellent impact resistance. The team¹⁵ also validated the influence of particle morphology on the mechanical strength of the composites. Based on experimental results, they further optimized both the nanoparticle content and the fabrication process of the composite structures.

However, the advent of shaped charge warheads necessitates armor systems that resist not only kinetic threats but also thermal damage. Ceramic materials have emerged as an effective solution for mitigating metal jet penetration, with their energy-absorbing fracture mechanisms demonstrating remarkable advantages in anti-penetration applications.^16–19 Nevertheless, ceramic plates exhibit inherent limitations as ballistic materials due to their propensity for crack propagation throughout the structure after initial penetration events. These rapidly expanding fractures drastically reduce mechanical integrity, thereby compromising the material’s ability to withstand subsequent impacts. To mitigate damage propagation, replacing monolithic ceramic plates with discrete ceramic particles presents a viable strategy. By embedding ceramic particles within a PU elastomer matrix, a synergistic integration of PU and ceramic advantages is achieved. This configuration not only utilizes the PU phase to constrain ceramic particles but also enhances the composite’s energy absorption capacity, enabling the fabrication of ceramic/polyurethane composites with exceptional anti-penetration performance.^20–22

Our laboratory has explored the potential of combining ceramics with polymeric materials. He Xingwei²³ fabricated resin-based ceramic/glass fiber composites by bonding ceramic plates with resin, revealing strong interfacial adhesion but also highlighting the inherent drawbacks of ceramic plates as protective components. Yang Liu²⁴ investigated the anti-penetration performance of PU and nano-sized ceramic particle-reinforced composites through ballistic experiments and numerical simulations. Analysis of ballistic limit velocity, deformation modes, and failure mechanisms demonstrated that incorporating ceramic spheres substantially elevates the material’s resistance threshold. Subsequent simulations revealed that irregular ceramic particle distribution induces non-uniform stress fields under extreme loading conditions.

Polyurethane (PU) exhibit flexibility comparable to rubber, yet demonstrate significantly superior interfacial adhesion properties. Compared to composites fabricated using epoxy resin as the filling material, the PU employed in this study offers not only excellent interfacial bonding but also enhanced weather resistance and flexibility. Furthermore, similar to resins, the mechanical properties of PU can be tailored by adjusting the ratio of its components during preparation. This tunability allows the material to better match the properties of other internal components and adapt to varying mechanical conditions in practical applications. This study designs and fabricates a PU-based ceramic particle composite with a spatially ordered lattice arrangement of ceramic spheres, wherein PU fills the interstitial gaps. The composite’s distinctive features include balanced strength, superior energy absorption, and thermal damage resistance.

The incorporation of millimeter-scale, large-sized ceramic particles endows the composite structure with the ability to resist thermal shock damage, while avoiding the common issue of uneven particle distribution often encountered in nanocomposites with high ceramic content. However, this approach also introduces challenges in analyzing the stress distribution within the composite under impact loading due to the resulting heterogeneity. Consequently, the research systematically examines the influence of material parameters—including PU elastomer properties and ceramic particle characteristics—on the dynamic response under spherical projectile impact. To comprehensively evaluate the material’s viability for protective applications, a combined experimental and numerical simulation approach is employed to assess its anti-penetration performance.

Experimental study

This study employs modified isocyanate MDI8617 and castor oil as raw materials to synthesize the PU matrix. The ceramic/polyurethane composite was fabricated via a prepolymerization method²⁵ and pressureless infiltration technique.²⁶

According to the experimental design parameters, ceramic particles with a diameter of 5.8 mm were arranged in a hexagonal close-packed configuration across three layers and placed into a mold coated with a PU release agent. A ruler was used to precisely align one ceramic particle from both the first and third layers with the center of the mold. Castor oil was cooled to 90 °C in a vacuum flask and then uniformly mixed with MDI8617.

After being cast, the uncured specimens were allowed to cool and undergo initial curing for 12 h in an environmental chamber set at 40 °C. Following this initial curing stage, the specimens were transferred to a light-shielded, ventilated fume hood, where they continued to cure for 40 days to ensure uniform properties between the surface and interior components. The preparation process is illustrated in Figure 1.

Figure 1.

Preparation process of granular ceramic/polyurethane composite material.

The mechanical properties of the resulting PU elastomer are closely related to the ratio of MDI to castor oil during preparation. The parameter λ is defined as the ratio of MDI8617 to the average molecular weight of castor oil in the synthesis process. Polyurethanes with different λ values exhibit significant variations in mechanical performance.

According to reference,²⁷ which conducted a systematic study on PU elastomers with λ values ranging from 1.0 to 1.6, this study selected three groups of PU elastomers with λ values of 1.0, 1.2, and 1.4, representing low to high hardness, respectively. These polyurethanes demonstrate markedly different mechanical properties at room temperature, making them suitable for comparing how matrix hardness influences the mechanical behavior of the composite material.

