Underwater Implosion and Energy Mitigation of Hybrid Glass-Carbon Composite Shells

Abstract

Experiments were conducted to investigate the dynamic buckling behavior of underwater hybrid composite tubes. The study focused on roll-wrapped hybrid layered glass-carbon fiber epoxy composite shells with a six-layer quasi-isotropic layup configuration. In addition to control specimens consisting of fully glass fiber-reinforced polymer and carbon fiber-reinforced polymer, four different hybrid layup patterns were examined. These specimens fitted with custom endcaps were placed inside a 7-kiloliter pressure vessel and subjected to increasing hydrostatic pressure until dynamic implosion occurred. High-speed cameras captured the failure event, and the resulting images were analyzed using Digital Image Correlation (DIC) techniques to obtain full-field displacement data. Additionally, tourmaline pressure transducers positioned around the specimens recorded local dynamic pressure histories. The results revealed that the contribution of each ply location varied in the overall failure behavior of the structures. The thickness of the internal plies played a dominant role in enhancing the structural performance, while the stiffness of the outer plies greatly influenced the bending stiffness. The energy released during the collapse was highly dependent on the failure mechanism of the internal plies. Specifically, for the considered geometries, tubes with glass fiber internal plies exhibited significantly lower energy emissions compared to carbon fiber inner plies.

1. Introduction

In recent years, extensive research has been conducted in the naval industry to enhance the durability and survivability of structures and vehicles. Composites have emerged as a promising alternative to metallic structures, offering various advantages such as superior corrosion resistance, increased potential operating depths for submerged structures due to their high strength-to-weight ratio, as well as reduced thermal, magnetic, and acoustic signatures, making them highly desirable for marine applications [1].

However, marine structures like underwater pipelines, unmanned underwater vehicles (UUVs), and forward-deployed underwater systems are susceptible to high external pressures as the ocean depth increases. These structures fail when the external pressure approaches their critical hydrostatic buckling pressure or when exposed to dynamic loads such as nearby explosions or structural collapses. The implosion of thin composite structures in a high-energy environment typically occurs in two stages. First, the cylinder becomes unstable and collapses inwards at an increasing velocity, causing a drop in local pressure as the surrounding fluid accelerates along with the structure. Second, a high-amplitude pressure pulse is emitted when the cylinder walls make contact, resulting in an abrupt change in the momentum of the surrounding fluid [2]. This pressure wave has been shown to induce damage to neighboring structures [3,4,5].

Extensive research has been conducted since the mid-twentieth century to understand implosion phenomena in various loading conditions, including space vehicle design [6], offshore pipelines [7], and collapse behavior studies [8]. Following several high-profile accidents, there has been a growing demand for a comprehensive understanding of implosion phenomena, leading to numerous new studies on the topic [9,10,11,12]. Early studies by Turner and Ambrico focused on characterizing the acoustic pulses released during the collapse of glass structures and their potential to cause damage to adjacent structures [13,14]. These studies contributed to the development of experimentally validated computational models for buckling characterization in metallic structures, highlighting the modifications caused by local pressures on the collapsing structure [14]. More recently, Sachin et al. utilized the Digital Image Correlation (DIC) technique in combination with high-speed photography to capture full-field displacements, velocities, and their correlation with emitted pressure pulses [15].

It is well established in the literature that carbon fiber exhibits significantly higher tensile modulus and tensile strength, while glass fiber has higher failure strains under both tensile and compressive loading conditions [16,17]. Several studies have independently investigated the collapse phenomena and energy emissions of carbon and glass composite tubes under hydrostatic loading conditions. Pinto et al. [17] conducted implosion experiments on filament-wound carbon-fiber/epoxy and glass-fiber/polyester tubes in a pressure vessel and employed 3D DIC techniques to capture full-field deformations and velocities during the collapse event. The study revealed that carbon fiber-reinforced tubes exhibit higher collapse pressures compared to glass fiber-reinforced shells with the same fiber orientation and wall thickness. Delamination and fiber pull-out were identified as dominant damage mechanisms in these composites due to glass fiber’s higher strain-to-failure. However, the brittleness of carbon fibers results in their fracture before more energy-intensive damage mechanisms can occur, leading to higher energy emissions from carbon fiber shells compared to glass fiber shells [18].

Hybridization of carbon fiber composites has garnered significant attention in recent studies due to the desire to enhance failure strain, overall performance, and address the cost implications. Hybridization can occur in three distinct ways: between layers (interlaminar), within layers (intralaminar), and at the yarn level (intrayarn) [19]. Models suggest that intrayarn hybrids are likely to achieve the most significant enhancements in failure strain [19]. However, interlaminar hybrids have been extensively studied due to their cost-effectiveness and ease of production. One study examined the impact performance of interlaminar GFRP/CFRP hybrid composite panels [20]. Pandya et al. investigated the ballistic limit velocity of various hybrid glass/carbon fiber composite laminates and achieved significant improvements by sandwiching carbon fiber layers between glass fiber layers [21]. Conversely, Reddy et al. demonstrated that a laminate incorporating a 50:50 weight ratio of the two fibers exhibited maximum energy absorption [21,22]. To the best of the author’s knowledge, no investigation into the underwater implosion of hybrid composite shells comprising carbon and glass fibers has been conducted. For this reason, this study aims to bridge this gap by designing interlaminar GFRP/CFRP hybrid composite implodables with enhanced capabilities for mitigating implosion energy.

2. Experimental Procedures

2.1. Specimen Design and Preparation

The hybrid implodable volumes investigated in this study were roll-wrapped glass-carbon/epoxy hybrid tubes. These tubes were fabricated using commercially available unidirectional e-glass/epoxy (470 0AW) and carbon/epoxy (277 GSM 0AW) prepregs obtained from Rockwest Composites (West Jordan, UT). The tube architecture followed a roll-wrapped quasi-isotropic pattern of [90°/30°/−30°]s, where the 90° direction represented the circumferential orientation of the cylinder. The glass and carbon prepregs had thicknesses of 0.28 mm and 0.15 mm, respectively.

