Damage Evaluation of Typical Aircraft Panel Structure Subjected to High-Speed Fragments

Abstract

This study explores the damage behavior of typical titanium alloy aircraft panel structures under high-speed fragment impacts via ballistic experiments and FEM-SPH simulations. Using a ballistic gun and two-stage light gas gun, tests were conducted with spherical, rhombic, and rod-shaped fragments at 1100–2100 m/s to analyze damage morphology. The FEM-SPH method effectively modeled dynamic impacts, capturing primary penetration and debris cloud-induced secondary damage. Residual strength under tension was evaluated via multiple restart analysis, linking impact dynamics to post-damage mechanics. Experimental results revealed fragment-dependent damage modes: spherical fragments caused circular shear holes with conical/jet-like debris clouds; rhombic fragments induced irregular tearing and triangular perforations due to unstable flight; rod-shaped fragments produced elongated breaches with extensive plastic deformation in stringers. Numerical simulations accurately reproduced debris cloud diffusion and secondary effects like spallation. Residual strength analysis showed tensile capacity was governed by breach geometry and location: rhombic breaches (34.6 kN) had lower strength than circular/square ones (38.1–38.3 kN) due to tip stress concentration, while stringer-located damage increased ultimate load by 8–12% via structural redundancy. In conclusion, high-speed fragment impacts dominate shear/tensile tearing, with morphology dependent on fragment characteristics and impact conditions. Debris cloud-induced secondary damage must be considered in structural assessments. The FEM-SPH method is effective for complex damage simulation, while breach geometry and damage location are critical for residual strength. Stringer involvement enhances load-bearing capacity, highlighting component-level design importance for aircraft survivability. The study results and methodologies presented herein can serve as references for aircraft structural damage analysis, residual strength evaluation of battle-damaged structures, and survivability design.

1. Introduction

Since 1911, when aircraft were first introduced as weapons of war, battle damages have been a recurring occurrence. The repair of battle-damaged aircraft has gradually gained prominence. During the Pacific War of 1942, the ratio of aircraft battle loss to battle damage was 1:3. Notably, during the Middle East War and the Falklands War, a substantial number of aircraft were repaired by operational air forces in the midst of conflict [1]. Historical evidence underscores that the number of battle-damaged aircraft far surpasses the count of war-damaged aircraft. Consequently, repairing battle-damaged aircraft holds immense significance in restoring their combat capability. As warfare evolves with new forms, military theories continue to develop, and novel operational modes and concepts emerge. However, the pursuit of air superiority and its maintenance remains a central focus in the military construction efforts of various nations [2].

Combat aircraft serve as the pivotal element in air operations, with their availability and attrition rates significantly influencing the outcome of conflicts. In contemporary times, the evolution of warfare has seen the high-speed fragmentation impact from warheads supplant anti-aircraft guns as the principal threat to aircraft. Consequently, the combat survivability of aircraft has emerged as a critical design criterion for military aircraft globally, leading to the establishment of survivability support systems encompassing design standards and testing facilities [3]. Airplane Combat Survivability (ACS) is conceptualized as the capacity of an aircraft to evade or endure a man-made adversarial environment. This concept is bifurcated into two domains: sensitivity and vulnerability. Sensitivity encompasses a sequence of events including detection, tracking, identification, engagement, weapon control, guidance, fuse activation, and impact, quantified by the probability of an aircraft being struck by a threat. Vulnerability delves into the damage traits of an aircraft post-impact by a terminal weapon, with kill probability or the vulnerable area under hit conditions serving as common metrics [2]. There exists an exponential relationship between survivability and combat efficacy, with the aircraft’s structure acting as the foundation for the combat aircraft to fulfill its functions. The focus of research on combat aircraft vulnerability is structural vulnerability, which includes the categorization of damage effects, identification of critical vulnerable structures, methods for vulnerability modeling, criteria for vulnerability assessment, and other essential technologies [4]. Historically, research on structural vulnerability primarily relied on the synthesis of actual combat outcomes or live-fire test data. However, with the advancement of computational mechanics, numerical simulation has become the predominant method for investigating structural vulnerability [5]. The mechanisms and effects of damage to aircraft structures are fundamental and integral to the study of aircraft structural vulnerability, with the variety of damage mechanisms dictating the structural response. The diversity of damage modes plays a crucial role in determining the structural response. For instance, fuel tank structures can experience various damage modes, including perforation deformation and explosion. The specific damage mode a structure undergoes depends on both the characteristics of the damage source and the inherent properties of the structure itself. Different damage sources may lead to distinct damage modes, and even when faced with the same damage source, variations in structural characteristics can result in different modes of damage. Ultimately, the damage mode directly influences the overall effect on the structure, which can manifest as the loss of its intended function or the impairment of other interconnected structures [6].