The ceramic particle-reinforced PU composites prepared in this study were fabricated in disk-shaped specimens measuring 120 mm in diameter and 20 mm in height, with their dimensional characteristics and morphology illustrated in Figure 2. Two ceramic materials both with a Mohs hardness of 9 were selected as components of the composite structure: alumina ceramic offers excellent wear resistance, while zirconia ceramic possesses higher fracture toughness. Based on variations in PU hardness (determined by the λ parameter) and ceramic material type, the samples were systematically classified into four distinct categories as detailed in Table 1: HPU/Al₂O₃ MPU/Al₂O₃, LPU/Al₂O₃, and MPU/ZrO₂. These classifications respectively represent: (1) high-hardness PU (λ=1.4) composite with alumina ceramic spheres (Al₂O₃), (2) medium-hardness PU (λ=1.2) composite with alumina ceramic spheres (Al₂O₃), (3) low-hardness PU (λ=1.0) composite with alumina ceramic spheres (Al₂O₃), and (4) medium-hardness PU (λ=1.2) composite with zirconia ceramic spheres (ZrO₂). To ensure experimental reliability and minimize potential errors, each composite variant underwent 4-5 repeated penetration tests. The ballistic penetration experiments were conducted using a gas gun apparatus featuring a 16 mm bore diameter and 7 m long barrel, with the detailed structural configuration of the experimental setup presented schematically in Figure 3.

Figure 2.

Penetrating specimen of granular ceramic/polyurethane composite materialm.

Table 1.

Penetration test samples.

Name	Polyurethane parametersλ	Particle ceramic material
HPU/Al₂O₃	1.4	Al₂O₃
MPU/Al₂O₃	1.2	Al₂O₃
LPU/Al₂O₃	1.0	Al₂O₃
MPU/ZrO₂	1.2	ZrO₂

Figure 3.

Gas gun.

The experimental setup was equipped with observation windows on the protective chamber for real-time monitoring of the test process. During experiments, projectiles were propelled by high-pressure gas and continuously accelerated through the gun barrel. The impact velocity could be precisely controlled by adjusting the gas pressure and was accurately measured using a laser velocimetry system. Upon impact with the target plate, residual velocities of penetrating projectiles were determined using a sky-screen chronogragh. To mitigate the influence of projectile impact position on experimental results in anti-penetration tests of heterogeneous composite structures, a laser positioning system was employed to ensure precise alignment between the muzzle and the ceramic sphere located at the center of the composite plate.

Results of anti penetration experiment

Table 2 represent the projectile velocity and residual velocity of penetration experiment. In the HPU/Al₂O₃ third group experiment and the MPU/ZrO₂ third group experiment, spherical projectiles were embedded in the target plate (Table 3).

Table 2.

Penetration experiment results.

HPU/Al₂O₃			MPU/Al₂O₃
No.	Penetration speed/ $v_{i}$	Residual velocity/ $v_{r}$	No.	Penetration speed/ $v_{i}$	Residual velocity/ $v_{r}$
1	263	131	1	252	160
2	242	100	2	240	138
3	220	0	3	218	34
4	216.5	0	4	210	0

LPU/Al₂O₃			MPU/ZrO₂
No.	Penetration speed/ $v_{i}$	Residual velocity/ $v_{r}$	No.	Penetration speed/ $v_{i}$	Residual velocity/ $v_{r}$
1	244	181	1	239	101
2	240	170	2	211	56
3	232	138	3	180	0
4	200	0

Table 3.

Debonding area.

No.	Penetration speed/ $v_{i}$	Debonding area/mm²
HPU/Al2O3	216	1892
HPU/Al2O3	220	5063
MPU/Al2O3	210	1127
LPU/Al2O3	200	1412
MPU/ZrO₂	180	347

The experimental results demonstrate that the penetration resistance of the composites follows the order: HPU/Al₂O₃ > MPU/Al₂O₃ > LPU/Al₂O₃ when using PU matrices of varying hardness. For composites incorporating zirconia ceramic particles, distinct energy absorption characteristics were observed at different impact velocities. When the projectile velocity approached the critical penetration threshold, the MPU/Al₂O₃ composite with alumina ceramic particles exhibited superior energy absorption performance. However, as the projectile velocity increased further, the MPU/ZrO₂ composite demonstrated enhanced energy absorption capacity due to the higher hardness of zirconia particles. These findings indicate that the dynamic mechanical properties of ceramic/polyurethane composites depend not only on the PU matrix but are also significantly influenced by the ceramic material characteristics and the interfacial coupling effects between the ceramic and PU phases.

Figure 4–7 present the penetration damage morphologies of HPU/Al₂O₃, MPU/Al₂O₃, LPU/Al₂O₃, and MPU/ZrO2 composites at different impact velocities, including both the frontal (front) and backside (rear) surfaces.

Figure 4.

Penetration experiment results of HPU/Al₂O₃.

Figure 5.

Penetration experiment results of MPU/Al₂O₃.

Figure 6.

Penetration experiment results of LPU/Al2O3.

Figure 7.

Penetration experiment results of MPU/ZrO₂.