The manufactured tubes had an inner diameter (ID) of 50.8 mm (2 inches) and an unsupported length of 304.8 mm (12 inches), resulting in a length-to-diameter ratio (L/D) of 6. The nominal thicknesses of the tubes used in this study ranged from 0.98 mm to 1.50 mm, corresponding to diameter-to-thickness (D/h) ratios between 33.9 and 51.8. These dimensions were selected to promote circumferential Mode II (a deformed tube with two circumferential lobes) buckling [5].

Four different hybrid shells were compared against benchmark glass-fiber (GFRP) and carbon-fiber (CFRP) shells, as depicted in Figure 1a. For clarity, the outermost and innermost plies were referred to as the outer plies (layers 1 and 6), while the four center layers (layers 2, 3, 4, and 5) were considered internal plies. The large prepreg sheets were cut to suitable sizes for manufacturing these structures. The width and fiber orientation of each sheet varied depending on the layer and case, while the length was fixed at 457.20 mm (18 inches) to obtain short specimens for quality evaluation.

To fabricate the tubes, a mold release agent was applied to a 558.80 mm (22 inches) long, 50.8 mm (2 inches) outer diameter aluminum 6061-T6 mandrel. The cut prepreg sheets were then placed on a flat, smooth glass table with approximately a 2 mm overlap between adjacent sheets (Figure 1b). The aluminum mandrel heated to 50 °C was rolled over the prepreg sheets while applying even and continuous pressure to form the tube perpendicularly to the table (Figure 1c). A release film was subsequently applied over the final layer, followed by a breather fabric to absorb excess resin during the curing process. Finally, shrink tape was wrapped around the molded shell to apply pressure during curing.

The rolled tube was baked in an oven at a temperature of 121 °C for two hours, with a temperature rise and drop rate of 3 degrees per minute maintained during the heating and cooling phases (This process is summarized in the flow chart presented in Figure 2). Subsequently, portions measuring 355.60 mm (14 inches) in length were cut from the baked shell for experimentation (Figure 1d), while 50.8 mm (2 inches) length sections were used for compression tests to ensure quality control (details provided in Appendix A).

2.2. Material Characterization

The mechanical properties of each carbon and glass ply were determined according to ASTM standards. In-plane shear values (G12) were obtained using an Instron 3366 with a 10 KN load cell, following ASTM D5379, at a loading rate of 3 mm/min. Tensile moduli (E11 and E22) and Poisson’s ratio (ν12) were measured using the Shimadzu AG-X Plus Universal Testing Machine-UTM (Shimadzu Corporation, Kyoto, Japan) with a 300 kN load cell, following ASTM D3039, at a loading rate of 2 mm/min [23,24]. The strains were obtained using a 2D Digital Image Correlation (DIC) technique. The results of these tests are presented in

Table 1. Mechanical properties of unidirectional composite plies.

	E11 (GPa)	E22 (GPa)	ν12	G12 (GPa)	Density (kg/m3)	Fiber Diameter (µm)	Fiber Mass Fraction	Fiber Volume Fraction	Ply Thickness Post-Cure (mm)
Carbon	127	7.25	0.35	5.53	1440	7	28.8	58.4	0.145
Glass	49	11.31	0.33	5.38	1890	15	22.7	56.3	0.218

.

The fiber volume and mass fractions were determined following ASTM D792. The mass of each specimen in air (M_air) and in water (M_water) was measured, and the specific gravity (S = M_air/(M_air − M_water)) was calculated. The density (ρ) of each specimen was then obtained by multiplying S with the density of water at room temperature. To calculate the mass and volume fractions, a 10% solution of KOH in Ethylene glycol was used to digest the epoxy matrix from 25.4 mm × 25.4 mm weighed specimens (M_s). The fibers were rinsed with dimethylformamide and demineralized water, and then dried in an oven at 100 °C for 90 min. After cooling down, the fibers were weighed to the nearest 0.1 mg (M_f), and the mass and volume fractions were calculated.

2.3. Experimental Setup

The experiments presented in

Table 2. Geometry properties with experimental collapse pressure.

Experiment Name	Critical Collapse Pressure CP (MPa)	Nominal Thickness, t (mm)	Specimen Mass, M (g)
CFRP	1.04 ± 0.01	0.98 ± 0.03	79.3 ± 1.0
Hybrid–[C/G/G/G/G/C]	1.95 ± 0.06	1.39 ± 0.04	130.2 ± 1.3
Hybrid–[G/C/C/C/C/G]	0.89 ± 0.02	1.17 ± 0.03	101.6 ± 1.0
Hybrid–[G/G/G/C/C/C]	1.21 ± 0.03	1.37 ± 0.03	118.0 ± 0.7
Hybrid–[C/C/C/G/G/G]	1.14 ± 0.04	1.28 ± 0.03	117.7 ± 1.0
GFRP	1.35 ± 0.07	1.50 ± 0.03	149.3 ± 1.4

were conducted inside a semi-spherical pressure vessel. Each experimental case was repeated three times, and the mean and standard deviation of the collapse pressure are presented in Table 2. The vessel was designed to simulate a deep ocean environment, capable of reaching a maximum depth of 687 m and with a pressure rating of 6.89 MPa. To facilitate lighting and photography, the vessel is equipped with eight optically clear acrylic windows mounted at its mid-span. Stereo imaging of the implodables was captured using two high-speed cameras (Photron SA1, Photron USA, Inc., San Diego, CA, USA) positioned at a 17-degree angle from each other, operating at a frame rate of 40,000 frames per second (fps). Two high-intensity lamps provided illumination during the implosion event.

The cylindrical specimen was mounted horizontally at the center of the tank, as depicted in Figure 3a,c. Prior to the setup, the ends of the cylindrical specimens were sealed with Aluminum 6061-T6 endcaps fitted with rubber O-rings (Figure 3b). The cylinder was securely fixed within the frame, as shown in Figure 3c. The frame itself was anchored at the center of the tank using a system of 1.6 mm thick steel woven cables attached to the walls of the pressure vessel. Underwater Digital Image Correlation (DIC) was employed to capture full-field displacements of the tubes during the buckling event.