In recent times, numerous scholars have conducted extensive research on the damage effects experienced by typical aircraft structures. These structures include the aircraft fuel tank, wing, rudder, and fuselage skin. Notably, Vara et al. have focused their investigations on the anti-fragment impact damage of fuel tank structures. Employing a research approach that combines experimental testing with numerical simulations, Vara explored the influence of factors such as fragmentation velocity, liquid filling ratio, and the material composition of fuel tank structures. Their work yielded valuable insights, including fragmentation velocity data, strain–time curves for front and rear panels, and fluid pressure variations [7]. Ren et al. conducted a comprehensive investigation into the damage effects resulting from the impact of fragmentation on a fully loaded kerosene-riveted aircraft fuel tank. Their study also involved a simultaneous analysis of the failure scenarios for both the tank and the rivets. To achieve this, they combined ballistic gun testing with numerical simulations [8]. Wu et al. have delved into the dynamic response of a polyurea-coated fuel tank when subjected to the concurrent forces of fragmentation and a shock wave. Their research encompasses the analysis of the protective benefits of polyurea coatings in mitigating damage from high-velocity impacts and explosive forces [9]. Wang et al. conducted simulations on the vulnerable components of a specific type of aircraft using a trace shooting method. They investigated the damage mechanisms and secondary effects resulting from high-speed fragment impacts on the typical skin and joint structures of the aircraft, employing a combination of experimental tests and finite element simulations [10,11]. The degradation of an aircraft’s structural bearing capacity following battle damages necessitates the redistribution of internal loads within the structure. Particularly under the influence of fragments, shock waves, and other destructive elements, the formation of holes and cracks alters the local stress field, ultimately leading to structural damage. Consequently, the analysis and prediction of residual strength in war-damaged structures play a crucial role in assessing structural vulnerability. T. P. Rich et al. proposed a failure probability model for aluminum alloy (7075-T6 and 2024-T81) thin plate structures after impact penetration damage, based on fracture mechanics [12]. Scheider et al. analyzed the residual strength of the complex stringer plate structure of Al2024-T351 based on crack development [13]. Binbin Liao et al. employ an explicit and implicit combined model based on the evolution law of stress damage and damage to predict the residual strength of a composite cylinder under low-speed impact [14]. E. Cestino et al. introduced the characteristics of low-speed impact damage and its influence on residual tensile and buckling behavior of composite structures [15]. Mo Yang et al. conducted a comprehensive investigation into the residual strength of Carbon Fiber Reinforced Polymer (CFRP) single-lap joints subjected to transverse impacts of varying energies. This study was accomplished through an integrative approach that combined both numerical simulations and empirical experimentation [16].