As evident from Figure 4, when subjected to a penetration velocity of 263 m/s, the spherical projectile completely penetrated the HPU/Al₂O₃ composite. The damage area on the frontal surface was slightly larger than that on the backside surface, with partial ceramic particle detachment from the PU matrix creating visible pores. Notably, the ceramic particles at the impact surface exhibited crushing failure at fracture locations.

Reducing the projectile velocity to 242 m/s resulted in more extensive crack propagation. At 220 m/s, the projectile failed to penetrate the composite plate, where the impact crater diameter measured slightly smaller than the projectile diameter, demonstrating the effective protective capability of the self-healing PU material. Under this impact condition, the backside surface showed significant bulging accompanied by large-area interfacial debonding of the PU layer adjacent to the surface.

Further decreasing the velocity to 216 m/s produced frontal surface damage morphology similar to the 220 m/s case. However, the backside surface exhibited reduced bulging area and markedly diminished debonding zone, indicating velocity-dependent damage characteristics.

Figure 5 demonstrates that when the projectile penetrated the MPU/Al₂O₃ composite at 252 m/s, the damage morphology on the frontal surface resembled that observed in HPU/Al₂O₃ composites under penetration conditions, with the crater diameter being smaller than the projectile diameter. However, the backside surface exhibited smaller perforation holes and reduced damage area compared to HPU/Al₂O₃.

At reduced velocities of 240 m/s and 233 m/s, the spherical projectiles still achieved complete penetration of the composite. Under these conditions, the damage areas on both impact and backside surfaces became nearly identical in size.

At a speed of 210m/s, the projectile became embedded in the composite without full penetration, causing a slightly larger crater on the frontal surface and only minor localized debonding on the backside surface.

Figure 6 demonstrates that when impacted by spherical projectiles at velocities exceeding 232 m/s, the LPU/Al₂O₃ composite was completely penetrated, with the frontal surface damage morphology showing similar characteristics to both HPU/Al₂O₃ and MPU/Al₂O₃ composites. However, compared with other composite plates, the ballistic deflection of the projectile is less significant. Hen the projectile velocity was reduced to 200 m/s, penetration was prevented, resulting in the formation of a significantly larger damage zone on the frontal surface.

Figure 7 shows that when using zirconia (ZrO₂) ceramic particles with higher hardness, the spherical projectiles penetrated the composite at velocities of 239 m/s and 211 m/s. The backside surface morphology resembled that of MPU/Al₂O₃ composites, while the damage area on frontal surfaces exceeded that observed in alumina-reinforced counterparts. At 180 m/s impact velocity, the projectile became lodged within the composite thickness, creating a slightly larger crater on the frontal surface compared to alumina-based composites under similar conditions. The results demonstrate the influence of ceramic particle hardness on composite damage characteristics and penetration resistance.

The energy absorption capacity of the composite material is calculated by processing the experimentally measured penetration velocity and residual velocity, followed by a discussion on the energy-absorbing characteristics of different structural configurations. The energy absorption efficiency of the target plate is defined as η, with the calculation formula specified as follows:

η = \frac{E_{0} - E_{1}}{E_{0}} = \frac{\frac{1}{2} m v_{i}^{2} - \frac{1}{2} m v_{r}^{2}}{\frac{1}{2} m v_{i}^{2}} = \frac{v_{i}^{2} - v_{r}^{2}}{v_{i}^{2}}

(1)

E₀ denotes the initial kinetic energy of the projectile; E₁ represents the residual kinetic energy of the projectile; m is the mass of the projectile; v_i and v_r correspond to the penetration velocity and residual velocity.

The numerical values above the histogram bars in Figure 8 represent the penetration velocities. The data demonstrate that as the projectile’s penetration velocity decreases, the energy absorption rate increases for each composite type until reaching the non-penetration threshold. At higher penetration velocities, the reduced interaction time between the projectile and composite material results in diminished deformation extent, consequently lowering the energy absorption rate.

Figure 8.

Energy absorption of granular ceramic/polyurethane composite materials.

SEM analysis of the perforation region in the MPU/Al₂O₃ composite specimens reveals the following observations. As illustrated in Figure 9(a), after impact loading induces simultaneous fracture of both the ceramic and the PU phases, the majority of the PU matrix remains well-bonded to the ceramic filler; the interface between the two phases is not torn apart by crack propagation. This indicates a strong interfacial coupling between the particulate ceramic and the PU. Owing to the stable interfacial strength of the composite, cracks generated by projectile penetration traverse both the PU matrix and the ceramic particles, enabling all constituents of the composite to collectively resist the penetration event. Moreover, the high-velocity impact generates stress waves that undergo repeated reflection and attenuation within the composite, thereby enhancing the material’s capacity to absorb such waves. Concurrently, a tearing zone oriented perpendicular to the direction of crack extension forms on the fracture surface of the PU matrix (Figure (b)). Figure (c) displays the fine ceramic debris at the fracture surface of the ceramic phase, while Figure (d) shows larger ceramic fragments that remain adhered to the PU after breakage. As a brittle material, ceramic exhibits uncertain damage evolution under complex impact loading. Both macroscopic inspection and electron-microscopic scanning of the ceramic fracture surfaces demonstrate that, under penetration, the ceramic not only produces coarse, irregular fragments but also generates a substantial amount of fine particulate debris. The brittle fracture and associated energy-dissipation mechanisms of the ceramic are the primary drivers for the deflection of crack propagation in the polymer matrix.