To measure changes in local pressure throughout the collapse, three piezoelectric underwater blast transducers by PCB Piezotronics, INC. (Depew, NY, USA) were strategically mounted at different positions along the length of the tube. Sensor S1 was positioned 304.8 mm (12 in) from the surface of the shell along its midspan, while S2 and S3 were located 50.8 mm (2 in) from the tube surface. S3 was positioned above the tube, whereas S2 was positioned behind it along the midspan. These dynamic pressure transducers have a rise time of 1.5 µs, a resolution of 0.7 kPa, and an upper-frequency response of 200 kHz. Pressure outputs were monitored using Dewesoft SIRIUS XHS (Dewesoft LLC, Whitehouse, OH, USA) in conjunction with a computer, sampling at a rate of 15 MHz.

To initiate the experiment, the vessel was filled with optically clear water, leaving an air pocket at the top. Nitrogen was then introduced into the air pocket at the top of the tank to pressurize the system at a rate of 6895 Pa/s (1 psi/s). The pressure continued to increase until the tube imploded, at which point a manual switch was used to trigger the Dewesoft data acquisition system and the high-speed cameras.

2.4. Digital Image Correlation (DIC)

To ensure accurate measurements during the experiments, a high-contrast random speckle pattern was applied to the tubes. This was achieved by coating the tubes with white paint and randomly placing speckles with an approximate diameter of 2 mm across the coated surface. The high-speed Photron FastCam SA1 cameras, positioned outside the pressure vessel at a 17-degree offset, were set to record the event at a frame rate of 40,000 fps.

The acquired high-speed images were subsequently analyzed using commercially available VIC-3D (version 9) software from Correlated Solutions, Inc. (Columbia, SC, USA). This software employs a matching algorithm to identify common pixel subsets of the random speckle pattern between reference undeformed images and deformed images captured during the experiment. To calibrate the VIC-3D software, a calibration grid was submerged and positioned at the same locations as the specimens within the vessel, with the vessel filled with water. The grid was then manually translated and rotated along all six degrees of freedom while the corresponding grid images were recorded. This calibration process enabled accurate measurements by establishing a reference for the software.

After successfully calibrating the cameras using the grid, Digital Image Correlation (DIC) technique was used to measure the diameter of the undeformed tube. This value was compared against the actual value measured with a vernier caliper and, the calibration was accepted with the error of less than 1%. It is worth noting that this DIC analysis was conducted within the water chamber, as illustrated in Figure 3. Previous studies [25,26,27] have demonstrated that these procedures can yield in-plane and out-of-plane displacements with 97% accuracy under underwater conditions.

3. Theoretical Procedures

3.1. Laminate Composites

The forces per unit length, $N_{ij}$ and moments per unit length, $M_{ij}$ of a composite laminate can be expressed in terms of uniaxial strains ${\epsilon }_{ij}$, shear strains ${\gamma }_{ij}$, curvature $k_{ij}$ and a stiffness matrix presented in Equation (1). Where the subscripts $i$ and $j$ are coordinate components $x$, $y$ and $z$. For simplicity, just one subscript ($i$) is shown for terms with repeated subscripts ($ii)$. The stiffness matrix is a function of the layup angles, layup locations and material properties according to classical laminate theory [28].

$$\begin{array}{c}\left\{\begin{array}{c}{N}_x\\ N_y\\ N_{xy}\\ M_x\\ M_y\\ M_{xy}\end{array}\right\}=\left[\begin{array}{cccccc}{A}_{11}& A_{12}& A_{16}& B_{11}& B_{12}& B_{16}\\ A_{12}& A_{22}& A_{26}& B_{12}& B_{22}& B_{26}\\ A_{16}& A_{26}& A_{66}& B_{16}& B_{26}& B_{66}\\ C_{11}& C_{12}& C_{16}& D_{11}& D_{12}& D_{16}\\ C_{12}& C_{22}& C_{26}& D_{12}& D_{22}& D_{26}\\ C_{16}& C_{26}& C_{66}& D_{16}& D_{26}& D_{66}\end{array}\right]\left\{\begin{array}{c}{\epsilon }_x^0\\ {\epsilon }_y^0\\ {\gamma }_{xy}^0\\ k_x\\ k_y\\ k_{xy}\end{array}\right\}\end{array}$$

(1)

The laminate extensional stiffness ($A_{ij}$), coupling stiffnesses ($B_{ij},C_{ij}),$ and laminate-bending stiffnesses ($D_{ij})$ can be calculated with Equations (2)–(4) using the globalized reduced stiffness ${\overline{Q}}_{ij}$ and ply locations, $Z$. The ply locations are the distance from the mean laminate thickness to the ply.

$$A_{ij}={\sum }_{k=1}^N{\left({\overline{Q}}_{ij}\right)}_k\left(Z_k-Z_{k-1}\right)$$

(2)

$$\begin{array}{c}{B}_{ij}=C_{ij}=\frac{1}{2}{\displaystyle \sum _{k=1}^N}{\left({\overline{Q}}_{ij}\right)}_k\left(Z_k^2-Z_{k-1}^2\right)\end{array}$$

(3)

$$\begin{array}{c}{D}_{ij}=\frac{1}{3}{\displaystyle \sum _{k=1}^N}{\left({\overline{Q}}_{ij}\right)}_k\left(Z_k^3-Z_{k-1}^3\right) fori,j=1,2and6\end{array}$$

(4)

The ABCD matrix for the different configurations considered in this study are presented in Appendix B.

3.2. Critical Buckling Pressure Prediction

In the context of calculating the hydrostatic buckling pressure of composite shells, several methods have been proposed by different researchers. Koudela and Strait [29] introduced a buckling solution specifically for orthotropic shells. They made empirical modifications to the Von Mises solution, originally developed for isotropic shells, in order to consider the effects of anisotropy and non-uniform stress distribution across the thickness of the laminate. However, this solution relied on effective properties that may not accurately predict the buckling behavior of complex structures.