Currently, the utilization of explicit dynamic numerical simulations for analyzing structural failure behaviors under impact loads is prevalent, and the assessment of structures’ residual strength post-impact is typically conducted through experimental means. The temporal disparity between impact analysis and residual strength evaluation poses challenges in assessing post-impact residual strength using a solitary numerical model. This difficulty is compounded in the context of intricate aircraft structures, where experimental procedures are often not feasible. This study introduces a novel approach by amalgamating the impact damage finite element analysis model with the quasi-static tensile strength finite element analysis model through the restart analysis method. This fusion facilitates a thorough numerical examination of both the damage manifestation and the residual strength of standard metal aircraft panels post-impact. To corroborate the simulation outcomes, impact experiments employing ballistic guns and two-stage light gas guns were executed. The research delves into the effects of fragment type and quantity on the structure’s post-impact residual strength. The advanced finite element analysis model presented herein significantly augments our comprehension of the typical aircraft panel structure’s response to impact and its subsequent residual strength, thereby proving instrumental in advancing research and assessment of aircraft structural vulnerability.

2. Ballistic Impact Experiments

In pursuit of understanding the behavior of titanium alloy panel structures commonly found in the rear fuselage of aircraft (as depicted in Figure 1), a series of high-speed impact ballistic experiments were conducted. These experiments utilized both a ballistic gun and a two-stage light gas gun. The experimental setup for the ballistic gun consists of several components, including the ballistic gun itself, a retaining device, a velocity target, a target plate, and a high-speed camera (Phantom (Wayne, NJ, USA) V2512, 160,000 fps at 386 × 216 resolution), as is illustrated in Figure 2. By adjusting the charge of the propellant, the fragment can obtain the required impact speed. The retaining device is a thick steel plate with a central opening, which is used to block the separated sabot. A velocity target is used to measure the impact velocity of the fragment. The high-speed camera is used to record the whole process of the fragment impacting the target board, and to assist in measuring the fragment’s impact velocity and residual velocity. To facilitate clear recording of the fragment’s trajectory by the camera, a white background cloth is placed behind the target board. The ballistic muzzle is positioned 560 mm away from the support device. The two-stage light gas gun experimental system consists of an inflation system, a gas chamber, a first-stage barrel, a conical section, a second-stage barrel, a target box, and observation equipment, as shown in Figure 3 and

Table 1. Structural composition.

No.	Segment	Material	Geometrical Aspect (mm)
1	skin	TC4	bent plate, 245 × 220 × 2
2	stringer 1	TC4	S-shaped bar, 245 × 1
3	stringer 2	TC4	S-shaped bar, 245 × 1

. The exit velocity of the fragments is measured using a laser grating speed measurement, while the remaining velocity is acquired through the speed measurement target.

The experimental fragments are made of 10# steel and come in three shapes: spherical, rhombic, and rod-shaped; their masses are 2.1 g, 3.12 g, and 6.8 g, respectively. The fragments are launched using a 25 mm ballistic gun. The specific structures of the test fragments and their supports are depicted in Figure 4. The support sabots are made into different shapes to fit the fragments. The sabot materials include a dual-layer polycarbonate (a), nylon (b) and 12-T4 aluminum alloy structure (c).

The ballistic gun and the two-stage light gas gun exhibit certain differences in their launch capabilities. By controlling the propellant, the ballistic gun achieves a launch velocity range from 1100 to 1500 m/s for the three types of fragments mentioned. In order to prevent the breech from scratching the gun barrel, the secondary light gas gun only fires spherical and rhombic fragments. By adjusting the pressure level, it can achieve a launch velocity range from 1900 to 2100 m/s.

3. Numerical Simulation Setups

3.1. Material Constitutive

The Johnson–Cook constitutive model is widely used in impact dynamics and is generally employed to describe the strength limits and failure processes of metal materials under conditions of large strain, high strain rates, and elevated temperatures. Unlike conventional plasticity theories, the Johnson–Cook model characterizes the material response after impact or penetration using parameters such as hardening, strain rate effects, and thermal softening [17]. Each of these parameters accumulates effects through multiplication.

$${\sigma }_y=\left(A+B{\epsilon }^n\right)\left(1+C\ln {\displaystyle \frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}}\right)\left(1-T^{\ast }\right)$$