Figure 9.

SEM image of ceramic/polyurethane composite board.

Cracks are observed within ceramic particles located near the perforation zone, arising from the transmission of stress waves through the composite. These cracks occur at the contact interfaces between ceramic particles situated close to the projectile path and those positioned along the ballistic trajectory. In this region, the PU matrix is scarce, providing insufficient attenuation of the stress-wave energy. Nevertheless, due to the high toughness of PU, ceramic particles retain their original morphology after cracking and continue to bear load to a certain extent. Because of the relatively high acoustic.

Finite element simulation analysis

To investigate the failure process of the composite under impact, a numerical model of spherical projectile penetration was established using LS-DYNA software. The target plate and projectile models maintained identical dimensions to the experimental specimens. Considering the structural symmetry, a quarter-model was adopted to improve computational efficiency while ensuring accuracy. Symmetry plane constraints were applied perpendicular to the cut surfaces, with fixed boundary conditions implemented on the outer edges of the target. The central region of interest was meshed with refined elements as illustrated in Figure 10.

Figure 10.

Penetration numerical model of granular ceramic/polyurethane composite material.

The contact between the fixture and target plate was defined as AUTOMATIC_SURFACE_TO_SURFACE contact, while the interaction between the spherical projectile and target was modeled using ERODING_ SURFACE_ TO_ SURFACE contact. This contact algorithm effectively prevents computational errors caused by element failure during the penetration process.

Through comparative analysis of experimental results and reference,²⁸ the interfacial normal failure stress (NFLS) and shear failure stress (SFLS) used in this study were determined to be 31.7 MPa and 27.2 MPa, respectively, for numerical simulations.

Ceramics, as brittle materials with high compressive strength, can be treated as elastic materials prior to reaching their elastic limit. However, progressive fracture damage occurs when this limit is exceeded. The Johnson-Holmquist II (JH-2) constitutive model integrates a strength model with damage evolution parameters,²⁹ specifically developed to characterize the behavior of brittle materials under large deformations, high strain rates, and high pressures. This model incorporates the damage weakening effect, where material softening progressively occurs with accumulated damage. The JH-2 model quantitatively describes the dynamic response of both intact and fractured materials through the relationship between material strength, damage state, and pressure. It has been widely adopted for simulating brittle materials like ceramics and rocks under extreme loading conditions involving high strain rates and pressures. The constitutive model is expressed as:

σ = (1 + Cln \dot{ε}) σ_{H E L} {A {(\frac{P + T}{P_{H E L}})}^{N} - D [A {(\frac{P + T}{P_{H E L}})}^{N} - B {(\frac{P}{P_{H E L}})}^{M}]}

(2)

σ represents the normalized equivalent stress of the material under hydrostatic pressure P and strain rate ε̇;

D denotes the damage parameter (0 ≤ D ≤ 1);

T is the normalized maximum tensile strength; A, B, N, C, and M are dimensionless material constants;

For this study, the material parameters of Al₂O₃ ceramics were obtained from manufacturer specifications, while other parameters referenced the properties of 95-grade ceramics ^30,31.The specific numerical values are listed in Tables 4 and 5.

Table 4.

Ceramic material parameters (Al₂O₃).

Parameter
ρ (kg/m³)	3500	C	0.007	K₂ (GPa)	2.74
E (GPa)	152	$M$	0.4	K₃ (GPa)	30
A (MPa)	923.6	D ₁	0.01	HEL (GPa)	0.07
B (MPa)	900	D ₂	1	BETA	1
n	0.44	K₁ (GPa)	2.5

Table 5.

Ceramic material parameters (ZrO₂).

Parameter
ρ (kg/m³)	6050	C	0	K₂ (GPa)	0
E (GPa)	239	$M$	0.6	K₃ (GPa)	0.23
A (MPa)	930	D ₁	0.05	HEL (GPa)	2.79
B (MPa)	310	D ₂	1	BETA	1
n	0.6	K₁ (GPa)	130.95

PU exhibits strain-rate-dependent viscoelastic behavior, demonstrating distinct mechanical properties under different strain rates. Based on the quasi-static and dynamic impact experimental results, Figure 11 presents the static and dynamic mechanical characteristics of PU matrices with varying hard segment contents within the strain rate ranges of 0.0025∼0.128 s^-1 and 800∼1900 s^-1. The first quadrant displays tensile test curves, while the third quadrant contains compression test data. To characterize the strain rate effects of the PU elastomer, the Cowper-Symonds model was employed, which utilizes the dynamic increase factor (DIF) of stress to quantify the material’s strain rate sensitivity.³²

Figure 11.

The stress-strain curve of PU and the fitting of C-S strain rate strengthening model (Figures (a) and (b) show the curves at λ=1.0); Figures (c) and (d) show the curves at λ=1.2; Figures (e) and (f) show the curves at λ=1.4).