On the other hand, Matos et al. [30] developed analytical closed-form solutions for determining the critical buckling pressures of composite thin-walled cylinders with arbitrary configurations and finite length. Their approach showed strong agreement with experimental data. In this study, the analytical solution developed by Matos et al. will be utilized to evaluate hybrid configurations that have not been experimentally investigated before. By employing this analytical solution, a broader range of hybrid composite structures can be assessed, and their buckling behavior can be predicted without the need for extensive experimental testing.

3.3. Normalization of Collapse Velocity, Pressure, and Time History

To account for the difference in collapse pressure and explore the physical processes associated with the implosion of the different tube configurations, the pressure versus time data and collapse velocity vs. time data can be non-dimensionalized. Ikeda et al. showed that a thin shell imploding in Mode II could be modeled as a collapsing cavitation bubble because, after instability, the collapsing structure becomes exceedingly weak compared to the pressure in its immediate environment [31]. Thus, the dynamic pressure can be non-dimensionalized with the critical collapse pressure ($P_C$) following the scaling of a cavitation bubble. Therefore, the normalized pressure is presented by.

$$\begin{array}{c}\overline{P}=\frac{P-P_C}{P_C}\end{array}$$

(5)

Also, the collapse time can be non-dimensionalized following bubble dynamics. The time is scaled by the collapse time of a spherical bubble which is proportional to $R_i\sqrt{\frac{\mathsf{\rho }}{P_C}}$, where $R_i$ is the bubble radius but in the case of a thin shell the internal tube radius and $\mathsf{\rho }$ the density of water. This non-dimensionalized time is thus,

$$\begin{array}{c}\overline{t}=\frac{t}{R_i\sqrt{\frac{\mathsf{\rho }}{P_C}}}\end{array}$$

(6)

The collapse velocity of the imploding structure must also be scaled in terms of time and velocity magnitude to account for the difference in critical collapse pressure (CP) between the tubes. Time is dimensionalized following Equation (6) as discussed. The collapse velocity, however, is normalized similarly to kinetic energy thus removing the effect of pressure on velocity. This procedure was successfully employed in recent work on the implosion of composite tubes with polymeric coatings [32]. This non-dimensionalized velocity is given by

$$\begin{array}{c}\overline{v}=\frac{\mathsf{\rho }{v}^2}{2P_c}\end{array}$$

(7)

where $v$ is the magnitude of the measured collapse velocity.

3.4. Impulse Analysis

In the analysis of pressure pulses, another important parameter to consider is impulse. Impulse provides a measure of a wave’s damage potential, taking into account both the magnitude of the pressure and the duration of the pulse. It has a significant impact on the response of a structure to the pressure wave.

To calculate the specific impulse of the local pressure histories for each specimen in this study, the impulse is determined by integrating the underpressure region of the pressure pulse. It is worth noting that the overpressure pulse may be influenced by reflections from the pressure vessel walls, given the long suction region of the pulse, which exceeds the reflection-free time of the pressure vessel (1.4 ms). However, previous studies on implosion have shown that the negative underpressure region is expected to be equal in magnitude to the implosion overpressure region [14,15,25]. Therefore, for calculating the impulse, only the underpressure region is considered.

In the analysis, the implosion pressure pulse of the shells is assumed to be spherical, which is a critical assumption when calculating the energy [33,34]. The specific impulse delivered to a structure from an initial time, $t_i$, to a final time, $t_f$, is described by Equation (8).

$$\begin{array}{c}I={\int }_{t_i}^{t_f}\mathsf{\Delta }pdt\end{array}$$

(8)

where $\mathsf{\Delta }p$ is the dynamic pressure at time t. To ensure a better comparison between the impulses of the different experimental cases with different collapse pressures, a normalized impulse is defined as follows,

$$\begin{array}{c}{I}_{norm}=\frac{I\ast C_o}{R_s\ast P_c}\end{array}$$

(9)

where $C_o$ is the acoustic wave speed in water and $R_s$ the distance from the sensor to the center of the tube.

3.5. Energy Analysis

An underwater implosion event emits energy into the surrounding fluid. This energy is calculated using an approach proposed by Arons et al. [33] for underwater explosions. The approach by Arons et al. is used because of the similarities Ikeda et al. theorized about imploding a Mode II thin tube and a collapsing explosion bubble [31]. Similar to the specific impulse, just the underpressure region will be considered in this study as it is assumed to be equal to the overpressure region. The pressure pulse carries energy in two forms: afterflow and radiated [33]. The afterflow energy is the kinetic energy of the mass of fluid moving past the sensor and is given by,

$$\begin{array}{c}{E}_{Afterflow}=\frac{2\ast \pi \ast R_s}{\rho }{\left[{\int }_{t_i}^{t_f}\mathsf{\Delta }pdt\right]}^2\end{array}$$

(10)

While the radiated energy is the compressional energy capable of doing work against the fluid and is given as

$$\begin{array}{c}{E}_{Radiated}=\frac{4\ast \pi \ast {R_s}^2}{\rho C_o}{\int }_{t_i}^{t_f}{\left(\mathsf{\Delta }p\right)}^{2}dt\end{array}$$

(11)

where, $\rho$ the fluid density, $R_s$ the distance from the sensor to the center of the tube and $C_o$ the acoustic wave speed. Because the collapse pressures for the different cases in this study were different, the after-flow and radiated energies were normalized as a percentage of the potential hydrostatic energy ${\frac{1}{2}P}_{cr}V$ for comparison purposes where: V is the collapsible shell and $P_{cr}$ is the critical collapse pressure [30].