(1)

where $\epsilon$ is the equivalent plastic strain, $\dot{\epsilon }/{\dot{\epsilon }}_0$ is the reference equivalent strain rate (usually normalized as 1 s⁻¹), T* is the relative temperature, which is calculated as follows:

$$T^{\ast }={\displaystyle \frac{T-T_r}{T_m-T_r}}$$

(2)

where T represents the local temperature, T_r is the room temperature, and T_m is the melting point of the material. The other five constants are the material physical property constants of the Johnson–Cook model: A is the initial yield stress, B is the hardening constant, C is the strain rate constant, n is the hardening exponent, and M is the thermal softening exponent. These can be fitted with the following formula after determining the data through material testing:

$$\ln (\sigma -A)=n\ln \epsilon +\ln B$$

(3)

$$\sigma =K_1\left(1+C\ln {\displaystyle \frac{\dot{\epsilon }}{{\dot{\epsilon }}_0}}\right)$$

(4)

$$\ln \sigma =M\ln T^{\ast }\left(T^{\ast }>>1\right)$$

(5)

In the Johnson–Cook model, the yield stress is determined by strain, strain rate, and temperature; the model is composed of three parts, representing material strain hardening, strain rate strengthening, and thermal softening, respectively. It comprehensively considers the relationship between rheological stress and strain, strain rate, and temperature, meeting the simulation material requirements under most conditions.

The Gruneisen state equation can accurately describe the dynamic behavior of metallic materials under conditions of high temperature, high pressure, and high strain rates. Initially, this equation was an accurate thermodynamic description for a large number of solid-state metals. Subsequent improved forms could describe the constitutive relationships of gases and solid explosives, real gases, and high-pressure solids.

The Gruneisen state equation defines the shock wave speed as a function of particle velocity, v_s(v_p). For compressible materials, the pressure it defines is

$$p={\displaystyle \frac{{\rho }_0{C}^2\mu \left[1+\left(1-\frac{{\gamma }_0}{2}\right)\mu -\frac{a}{2}{\mu }^2\right]}{{\left[1-\left(S_1-1\right)\mu -S_2\frac{{\mu }^2}{\mu +1}-S_3\frac{{\mu }^3}{{(\mu +1)}^2}\right]}^2}}+\left({\gamma }_0+a\mu \right)E$$

(6)

For ductile materials such as metals, the pressure is defined as

$$p={\rho }_0{C}^2\mu +\left({\gamma }_0+a\mu \right)E$$

(7)

where C is the intercept of the v_s(v_p) curve (expressed in units of speed), S1, S2, and S3 are the dimensionless coefficients of the slope of the v_s(v_p) curve, γ₀ is the dimensionless Gruneisen gamma value, a is the dimensionless first-order volume correction to γ₀, and for µ has

$$\mu ={\displaystyle \frac{\rho }{{\rho }_0}}-1$$

(8)

Johnson–Cook model parameters and Mie-Gruneisen equation of state parameters of the TC4 titanium alloy are shown in

Table 2. TC4 Johnson–Cook model parameters [18,19].

Parameters	Symbol	TC4
Static yield limit (MPa)	A	1003.132
Strain hardening modulus (MPa)	B	1003.510
Strain hardening exponent	n	0.663
Strain rate coefficient	C	0.0137
Spall type	SPALL	3
Failure parameters D1	D1	−0.197
Failure parameters D2	D2	2.332
Failure parameters D3	D3	3.138
Failure parameters D4	D4	0.034

.

3.2. Model Setups

The aircraft panel model employs solid hexahedral ten-node elements, with a total mesh count of 610,272. To enhance overall computational efficiency while ensuring accuracy, the model is divided into two types of density grids using a local mesh refinement approach. Specifically, the impact-penetrated region utilizes a finer mesh, while the transition between the two regions is achieved by connecting trapezoidal transition meshes at shared nodes, as illustrated in Figure 5.