This study adopted a reference strain rate of 0.0025 s^-1 as the baseline for strain rate effects. The dynamic increase factor (DIF) was calculated by dividing the stress at each strain level under different strain rates by the corresponding stress at the reference strain rate. The resulting DIF values are plotted in Figure 10 (b), (d), and (f), with fitted parameters shown accordingly.

The model incorporates these parameters to account for strain rate effects in the material’s mechanical properties. The strain rate strengthening effect is expressed by the following equation:

D I F = \frac{σ_{T P U}}{σ_{T P U}^{'}} = 1 + {(\frac{\dot{ε}}{C_{T P U}})}^{\frac{1}{P_{T P U}}}

(3)

DIF represents the dynamic increase factor;

C_TPU and P_TPU are the strain rate parameters of the PU elastomer, corresponding to its dynamic and static yield stresses, respectively. The PU material selected is MAT-PLASTICITY-POLYMER, which can add strain rate strengthening effect to the mechanical properties of the material. The specific parameters are shown in Table 6.

Table 6.

Polyurethane (PU) material parameters.

λ	C_TPU(s^-1)	P _TPU
1.0	160.54	0.1833
1.2	208.64	0.3564
1.4	321.22	0.5007

Table 7 is material parameters used for the steel pole.

Table 7.

Steel material parameters.

Material	E (MPa)	μ	ρ(kg/m³)
Steel	200000	0.3	7850

Using the aforementioned material parameters, finite element simulation of penetration tests was conducted. Taking the MPU/Al2O3 sample as an example, the simulation results under different projectile velocities were verified for linear tetrahedral meshes with sizes of 1 mm, 1.5 mm, 3 mm, and 6 mm. It was observed that significant deviations occurred when the mesh size exceeded 3 mm. When the mesh size was larger than 6 mm, the error in the residual velocity of the projectile exceeded 10% compared to the experimental results at an initial projectile velocity of 255 m/s, and the error further increased as the initial velocity decreased. In contrast, when the mesh size was less than 1.5 mm, the simulation results closely matched the experimental data, demonstrating good convergence. To achieve a balance between simulation accuracy and computational cost, a tetrahedral mesh element size of 1.5 mm was adopted for the simulations in this study (Figure 12).

Figure 12.

Influence of different mesh sizes on simulation results.

A comparison between experimental and simulation results demonstrates good agreement, with the numerical model exhibiting high accuracy and satisfactory mesh convergence. To replicate the material’s damage behavior, element erosion was implemented in the mesh properties, while damage parameters for the material model were referenced from Wu’s study.³³

The ballistic limit velocity, a key metric for evaluating a composite’s penetration resistance, represents the impact velocity at which a spherical projectile has a 50% probability of fully penetrating the target. Recht and Ipson³⁴ derived the theoretical ballistic limit equation based on energy and momentum conservation principles, expressed as:

v_{r} = a {(v_{i}^{p} - v_{50}^{p})}^{1 / p}

(4)

In the formula, v_i and v_r are the initial impact velocity and residual velocity of the projectile;

V₅₀ is the maximum ballistic velocity;

a and P is an undetermined constant.

Through combined numerical simulation and experimental testing, the penetration velocities for MPU/ZrO₂, HPU/Al₂O₃, MPU/Al₂O₃, and LPU/Al₂O₃ composites were determined, along with their respective ballistic limit velocities, as illustrated in Figure 14(a) comparison between experimental and simulated penetration velocities and residual velocities across all composite types revealed discrepancies of less than 10%. This close agreement indirectly validates the accuracy of the numerical model.

Figure 13(a) presents the ballistic limit velocities for three composite materials: HPU/Al₂O₃ at 222.7 m/s, MPU/Al₂O₃ at 217.3 m/s, and LPU/Al₂O₃ at 211.5 m/s. The corresponding fitting parameters were determined as a=0.75 and p=2.6 for HPU/Al₂O₃, a=1.0 and p=2.5 for MPU/Al₂O₃, and a=1.1 and p=2.5 for LPU/Al₂O₃., indicating that the ballistic limit velocity expressions for HPU/Al₂O₃, MPU/Al₂O₃, and LPU/Al₂O₃ are as follows:

v_{r} = 0.75 {(v_{i}^{2.5} - 222 . 7^{2.5})}^{1 / 2.5}

(5)

v_{r} = 1 {(v_{i}^{2.5} - 217 . 3^{2.5})}^{1 / 2.5}

(6)

v_{r} = 1.1 {(v_{i}^{2.5} - 211 . 5^{2.5})}^{1 / 2.5}

(7)

Figure 13.

The penetration performance of granular ceramic/polyurethane composite materials (Figure (a) shows the ballistic limit velocities of HPU/Al2O3、MPU/Al2O3、LPU/Al2O3; Figure (b) shows the ballistic limit velocities of HPU/ZrO2、MPU/ZrO2、LPU/ZrO2).

Figure 14.

The influence trend of granular ceramic materials on ballistic ultimate velocity.