4. Results and Discussion

4.1. Collapse Pressure (CP)

The critical buckling pressures for the different shells are presented in Figure 4, and the layer thickness effects explained in the previous section are immediately evident. The CP of GFRP is 30% higher than CFRP because of this thickness variation as discussed in Appendix B. The symmetric hybrid tubes with glass fiber internal plies and carbon fiber outermost plies had the highest critical collapse pressure (CP), 119% higher than shells with the reverse configuration. This is because these tubes benefit from both the high bending stiffness of carbon fiber as outer sheets and 1.5 times the thickness of the glass layer (internal plies). No significant difference in CP is seen in shells with a 1:1 carbon/glass layer ratio which is expected after looking at the stiffness matrices presented in Appendix B. Nevertheless, the mean CP of Hybrid–([G/G/G/C/C/C]) is 6% above that of Hybrid–([C/C/C/G/G/G]) mainly due to the negative effect of the coupling stiffnesses.

4.2. Collapse Behavior

The collapse mechanism of carbon and glass composite tubes has been extensively studied in previous literature, and the findings from this study are consistent with those reports [35,36,37]. The distribution of Digital Image Correlation (DIC) contours and the pressure histories obtained for the shells used in this study align with the observations made in previous studies.

A summary diagram illustrating the implosion mechanism and its corresponding pressure pulse is presented in Figure 5. The sequence of events is as follows:

I.

Initially, there is a force imbalance on the structure due to the difference between the internal pressure and the ambient hydrostatic pressure as the external pressure increases.

II.

As the external pressure reaches a critical point, the structure becomes unstable and starts buckling inward.

III.

During the collapse, the surrounding fluid also accelerates along with the shell walls, decreasing the ambient pressure. The shell continues to accelerate inward until the walls of the shell make contact, resulting in a high-amplitude pressure pulse being emitted into the surrounding fluid. This pressure pulse arises from the change in momentum of the fluid as it is abruptly stopped.

IV.

The wall contact propagates longitudinally along the shell until it is arrested at the endcaps, generating additional positive pressure waves.

These stages illustrate the sequential behavior of the implosion process in the composite tubes.

In this study, all the composite tubes experienced failure in Mode II, characterized by a two-lobed collapse profile resembling a tube that has been flattened in a vise. The collapse profiles of all the tubes in this study exhibited similar characteristics, and a sample pressure profile is presented in Figure 5b.

To compare the velocity and pressure profiles of the structures, the data was first scaled using Equations (5)–(7). These equations account for the discrepancies arising from variations in the collapse pressures. The scaled pressure and velocity plots are depicted in Figure 6.

In the analysis, the time t = 0 was defined as the moment of initial wall contact during the collapse of the shell. The subsequent discussions regarding the collapse event primarily focus on the pressure vessel’s reflection-free time, which is specified as 1.4 ms. This duration excludes the overpressure region in most experiments, and thus the discussions concentrate on the behavior within this time frame.

The velocity and pressure plots presented in Figure 6 highlight the discrepancy in the collapse mechanism between CFRP and GFRP roll-wrapped tubes. In CFRP tubes, the velocity profile exhibits a rapid rise at the beginning of the collapse, reaching a constant value of 0.12. In contrast, GFRP tubes show a slower rise to their maximum velocity of 0.09, which is 25% lower than that of CFRP. The velocity then drops to 0 at the point of wall contact. This difference can be attributed to the failure mechanisms of carbon fiber and glass fiber.

Carbon fiber tubes tend to fail in a brittle manner, significantly reducing the structure’s rigidity and stiffness. This leads to drastic accelerations during the collapse. In contrast, glass fiber tubes have higher failure strains and their failure is dominated by fiber pull-out and delamination, resulting in a slower loss of structure rigidity. These differences in failure behavior are reflected in the velocity profiles.

The under-pressure region of the tubes further emphasizes the fiber pull-out and delamination in glass fiber. The presence of small jumps and changes in slope indicate these failure mechanisms.

In symmetric hybrid cases ([C/G/G/G/G/C] and [G/C/C/C/C/G]), significant discrepancies can be observed in velocity, maximum and minimum pressures, and collapsed profiles. The high collapse pressure in shells with glass fiber inner layers and carbon fiber outermost sheets leads to a dramatic increase in collapse velocity after instability. The lower energy available in the surroundings after the instability of the Hybrid–[G/C/C/C/C/G] configuration results in a normalized velocity of 0.06, which is more than 2.8 times lower than that of Hybrid–[C/G/G/G/G/C]. The under-pressure regions of these tubes exhibit similar stick-slip characteristics to glass fiber. However, this phenomenon is more pronounced in Hybrid–[G/C/C/C/C/G], likely due to the presence of glass fiber sheets in the outermost layers, which control the overall strength of the structure.

A significant discrepancy is observed in the collapse behavior of the asymmetric hybrid cases ([G/G/G/C/C/C] and [C/C/C/G/G/G]) despite having similar buckling pressures. Figure 7 provides a schematic of these asymmetric hybrid shells after instability, displaying ovality with compression and tension zones. Previous studies on hybrid composites have indicated that the dominant failure mode is compressive failure [38]. Therefore, it can be deduced that Hybrid–[G/G/G/C/C/C] tubes, with glass fiber plies in the compression region, exhibit a gradual loss in rigidity compared to Hybrid–[C/C/C/G/G/G] tubes, which have carbon plies in the compression region. This results in lower collapse accelerations for Hybrid–[G/G/G/C/C/C] compared to Hybrid–[C/C/C/G/G/G]. The emitted pressure wave for these tubes also exhibits small jumps and changes in slope, similar to GFRP tubes. These observations highlight the differences in collapse behavior and failure mechanisms between CFRP and GFRP tubes and the influence of hybrid configurations on the collapse characteristics.

4.3. Collapse Velocity and Pressure Comparison

4.3.1. Pressure Comparison

To assess the quantitative impact of different reinforcements and layups on the obtained pressure histories, it is useful to compare the extreme pressure values reached in each experiment. However, due to the slow collapse of these tubes, reflections of the underpressure region may interact with the pressure vessel walls and affect the peak overpressure values in the overpressure region, leading to reduced recorded values. Therefore, this section will focus solely on the underpressure region of the pressure histories.

To facilitate the comparison of tubes with different critical collapse pressures (CP), the minimum pressure values in the underpressure region are normalized using Equation (5) and presented in

Table 3. Summary of experimental results from sensor S2.