In the numerical simulation of battle damage to typical aircraft structures described in this paper, the FEM-SPH adaptive method is employed. This approach provides a relatively accurate characterization of the damage morphology and mechanisms of the target structure after simulated impact. Additionally, it effectively models the entire impact process and fragment cloud phenomena resulting from projectile impact, while maintaining computational efficiency. The FEM-SPH adaptive coupling algorithm combines the advantages of traditional FEM and SPH methods. The initial model of the FEM-SPH adaptive coupling algorithm uses hexahedral finite elements based on the Lagrange algorithm. When the material defined by the structure satisfies failure criteria, the method replaces the failed elements with particles while inheriting all the original element’s node properties. The overall structure of the model is represented using hexahedral elements, similar to traditional finite element methods. Material properties, failure criteria, boundary conditions, and contact algorithms can be directly defined on the elements. Furthermore, specific keywords should be defined at element locations to replace failed elements with SPH particles during the computation process, as is shown in Figure 6 [20]. In LS-DYNA, the keyword DEFINE_ADAPTIVE_SOLID_TO_SPH is used to implement the FEM-SPH adaptive coupling method. During computation, particles and elements are separately calculated using SPH and FEM, with no interaction between them. Detailed descriptions and relevant cards for this keyword are provided in the LS-DYNA user manual [21].

When analyzing the residual strength of structures based on numerical methods, it is common to examine the structure’s compression or tension strength under static/quasi-static conditions. The residual strength of structural components depends not only on the shape, scale, and material properties of the components themselves but is also greatly influenced by structural deflection and residual stress. Generally, the presence of initial deflection and residual stress will reduce the stiffness and ultimate strength of the structure. Therefore, in the analysis of the structure’s residual strength, the impact of these two factors must be fully considered. Due to the significant difference in time step scales between the impact penetration of fragments into the structure and the analysis of the structure’s residual strength, it is generally difficult to perform directly through a single model.

After the fragment has completed its impact on the target structure (about 200 μs), the restart function of the LS-DYNA (Ver. R13) software is used, and parts of the model such as fragments, plugging, and SPH particle groups that do not require calculation are removed, so as to reduce the overall model’s mesh calculation scale and increase the calculation time step. At the same time, by setting non-reflective boundaries, the overall structure’s elastic oscillation tends to stabilize. After a sufficiently long calculation time, the structure’s energy curve tends to a stable value, at which point the finite element model with all elements’ stress–strain information is output.

Combining the force characteristics of the titanium alloy aircraft panel structure in this paper, a residual strength analysis is performed on the obtained damaged structure finite element model. Displacement loads are applied to the boundaries at both ends of the model, and dynamic tension is carried out under quasi-static conditions to observe the structural failure mode. The model’s peak load-displacement curve is obtained, and the structure’s residual strength is analyzed. The analysis process is shown in Figure 7.

3.3. Model Validation

Coarse, moderately refined, and fine-refined mesh models were employed to verify the mesh independence of the finite element model; the mesh sizes were 1 mm × 1 mm, 0.5 mm × 0.5 mm, and 0.2 mm × 0.2 mm, respectively, resulting in a total number of grid points of 119,145, 610,272, and 2,622,664. As an illustrative example, the maximum equivalent stress (Von Mises stress) of the structural body was extracted at each time step for a spherical projectile impacting a target plate, as shown in Figure 8.

The consistent trend in the maximum equivalent stress across different mesh scales indicates that all three mesh types adequately represent the impact dynamics. Furthermore, as the mesh size becomes finer, the variation in maximum equivalent stress decreases, suggesting better mesh quality and convergence stability.

The numerical model exhibits various energy change curves, as shown in Figure 9. The Total Energy remains relatively balanced, while the changes in Internal Energy and Kinetic Energy align with the actual projectile impact and penetration process. The Hourglass Energy, arising from the use of reduced integration in explicit analyses, contributes an incremental value of 0.0364 kJ. The Sliding Energy, which includes potential energy from contact springs and friction, is negligible. Both energy components remain below 2% of the global energy of 3.4 kJ, falling within an acceptable range. In this case, the simulation model’s accuracy and effectiveness are primarily validated by its representation of dynamic penetration processes, damage pattern morphology, and characteristic dimensions captured before and after experiments.