Figure 13(b) shows the fitted ballistic limit velocities for HPU/ZrO₂, MPU/ZrO₂ and LPU/ZrO₂ composites as 209.9 m/s, 199.9 m/s and 192.9 m/s respectively. The corresponding fitting parameters are: a=0.68 and p=1.87 for HPU/ZrO₂; a=1.02 and p=1.69 for MPU/ZrO₂; while for LPU/ZrO₂, the parameters a=0.80 and p=2.24 remain as undetermined constants. These results lead to the following expressions for the ballistic limit velocities of HPU/ZrO₂, MPU/ZrO₂ and LPU/ZrO₂ composites:

v_{r} = 0.68 {(v_{i}^{1.87} - 209 . 9^{1.87})}^{1 / 1.87}

(8)

v_{r} = 1.02 {(v_{i}^{1.69} - 199 . 9^{1.69})}^{1 / 1.69}

(9)

v_{r} = 0.8 {(v_{i}^{2.24} - 192 . 9^{2.24})}^{1 / 2.24}

(10)

Analysis of the penetration performance of ceramic/polyurethane composites in Figures 13 and 14 yields the following key conclusions.

The study demonstrates that alumina (Al2O3) ceramic particle reinforced composites exhibit significantly superior penetration resistance compared to their zirconia (ZrO2) counterparts. Within the same ceramic system, increasing the hardness parameter (λ) of the PU matrix enhances the composite’s anti-penetration capability. These findings clearly indicate that both ceramic particle selection and PU matrix hardness critically influence the composite’s ballistic performance. A PU matrix with higher elastic modulus provides greater resistance and energy absorption capacity during impact, thereby improving penetration resistance. However, the reduced toughness of high-hardness PU also leads to larger damage zones upon failure. Interestingly, despite zirconia’s higher intrinsic hardness, ZrO2-reinforced composites show inferior penetration resistance compared to Al2O3-based materials, which is attributed to interfacial coupling effects between the ceramic particles and PU matrix. Experimental observations and simulation results reveal that significant hardness differences between ceramic particles and PU matrix promote stress concentration at their interfaces upon impact, consistent with stress wave transmission and reflection theory. In such cases, interfacial debonding between PU and ceramic particles becomes the predominant failure mechanism of the composite structure.

Analysis of Figure 15 clearly reveals the velocity, acceleration and deformation characteristics during penetration. In the initial stage (marked as phase ① in Figure 13), the spherical projectile impacts the composite at 218 m/s. The projectile then begins penetrating through the PU surface layer and first ceramic particle layer. Due to the thin PU surface layer, this penetration phase is brief, with ceramic particles providing the primary resistance. During this process, acceleration rapidly reaches 1.8×10³ km/s² with minor fluctuations, while projectile velocity drops sharply to 130 m/s.

Figure 15.

Penetration process of MPU/Al₂O₃ and velocity variation of spherical projectile.

At 70 μs penetration time, the spherical projectile begins penetrating the second ceramic particle layer, corresponding to phase ② and phases IV-V in Figure 13. During this stage, the acceleration sharply decreases to 1.0×10³ km/s² while the velocity further reduces to approximately 60 m/s. Phase IV reveals significant damage to the PU matrix between the second and third ceramic particle layers, where interparticle collisions occur, facilitating damage propagation and serving as the primary damage mechanism of the composite under penetration. In phase V, the bottom PU matrix reaches its tensile limit and initiates cracking. Although the third ceramic particle layer remains intact, it undergoes downward displacement under stress impact, indicating the matrix can no longer effectively constrain particle movement, resulting in rapid acceleration decline.

By 130 μs, the projectile penetrates the third ceramic particle layer (phase ③ and phases VI-VII in Figure 13, where acceleration further diminishes to 1.0×10² km/s² and velocity declines to about 30 m/s. At 225 μs penetration time (phase ④ and phase VIII in Figure 13, the projectile completely perforates the composite. As penetration completes, the resisting force progressively diminishes until vanishing, causing the acceleration to stabilize while maintaining constant residual velocity. Under this intense impact, ceramic particles at the composite’s bottom center separate from the matrix and eject rapidly from their original positions. Simultaneously, surrounding particles experience varying degrees of impact, sequentially fracturing to generate extensive ceramic debris.

Figure 16 provides a clearer visualization of the stress states within each layer of the composite material during projectile penetration. The observation focuses on the frontal surface of the composite plate and the planes containing the three layers of ceramic spheres. The selected time points correspond to phases II, III, VI, and VIII marked in Figure 15. In phase II, the spherical projectile penetrates the surface PU layer and contacts the ceramic sphere directly beneath it. This ceramic sphere is observed to shatter easily. Concurrently, the area of the stress field on the surface PU layer is noticeably smaller than that on the plane containing the ceramic spheres. This difference is attributed to the significantly lower wave speed in PU compared to ceramic, indicating that the ceramic particles bear the primary load during the initial penetration stage. In phase III, the ceramic sphere directly under the projectile and those in its immediate vicinity are shattered. The projectile also displaces the second and third layers of ceramic spheres from their original positions, with partial fragmentation occurring in the second layer. By phase VI, the projectile has completely penetrated the second ceramic layer, but its velocity is substantially reduced. The remaining kinetic energy is insufficient to shatter the third layer of ceramic particles; instead, it merely pushes them away from their original plane. The Mises stress contour on these third-layer particles shows that, although displaced, they remain intact, as evidenced by the circular patches of adhering PU material visible on their surfaces. In phase VIII, the projectile fully perforates the ceramic/polyurethane composite, leaving a central hole through all layers.