Experimental Name	Critical Collapse Pressure (MPa)	Minimum Pressure, dPmin/Pcr	Underpressure Duration (ms)	Maximum Pressure, dPmax/Pcr	Overpressure Duration (ms)
CFRP	1.04 ± 0.01	0.32 ± 0.02	2.59 ± 0.05	0.59 ± 0.06	1.13 ± 0.05
Hybrid–[C/G/G/G/G/C]	1.95 ± 0.06	0.28 ± 0.01	2.20 ± 0.14	0.74 ± 0.25	1.89 ± 0.18
Hybrid – [G/C/C/C/C/G]	0.89 ± 0.02	0.30 ± 0.01	3.67 ± 0.01	0.47 ± 0.01	1.24± 0.06
Hybrid – [G/G/G/C/C/C]	1.21 ± 0.03	0.29 ± 0.02	3.01 ± 0.05	0.75 ± 0.02	0.93 ± 0.02
Hybrid – [C/C/C/G/G/G]	1.14 ± 0.04	0.26 ± 0.01	3.25 ± 0.05	0.72 ± 0.10	1.16 ± 0.07
GFRP	1.35 ± 0.07	0.29 ± 0.01	2.93 ± 0.13	1.22 ± 0.24	1.08 ± 0.03

. This normalization allows for a consistent comparison by accounting for the variations in CP among the different tubes.

The analysis of the pressure drop in the different tube configurations reveals interesting findings. The CFRP tubes exhibited a pressure drop of approximately 32% of the hydrostatic pressure, while the GFRP tubes reached an average minimum pressure of around 29%. These results align with previous research conducted by Pinto et al. [18] on the implosion of glass and carbon tubes. The failure mechanisms observed in carbon fiber tubes tend to be more catastrophic, resulting in shorter collapse durations and higher pressure drops compared to the failure of glass fiber shells, which is slower and more progressive.

When examining the symmetric hybrid configurations, it is observed that shells with carbon internal plies experienced a pressure drop of approximately 30%, while shells with glass internal plies showed a drop of around 28%. Post-mortem images of the shells with carbon inner plies reveal complete fiber breakage at the lobe locations, whereas shells with glass internal plies exhibit carbon layer fiber breakage only. This difference in failure mechanisms contributes to a higher-pressure drop-in tube with carbon inner plies compared to those with glass fiber inner plies. The higher energy released during the collapse of Hybrid–[C/G/G/G/G/C] results in a faster collapse and shorter underpressure duration, whereas Hybrid–[G/C/C/C/C/G] tubes exhibit a longer underpressure duration due to the lower available energy. For the asymmetric hybrid configurations, Hybrid–[G/G/G/C/C/C] demonstrates a pressure drop of approximately 29%, while Hybrid–[C/C/C/G/G/G] tubes exhibit a drop of around 26%.

4.3.2. Velocity Comparison

The maximum collapse velocity during the hydrostatic loading event is an important parameter to consider in understanding the behavior of these tubes. It is closely related to the emitted pressure pulse and provides insights into the structural response.

Table 4. Summary of CP, CenterPoint velocity and pre-buckling deformation.

Experiment Name	Critical Collapse Pressure	Maximum Local Center Velocity (m/s)	Pre-Buckling Deformation (mm)
CFRP	1.04 ± 0.01	17.0 ± 0.6	1.9 ± 0.1
Hybrid–[C/G/G/G/G/C]	1.95 ± 0.06	24.8 ± 1.4	2.2 ± 0.0
Hybrid–[G/C/C/C/C/G]	0.89 ± 0.02	11.0 ± 0.3	1.8 ± 0.4
Hybrid–[G/G/G/C/C/C]	1.21 ± 0.03	20.6 ± 3.2	1.0 ± 0.1
Hybrid–[C/C/C/G/G/G]	1.14 ± 0.04	23.3 ± 0.4	1.7 ± 0.4
GFRP	1.35 ± 0.07	17.1 ± 1.1	5.1 ± 0.1

provides a summary of the maximum collapse velocities and prebuckling deformations for all the tubes in this study, shedding light on their respective characteristics.

Comparing CFRP and GFRP specimens, it is noteworthy that they exhibited comparable maximum collapse velocities, despite the GFRP tube having a 29% higher collapse pressure (CP) than the CFRP tubes. This highlights the energy-intensive failure mechanism observed in glass shells as compared to carbon fiber shells. Furthermore, the prebuckling deformation of glass fiber shells was found to be 168% greater than that of carbon fiber shells, indicating the ductile behavior of glass fiber. For the symmetric hybrid specimens with glass inner plies, the highest maximum collapse velocity was observed. This can be attributed, at least in part, to the high CP of these tubes. The symmetric hybrids with carbon fiber inner plies show the lowest maximum collapse velocity compared to all of the specimens in this study. This can be attributed to the low CP of these tubes as well as the presence of glass fiber in the layup which exhibits a high energy-intensive failure as discussed earlier. Conversely, the symmetric hybrids with carbon fiber inner plies exhibited the maximum collapse velocity while having the lowest CP. In the case of asymmetric hybrids, similar maximum collapse velocities were observed. However, it is worth noting that the prebuckling values for Hybrid–[C/C/C/G/G/G] were 70% higher than those of Hybrid–[G/G/G/C/C/C]. These differences in prebuckling deformations highlight the contrasting behavior of these asymmetric hybrid configurations.

4.4. Post-Mortem Analysis

As previously discussed, the failure mechanism of composite tubes subjected to hydrostatic pressure is highly influenced by the constituent materials and the orientation of the different layers. Various types of failures can occur under hydrostatic loading, including tensile failures (such as brittle failure or fiber pull-out), compressive failures (such as kinking, micro buckling, shear, or splitting), and delamination. In order to examine the effect of different fibers and orientations on the energy released during failure, visual inspections were conducted on the tested specimens, and photographs depicting the damage to the different tubes are presented in this section.