In the experiment, the high-speed collision between the fragment and the test piece produced intense photothermal effects and a cloud of debris. The overall morphology of the debris cloud and its diffusion process were observed, indicating that the simulation closely approximates the debris cloud phenomenon seen in the experiments. Due to the limitations of experimental observation methods, the numerical simulation model can be used to study the interaction process between the projectile and the target, the damage patterns, and the mechanisms of the formation of the debris cloud (Figure 10).

From the perspective of external damage morphology, the simulation results are consistent with the experimental outcomes, effectively characterizing various forms of damage such as shearing and tearing, as illustrated in Figure 11. In terms of damage characteristic dimensions, the absolute errors between simulation and experiment are all below 15%, which is within an acceptable margin of error. However, in actual experiments, the orientation of the fragments during flight is uncontrollable and may involve a certain angular velocity, leading to differences in the fragment’s orientation upon exit.

Selecting the same working conditions (initial velocity, impact position) as in the tests, the velocity change of fragments in the process of penetration were analyzed. Corresponding to the actual penetration process, the different fragment velocities basically decreased linearly, and the error between the residual fragment velocities and the corresponding experimental values was less than 12%, as shown in Figure 12.

Under certain conditions where the fragment’s velocity is high enough (1900 m/s~2100 m/s, launched by two stage light gas gun), the sputtered debris cloud can reach a quite intense density, which can cause severe secondary damage to the structure, forming pits of various sizes on the surface. In the simulation, the solid particles within the debris cloud are represented as particles, and by defining the contact relationship between the particles and the test piece, groups of particles with different energies create pits of varying sizes on the base plate. Some elements undergo pit formation and deformation, while others fail and are removed. This corresponds to the impact pits of varying sizes observed in the experiments. However, due to the limitations of the simulation model’s mesh precision, it is not possible to simulate secondary damage smaller than the minimum mesh size. The distribution of secondary damage has a certain degree of randomness, and the range and form of damage obtained from the experiments and simulations are generally similar. Therefore, the simulation can reasonably predict the form and distribution of secondary damage caused by the debris cloud, as shown in Figure 13.

4. Results and Discussion

4.1. Damage Analysis

4.1.1. Impact Process Analysis

Utilizing the ballistic gun and the two-stage light gas gun, a total of 12 shots (four each) were conducted on titanium alloy aircraft panel target boards using spherical fragments, rhombic fragments, and discrete rods. By controlling the propellant, the launch velocities were consistently maintained within the range from 1100 to 1300 m/s. High-speed cameras and velocity-measuring targets were employed to capture the penetration process, allowing for the calculation of the projectile’s initial velocity (vi) and its remaining velocity (vr) after penetrating the target board. The penetration processes for the three types of fragments are illustrated in Figure 14 (spherical fragments: vi = 1244 m/s, rhombic fragments: vi = 1222 m/s, discrete rods: vi = 1205 m/s).

In this study, the moment of initial contact between the fragment and the target surface is defined as time zero (t = 0). Upon impact, the projectile penetrates the target board, accompanied by a significant amount of flash, resulting in a multitude of fragment clouds both on the surface of the target board and at the exit point of penetration. Notably, the fragment cloud carried by rhombic fragments and discrete rods is denser than that produced by spherical fragments. Under the impact of spherical fragments, the spallation at the entry end forms a conical cloud of fragments, while the spallation at the exit end resembles a jet-like cloud of fragments. The fragment cloud primarily consists of high-temperature microparticles, metal dust, and low-velocity fragment particles, collectively forming a spallation cluster.

As the impact velocity increases (as shown in Figure 15), the distribution of fragment clusters becomes denser and more uniform. Due to the aerodynamic forces acting on the rhombic fragments and discrete rods after launch, the final encounter attitude of the projectile and the target board exhibit a certain angle, resulting in irregularities in the formation of the jet and fragment cloud during penetration.