Figure 16.

Mises stress contour plot of MPU/Al₂O₃.

Conclusion

This study designed a ceramic/polyurethane composite based on a large-particle structure and systematically investigated its dynamic mechanical response under projectile impact. The experimental setup employed a two-stage light gas gun to launch 16-mm-diameter, 16-g steel spherical projectiles. Through combined experimental and numerical approaches, we examined how PU matrix properties and ceramic particle characteristics influence the composite’s penetration resistance, with particular focus on deformation/failure modes, ballistic limit velocities, and energy absorption characteristics under various impact conditions. The principal findings are summarized as follows.

(1) Composites with PU matrices of different elastic moduli exhibited similar frontal surface damage features, including penetration holes smaller than the projectile diameter. However, high-modulus PU composites showed larger backside surface damage areas with extensive radial cracking, whereas low-modulus variants demonstrated better elastic recovery with smaller backface deflections and localized particle-matrix debonding.

(2) For identical ceramic particles, increasing the polyurethane’s λ parameter (hardness) enhanced penetration resistance. The HPU/Al2O3 composite with highest matrix hardness and elastic modulus achieved the maximum ballistic limit velocity (222.7 m/s), followed by MPU/Al2O3 (217.3 m/s) and LPU/Al2O3 (211.5 m/s).

(3) When maintaining the same PU matrix, ZrO2-reinforced composites showed slightly inferior performance to Al2O3 counterparts. The HPU/ZrO2 configuration exhibited a 209.9 m/s ballistic limit, approximately 20 m/s lower than HPU/Al2O3 with identical matrix.

(4) Experimental-simulation correlation revealed two critical performance factors: particle-matrix interfacial adhesion quality, and stress wave concentration effects. During penetration, ceramic particles provided primary resistance during initial impact, while the PU matrix dominated later-stage penetration behavior and ultimately determined the final damage morphology. Therefore, in the design of similar composite structures, the quality of the interfacial bond between the ceramic and the PU matrix may be more critical than the inherent strength of the ceramic itself. While increasing the hardness of the PU enhances penetration resistance, it simultaneously leads to an enlargement of the debonding area upon impact. Thus, it is essential to select the PU with the lowest feasible hardness while ensuring the structure is not perforated, based on the anticipated load environment. This optimization aims to minimize the damaged area under ballistic impact.

Footnotes

ORCID iD

Na Xinyu

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was financially supported by the National Natural Science Foundation of China (Grant No:11972127).

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

References

Hao

Zhao

Miao

, et al. Multiple Impact-Resistant 2D Covalent Organic Framework. Nano letters 2023; 23(4): 1416–1423. https://doi.org/10.1021/acs.nanolett.2c04747

Zhang

Wang

, et al. Preparation of styrene-butyl acrylic latex films with impact resistance properties and their applications as water-based damping coating. Progress in Organic Coatings: An International Review Journal 2023; 52(3): 182–184.

Tian

Tay

Tan

, et al. Improving the impact performance and residual strength of carbon fibre reinforced polymer composite through intralaminar hybridization[J]. Composites, Part A. Applied science and manufacturing 2023; 33(7): 684–688.

Lei

Sun

, et al. Low-velocity impact and compression-after-impact behaviors of twill woven carbon fiber/glass fiber hybrid composite laminates with flame retardant epoxy resin. Composite structures 2023; 15(6): 321–328.

Pang

Yan

, et al. Dynamic response of polyurethane foam and fiber orthogonal corrugated sandwich structure subjected to low-velocity impact. Composite structures 2022; 23(12): 282–287.

Deng

Zeng

Wang

, et al. Research on the low-velocity impact performance of composite sandwich structure with curved-crease origami foldcore. Thin-Walled structures 2022; 15(7): 174–181.

Liu

Experimental Study on the Performance of Polyurethane-Steel Sandwich Structure under Debris Flow. Applied Sciences 2017; 7(10): 1018–1024. https://doi.org/10.3390/app7101018

Zhao

Yang

, et al. Mechanical properties and energy absorption capabilities of aluminium foam sandwich structure subjected to low-velocity impact. Construction and Building Materials 2021; 273(7): 121996. https://doi.org/10.1016/j.conbuildmat.2020.121996

Atiqah

Mastura

Ali

, et al. A Review on Polyurethane and its Polymer Composites. Curr Org Synth 2017; 2017,14(2): 233–248. https://doi.org/10.2174/1570179413666160831124749

10.

Senichev

Pogorel'Tsev

Slobodinyuk

, et al. Relationship between Abrasive Wear of Urethane-Containing Elastomers and Their Physical and Mechanical Properties. Inorganic Materials: Applied Research 2021; 12(4): 1100–1103. https://doi.org/10.1134/s2075113321040377

11.