Figure 8 provides representative post-mortem images of CFRP and GFRP tubes. In the case of CFRP specimens, the most notable damage consists of two longitudinal cracks along the lobes, spaced 180 degrees apart, which appear to penetrate through the entire thickness of the tubes. These cracks are predominantly characterized by fiber breakage, resulting in significant openings. Additionally, circumferential cracks are observed at the endcap locations, likely initiated when the longitudinal buckle propagation along the length of the tube is arrested at these points. The severity of the circumferential cracks is comparable to that of the longitudinal cracks. Conversely, GFRP tubes exhibit minor fiber breakage at the longitudinal lobe locations and minor delamination near the endcap region. This discrepancy can be attributed to the brittle nature (low strain to failure) of carbon fiber compared to the ductile nature (high strain to failure) of glass fiber, as demonstrated in previous studies [18].

These post-mortem images provide visual evidence of the specific damage patterns associated with CFRP and GFRP tubes under hydrostatic loading conditions. The observed differences in failure modes and damage severity are consistent with the varying mechanical properties and failure mechanisms of carbon fiber and glass fiber composites.

Figure 9 showcases the post-mortem images of the two symmetric hybrid configurations investigated in this study. The images reveal distinct failure modes for each configuration. Hybrid–[C/G/G/G/G/C] experienced catastrophic failure, characterized by delamination between the carbon and glass layers. Additionally, circumferential pull-out and breakage of the glass fibers can be observed at the endcap location. The observed glass fiber breakage is a consequence of the high longitudinal buckling velocity induced by the extremely high collapse pressure compared to the other shells examined in this study. On the other hand, Hybrid–[G/C/C/C/C/G] displays clean through-thickness cracks at the lobes, with accompanying fiber breakage and delamination between the glass and carbon layers at these locations. Notably, this specimen does not exhibit fiber pull-out, but a circumferential through-thickness crack is visible at the endcap locations. Overall, it is evident that the extent of damage in hybrid shells with carbon fiber internal plies is significantly greater compared to shells with glass fiber internal plies.

These post-mortem images provide visual evidence of the failure mechanisms and damage characteristics specific to the two symmetric hybrid configurations considered in the study. The differences in damage patterns between the configurations further highlight the influence of the internal ply materials on the failure behavior of the composite tubes.

The post-mortem images for the asymmetric hybrids in Figure 10 present similar failure patterns for the two cases considered. However, the influence of the glass and carbon fiber location is also apparent. The failure is predominantly characterized by two longitudinal cracks 180° at the lobe locations. This cracking is more violent on the tubes with carbon fiber as the interior layers as a complete opening is seen at several locations compared to shells with glass fiber as the interior layers. Circumferential cracks at the endcap locations are also observed; however, just delamination and carbon fiber breakage appear for Hybrid–([C/C/C/G/G/G]) compared to delamination, carbon, and glass fiber breakage for Hybrid–([G/G/G/C/C/C]).

The damage present in the different specimens considered in this study is summarized in

Table 5. Summary of the damage present in each specimen after the implosion.

Specimen Name	Summary of Damage
CFRP	○ Two longitudinal through-thickness cracks at lobes with fiber breakage ○ Circumferential crack with fiber breakage at endcap location
Hybrid–[C/G/G/G/G/C]	○ Glass fiber pull-out at endcap locations ○ Carbon fiber layer delamination ○ Fiber shearing at endcap locations
Hybrid–[G/C/C/C/C/G]	○ Through thickness cracks at lobes with complete fiber breakage creating a hole ○ Minor circumferential cracks at the endcap location
Hybrid–[G/G/G/C/C/C]	○ Circumferential carbon fiber breakage at endcap locations ○ Carbon fiber cracking at lobe locations
Hybrid–[C/C/C/G/G/G]	○ Fiber breakage at the longitudinal crack location with through holes observed at certain locations. ○ Circumferential crack with glass fiber delamination
GFRP	○ Two longitudinal cracks at lobes with minor fiber breakage ○ Minor delamination around the endcap location

.

5. Discussion

5.1. Analytical Predictions

The experimental collapse pressures obtained from the specimens and the properties described in Table 1 are utilized to validate the analytical model introduced by Matos et al. [30] in Section 3. The comparison between the experimental and analytical collapse pressures for the different laminates investigated in this study is illustrated in Figure 11. The results exhibit a close agreement between the experimental data and the analytical predictions, suggesting that the model is effective in evaluating various hybrid configurations.

To examine the influence of the inner ply thickness on the collapse pressure of these shells, different hybrid configurations were considered while maintaining the same geometrical properties and isotropic layup as the experimental specimens. The outcomes of this analysis are presented in

Table 6. Analytical collapse pressure predictions for different hybrid configurations.

Configuration	CP (MPa)
[G/G/C/C/G/G]	1.08
[C/C/G/G/C/C]	1.45
[G/G/G/G/G/C]	1.67
[C/C/C/C/C/G]	0.87
[C/G/C/C/G/C]	1.44
[G/C/G/G/C/G]	1.10

. It is evident that configurations with carbon as the outermost plies and glass as the inner plies exhibited the highest collapse pressures. When one of the carbon plies was replaced with glass in this layup, a reduction of nearly 14% in the collapse pressure was observed. Furthermore, substituting two inner glass layers with carbon resulted in an even greater reduction of approximately 25% in the collapse pressure. These findings further underscore the impact of inner ply thickness on the collapse pressure of these shells. Table 6 provides details of other layups considered in this analysis.

5.2. Impulse Analysis

Table 7. Energy and impulse calculations for different experiments from sensor S2.