Taking spherical fragments as an example, the penetration process of the fragments into the structure is analyzed. Within 0~15 µs, as shown in Figure 16a, the fragment contacts the upper panel of the structure. The annular shear force formed by the impact far exceeds the strength limit of the panel. The annular shear band gradually accumulates and extends to the back of the panel to form an annular shear plane. Once the shearing congestion is complete, a bulge forms. The radial tensile stress on the back of the rear panel bulge increases. As the penetration deepens, the tensile stress accumulates and expands. When the accumulation exceeds the strength limit of the panel, the bulge rapidly contracts and fractures, as shown in Figure 16b, forming an irregular petal-shaped rupture. The entire damaged area presents a relatively regular spherical shape, with its area being essentially consistent with the orthogonal projection area of the spherical fragment. During the high-speed collision process, the fragment and the panel undergo a phase change. The instantaneously accumulated thermal energy cannot be transferred to the surrounding medium in time, which can be considered an adiabatic process. In adiabatic shearing, the heat generated by friction accumulation continues to rise, forming a small range of serrated material accumulation along its edge. At the stringer connection, due to the reduced penetration force of the fragment, the stringer will form a large area of plastic deformation under the impact of the fragment, as shown in Figure 16c.

4.1.2. Damage Morphology Analysis of Target Plate

Under the impact of spherical fragments, the damage modes presented at different impact points of the target plate are shown in Figure 17. When fragments penetrated the skin, the damage at the incident end of the skin surface was mainly manifested as a spherical shear hole, and the damage diameter was slightly larger than the fragment diameter. The exit end also showed spherically shaped holes, and the edges of the holes were accompanied by irregular jagged material accumulation. Under the action of high-speed spherical fragments, a bulge area is formed at the impact site, and a ring shear zone is formed at the boundary of the projectile target. The strong shear force is much greater than the strength limit of the material, and then under the action of the annular shear band, the titanium alloy fails and breaks, forming a round fracture. When the fragment penetrates the stringer, the skin damage of the incident end is the same as that of the former, and at the exit side, it forms a stringer ribbon tear damage under the strong shear action of the fragment. At the bottom of the stringer, the broken hole continued to tear under the action of tensile force, forming a certain degree of curling. When the broken pieces penetrated the skin and the junction of the stringer, the skin damage of the incident end was the same as that of the former, and a slight bulge was formed before the broken hole of the exit end and the welding spot.

Under the impact of rhombic fragments, the uncertain rotation during their flight after sabot separation, owing to the geometric characteristics of the fragments, results in an indeterminate encounter attitude and position between the projectile and the target board. High-speed cameras cannot precisely capture the corresponding keyframes. The damage patterns observed at different impact points on the target board under the impact of rhombic fragments are depicted in Figure 18. When the fragment penetrates the skin, the rhombic fragment makes direct frontal contact with the target board. The entry hole exhibits a relatively regular rhombic feature, while the exit hole edge also shows some material accumulation, forming an irregular serrated protrusion similar to that observed when spherical fragments penetrate the skin. During penetration of the stringer, the rhombic fragment experiences more pronounced rotation, leading to a distinct tearing feature in the hole. The hole shape approximates a triangle due to the influence of rotation, and the surface retains a significant amount of black vaporized residue. Part of the backside of the stringer experiences impact, resulting in a noticeable rolled edge due to tensile forces.

After the sabot of the discrete rod is detached, its flight trajectory becomes equally unpredictable, making it difficult to control the final impact attitude of the projectile. Due to the large mass of the discrete rod, its impact destructive force is stronger, resulting in more pronounced cutting effects on the target plate, as shown in Figure 19. The skin surface will experience some curling due to the flipping action of the fragments. The stringers, subjected to intense cutting forces, exhibit extensive tearing. The failure of weld joints will lead to even more pronounced tearing and plastic deformation in the stringer section.