Liu

Zhao

, et al. Research on Porous Nano-SiO2/Graphene Oxide Modified Polyurethane Coating Materials. Journal of Ceramics 2020; 41(04): 531–536.

12.

Qiao

Pan

Wang

, et al. Preparation, Thermal and Me-chanical Properties of Nano Boron Nitride/Graphene Ox-ide/Polyurethane Based Composite Materials. J Chin Ceram Soc 2020; 48(07): 1062–1073.

13.

Zhong

Liu

Zhu

, et al. Preparation and impact resistance application of polyurethane foam reinforced by nanospheres. Packaging Engineering 2020; 41(01): 167–172.

14.

Mishra

Shukla

Patel

. Epoxy-alumina functionally graded nanocomposites: gradation and morphological effect of alumina on impact strength and viscoelastic properties. Iran Polym J 2025; 34: 157–169. https://doi.org/10.1007/s13726-024-01366-x

15.

Mishra

Maurya

Pandey

An Experimental Study on the Mechanical Properties and Microstructure of Epoxy-Al2O3 Polymer Nanocomposites. MAPAN (2025). https://doi.org/10.1007/s12647-025-00875-1

16.

Ren

Sun

Zhou

, et al. Impact response of a sandwich with a foam aluminum core enhanced by a ceramic tile: An experimental study. Journal of Sandwich Structures Materi-als 2023; 25(6): 625–644. https://doi.org/10.1177/10996362221130967

17.

Rae

. Thermoelastic analysis of functionally graded sandwich plates with a homogeneous core. Journal of Mechanical Science and Technology 2022; 36(9): 4583–4592.

18.

Moleiro

Madeira

Careear

, et al. Thermo-mechanical design optimization of symmetric and non-symmetric sandwich plates with ceramic-metal-ceramic functionally graded core to minimize stress, deformation and mass. Composite Structures 2021; 4(16): 27–33.

19.

Permoon

Farsadi

Askarian

. Vibration analysis of sandwich cylindrical shells made of graphene platelet polymer–viscoelastic–ceramic/metal FG layers. Functional Composites and Struc-tures 2023; 5(1): 37–45. https://doi.org/10.1088/2631-6331/acbd28

20.

Zheng

Zhou

Yuan

, et al. Microwave curing kinetics and properties of particle Al2O3 reinforced epoxy resin composites. Polymer Material Science & Engineering 2017; 33(10):65–71.

21.

Zou

, et al. Dynamic compressive properties of graphene/ceramic particle reinforced polyurethane based compo-sites. Acta Armamentarii 2023; 44(03): 728–735.

22.

. Effect of Different NCO Content on the Erosive Wear Re-sistance of Polyurethane Composite. Lubrication Engineering 2006; 21 (33):79–82.

23.

. Research on Penetration Resistance of Ceramic/Fiber/Aluminum Foam Composite Plates. Harbin Engineering University, 2020. https://doi.org/10.27060/d.cnki.ghbcu.2020.001660

24.

Yang

. Research on Impact Characteristics of Gra-phene/Polyurethane and Ceramic Ball Composite Structure. Harbin Engineering Uniwersity, 2022.

25.

Jiang

. Synthesis and application of various polyurethane prepolymers. Chemical Propellants & Polymeric Materials 2020; 18(05): 30–36.

26.

Zhang

, et al. Research progress on polymer based graphene oxide nanocomposites. Fine Chemicals 2020; 37(11):2161–2171.

27.

. Study on dynamic response of polyurethane steel composite structure under impact load [D]. Harbin Engineering University, 2023.

28.

Wetzel

Haupert

Zhang

, et al. Epoxy nanocomposites with high mechanical and tribological performance. Composites Science & Technology 2003; 63(14): 2055–2067.

29.

Rong

. Simulation Study of Tc Composite Bullet Penetrating Ceramic Composite Target. IOP Conference Series: Earth and Environmental Science 2019; 330(4): 79–86. https://doi.org/10.1088/1755-1315/330/4/042024

30.

Research status and development of polyurethane elastomers. Mechanical Management Development 2007; 023(06): 3–4. DOI: 10.16525/j.cnki.cn14-1134/th.2007.06.023.

31.

Liu

, et al. Numerical simulation of the influence of cutting parameters on the cutting process of ZrO2 ceramics. Diamond and Abrasive Tool Engineering 2023. https://doi.org/10.13394/j.cnki.jgszz.2023.0188

32.

Jiang

Zhang

Wei

, et al. Study on the dynamic response of polyurea coated steel tank subjected to blast loadings. Journal of Loss Prevention in the Process Industries 2020; 67: 2024–2031. https://doi.org/10.1016/j.jlp.2020.104234

33.

Zou

Shubo

, et al. Dynamic Compressive Properties of Graphene/Ceramic Particle Reinforced Polyurethane-Based Composites. Acta Armamentarii 2023; 44(3): 728–735.

34.

Recht

Ipson

. Ballistic perforation dynamics. Journal of Applied Mechanics 1963; 30(3): 384–390. https://doi.org/10.1115/1.3636566