Experimental Name	Under Pressure Impulse (N.s.m−2)	Under Pressure, Impulse Normalized (%)	Radiated Energy (J)	Radiated Energy Normalized (%)	After-Flow Energy (J)	After-Flow Energy Normalized (%)
CFRP	307.1 ± 21.9	5.71 ± 0.335	3.15 ± 0.45	0.98 ± 0.12	45.40 ± 6.66	14.04 ± 1.81
Hybrid–[C/G/G/G/G/C]	369.1 ± 6.4	4.03 ± 0.17	5.15 ± 0.55	0.94 ± 0.04	65.25 ± 2.25	11.86 ± 0.3
Hybrid– [G/C/C/C/C/G]	289.2 ± 16.0	6.20 ± 0.24	2 ± 0.02	0.72 ± 0.14	40.15 ± 4.45	14.30 ± 1.32
Hybrid– [G/G/G/C/C/C]	317.8 ± 13.2	5.04 ± 0.11	3.05 ± 0.35	0.80 ± 0.08	48.50 ± 4.00	12.82 ± 0.82
Hybrid– [C/C/C/G/G/G]	306.4 ± 15.7	5.20 ± 0.07	3.05 ± 0.35	0.86 ± 0.06	45.00 ± 4.5	12.72 ± 0.84
GFRP	310.4 ± 15.6	4.45 ± 0.01	3.22 ± 0.52	0.76 ± 0.08	46.3 ± 4.9	11.00 ± 0.56

presents the impulse and normalized underpressure impulse obtained from the underpressure region using Equations (8) and (9). Additionally, for better visualization, a histogram of the normalized impulse is provided in Figure 12.

A comparison between the carbon and glass control specimens reveals that CFRP tubes released pressure waves with a normalized impulse 37% greater than that of GFRP tubes. This difference can be attributed to the brittle failure mode observed in carbon fiber tubes, as also reported in previous studies [36]. In CFRP specimens, the presence of two horizontal cracks following instability leads to a significant reduction in structural rigidity, resulting in substantial movement of the surrounding fluid and a large underpressure region. This large region contributes to a higher impulse compared to GFRP tubes, which experience a more progressive loss of rigidity.

In the case of the symmetric hybrid configurations, the inclusion of glass fiber inner layers in Hybrid–[C/G/G/G/G/C] led to a 35% lower impulse compared to the symmetric Hybrid with carbon fiber inner layers (Hybrid–[G/C/C/C/C/G]). Post-mortem investigations of Hybrid–[G/C/C/C/C/G] revealed complete shearing along the length of the tube at the lobe locations, which would yield comparable results to CFRP tubes. This shearing phenomenon was absent in Hybrid–[C/G/G/G/G/C], resulting in a lower impulse. No significant difference in impulse emissions was observed for the asymmetric hybrid configurations.

5.3. Energy Calculations

The non-dimensionalized and dimensionalized afterflow and radiated energies for the different experiments calculated from the pressure pulse data using Equations (10) and (11) are presented in Table 7. For better visualization, histograms of the total normalized energy data (afterflow and radiated) are shown in Figure 13. Just calculations from the underpressure region are presented due to the pressure vessel’s 1.4 ms reflection free time discussed in the earlier sections. Early implosion work presented just the afterflow component of the energy. However, recent work by Kishore et al. on the implosion pressure pulses interaction with submerged plates demonstrated the effect of both the afterflow and radiated components on the deflections of an impacted plate [39]. However, near the implodable, the afterflow is much greater than the radiated term.

Figure 13 illustrates that GFRP tubes exhibit the lowest normalized energy release, while CFRP tubes exhibit the highest energy release, which is approximately 27% higher than that of GFRP. This observation indicates that a significantly larger amount of energy is dissipated during the deformation and collapse of glass fiber tubes compared to carbon fiber tubes, which is consistent with the findings from the post-mortem images. The post-mortem analysis section provides further explanation of this energy absorption mechanism.

In the case of symmetric hybrid tubes, those with glass fiber inner layers released approximately 17% less energy compared to those with carbon fiber inner layers. This discrepancy highlights the energy-intensive failure mechanisms associated with glass fiber. It suggests that the inner layers of the tubes play a more substantial role in the energy release compared to the outer plies.

No significant difference in energy release was observed for the asymmetric hybrid configurations. These asymmetric hybrids consist of two glass fiber layers in both the inner layers, further supporting the notion that the energy dissipation capabilities of the internal layers primarily influence the energy emission in these hybrids. Therefore, the released energy decreases with an increase in the number of higher energy-dissipating layers (glass fiber) positioned at the center of the composite.

6. Conclusions

The study focused on investigating the implosion behavior of carbon/glass hybrid composite tubes under hydrostatic loading, with particular attention given to the effects of different carbon/glass ratios and locations. Various experimental techniques, including high-speed photography, digital image correlation (DIC), and dynamic pressure sensors, were employed to analyze the collapse mechanics, local pressure distribution, and energy/pressure pulse mitigation.

Based on the findings, several conclusions can be drawn:

• The thickness of the internal ply layers significantly influences the bending stiffness of composite laminates and, consequently, the critical buckling pressure. Glass fiber layers, being 1.5 times thicker than carbon fiber layers, resulted in the Hybrid–[C/G/G/G/G/C] configuration exhibiting the highest collapse pressure among all tested specimens. Analytical predictions of the buckling pressures for different thin hybrid configurations further emphasized the importance of internal layer thickness in determining the bending stiffness of composite laminates. Therefore, to achieve maximum strength in a hybrid layup, it is preferable to use thicker plies for the internal layers and stiffer plies for the outer sheets.
• In general, glass fiber used as internal layers emits less energy during implosion compared to pure carbon fiber tubes due to the more energy-intensive failure mechanisms exhibited by glass fibers. This implies that structures with internal plies possessing higher energy absorption capabilities will release less energy into the environment upon failure, in contrast to structures with the opposite configuration.
• Changing the location of carbon and glass layers in an asymmetric hybrid configuration with a 1:1 carbon/glass ratio had an insignificant effect on the energy release. This is mainly attributed to the presence of an equal number of glass fiber plies in the inner layers of the hybrids, which leads to a similar energy dissipation behavior.
• The presence of carbon fiber as internal layers leads to a more catastrophic failure mechanism characterized by longitudinal through-thickness openings with complete fiber breakage, as compared to glass fiber.
• Hybrid composite tubes with very high buckling pressures exhibit a more catastrophic failure mechanism regardless of the properties of the individual plies.

These findings contribute to a better understanding of the collapse behavior of carbon/glass hybrid composite tubes and provide insights into optimizing the design of such structures for specific strength and energy absorption requirements.