The damage morphology of rhombic fragments and discrete rods to the structure is depicted in Figure 20. The penetration process of rhombic fragments into the target plate is akin to that of spherical fragments. Although their masses are comparable, the penetration force of the rhombic fragments is more pronounced due to the effect of their shape coefficient at the penetration end. At the point of impact, the fragment tip almost does not form a congestion block, and the bottom of the bulge tears directly along the area of stress concentration. The impact and tearing effect of rhombic fragments on the stringers is also more significant. Discrete rods, having a relatively larger mass, exhibit a more noticeable cutting effect on the structure at the same velocity, resulting in a breach that appears as a more regular strip shape, while also forming larger congestion blocks.

4.2. Residual Strength Analysis

When different fragments penetrated the skin, the breaks showed the projected area of fragments under the positive impact condition. When rhombic and spherical fragments penetrate the skin, the main perforation form layers appear to be rhombic, square, and round, as shown in Figure 21.

The structural load-displacement curve changes under three kinds of breaks are shown in Figure 22. The strength limit of rhombic broken structure decreased the most (34.6 kN), and the strength limit of the square broken structure was close to that of the round broken hole structure, which was 38.1 kN and 38.3 kN, respectively. Among them, the minimum cross-sectional area in the tensile direction of rhomboidal fracture structure and square fracture structure is basically the same, and they show the same behavior in the yield stage. The damage of the minimum cross-sectional area in the tensile direction of the round broken hole is small, and the yield stage is close to that of the intact structure. Since the rhombic break tip will lead to stress concentration and a greater stress intensity factor during the loading process, which is more serious than that of the square break, the process of crack initiation and crack development is accelerated, that is, the strength limit is lower than that of the square fracture, and the stress distribution in the tensile stage of the two is shown in Figure 23. The bearing capacity of the round broken structure is basically the same as that of the square broken structure.

Taking the round broken structure as an example, the influence of the broken location (skin, stringer, joint) on the bearing capacity of the structure is analyzed. Because the damage of the main body of the wall panel is basically the same (Figure 24), the performance of the three linear elastic stages is completely consistent. The change of the break location leads to the change of the minimum tensile section of the structure, which leads to the change of the fracture surface. Under tensile load, when the break is located in the stringer and the joint, the stringer shares part of the load, providing a gain in the tensile section area. Meanwhile, due to the greater damage in the stringer area of the broken hole structure at the joint, the ultimate load of the broken stringer structure is slightly higher than that of the broken structure at the joint, as is shown in Figure 25.

5. Conclusions

In this paper, damage analysis of the typical titanium alloy panel structure of aircraft under different types of fragment penetrations was carried out. Based on the ballistic gun and two-stage light gas gun system, ballistic tests were carried out, the damage morphology and mechanism of the structure were analyzed, and the validity of the finite element numerical damage model was verified. Based on the numerical model, the damage analysis of the structure under different incident conditions was expanded, and the residual strength analysis of the structure under tensile load was carried out by using the multiple restart method. The following conclusions can be drawn in this paper:

• Under the impact of high-speed fragments, the damage of typical titanium alloy panels of aircraft is mainly shear and tensile tear damage. The damage morphology is highly related to the fragment type and projectile-target intersection condition. During the second penetration, the impact plastic depression area of the structure is large and accompanied by tearing failure.
• The fragments generated by high-speed impact penetrating the metal structure still have considerable penetrating force, which will cause widespread secondary damage to the internal structure and components. The FEM-SPH method can effectively reproduce the effects of secondary damage in the numerical model.
• The residual strength of the structure under the tensile load mainly depends on the bearing area of the fracture surface, the break shape will lead to different tip crack strength factors, and then affect the ultimate bearing capacity of the structure.
• When the fracture surface is at the stringer, the stringer can provide part of the effective carrying area, share part of the load, and improve the ultimate strength of the structure.