Analysis of the Inclined Impact Resistance Characteristics of Concrete Structures Against Projectiles

Abstract

The research involved the use of commonly utilized concrete materials as the target plate, with a specially designed 76 mm projectile intended to impact the concrete structure at a specific angle. The goal was to conduct numerical simulation research on the deflection of the projectile under oblique impact conditions and analyze the concrete structure’s ability to resist penetration under such conditions. Through numerical simulation calculations, various aspects of the oblique impact were studied, including ricochet patterns under different projectile velocities and angles of incidence, as well as the resulting damage to both the projectile and the target plate, penetration depth, and deflection angle of the projectile. The findings showed that, compared to vertical penetration, the concrete structure exhibited superior deflection and cover-plate effectiveness under oblique impact conditions. The ricochet patterns observed could potentially inform the design of concrete anti-ballistic structures.

1 Introduction

With the continuous development of precise guidance technology, the threat of penetrating weapons is increasing. Therefore, the research and development of new camouflage technology is crucial to improve the protection capabilities of important engineering facilities on the battlefield, and the study of yaw structures has attracted widespread attention. For example, Reference [1, 2] developed a yaw layer composed of electrical ceramics and PRC spherical columns, and conducted a shooting test with a 57 mm semi-armor-piercing bullet. The results showed that the yaw layer had a significant effect on the deflection of the projectile, with a maximum deflection angle of 64°. References [3, 4] analyzed the impact resistance characteristics of ruby ball concrete. The study of oblique impact of bullet-target is the key to the study of yaw structure. Reference [5] conducted tests on the oblique penetration of C30 and C60 reinforced concrete by projectiles at speeds of 250–430 m/s. The results showed that the critical ricochet angle of C30 reinforced concrete was between 38°–44°, and that of C60 reinforced concrete was between 34°–42°. Reference [6] conducted oblique penetration tests on C40 concrete target plates using a 10 mm diameter projectile, and the results showed that when the inclination angle of the projectile increased to a certain degree, ricochet occurred. References [7,8,9,10] used cavity expansion theory and numerical simulation methods to study the ricochet problem when projectiles obliquely collided with concrete target plates. Currently, the yaw theory analysis of concrete spallation layer is difficult to achieve with high precision. Most research is based on projectile impact tests and numerical simulation results. Therefore, using simulation to analyze the ricochet situation of the projectile after oblique impact on the target, as well as the penetration depth and deflection angle of the projectile, is of great significance for studying the deflection effect of special structure concrete. It can also provide a reference for the design and optimization of spallation layer structures in protective engineering. Therefore, this paper carries out a numerical simulation study on the deflection of concrete structures under oblique impact conditions.

2 Simulation Conditions and Model Selection

2.1 Simulated Operating Conditions

The simulated projectile has a diameter of 76 mm, a length-to-diameter ratio of approximately 9, and a caliber radius head (CRH) of 7. The specific dimensions and weight parameters are shown in Table 1 below.

Table 1. Dimensions of the cartridges

The projectile velocity conditions range from 400 to 800 m/s, encompassing three different velocity conditions. The projectile impacts the C60 concrete target at two different angles. Using the dynamic finite element simulation software LS-DYNA, a numerical simulation of the oblique penetration of a 76 mm projectile into the concrete target is conducted. The pre-processing software HyperMesh is utilized to establish the finite element model of the oblique penetration of the 76 mm projectile into the concrete target. Through simulation calculations, the ricochet situation of the 76 mm projectile obliquely penetrating the C60 concrete target, as well as the damage situation of the projectile and the target plate, are obtained under different projectile velocities and different projectile incidence angle conditions. The deflection angle, penetration depth, projectile damage, and the diameter of the concrete target pit are statistically analyzed for each condition. The schematic diagram of the statistical results is shown in Fig. 1, where the projectile incidence angle is denoted as β, the projectile deflection angle as γ, the penetration depth as H, and the diameter of the concrete target pit as D.

Fig. 1.

Schematic diagram of intrusion results

A finite element model of the 76 mm projectile oblique impact on a C60 concrete target was established, with a total of 4 working conditions selected. Projectile velocities included 400 m/s, 500 m/s, and 600 m/s, while the incident angles were 45° and 60°, as shown in Table 2. By calculation, the ricochet situation of the 76 mm projectile obliquely penetrating the C60 concrete target under different projectile velocities and incident angles, as well as the damage situation of the projectile and the target plate, was obtained.

Table 2. Numerical simulation calculation table

2.2 Concrete Target Board Instructions

Based on the numerical simulation scheme for the oblique penetration of a 76 mm projectile into a C60 concrete target, a 3D model was created using the SolidWorks software platform. The concrete target has a diameter of 2000 mm and a height of 1200 mm, surrounded by 5 mm steel plates on all sides. Finite element mesh division was conducted using HyperMesh to construct the corresponding finite element mesh model. The finite element mesh model of the concrete target is shown in Fig. 2, with mesh refinement in the projectile-target contact area. The finite element model of the projectile is shown in Fig. 3.

Fig. 2.

Finite element model of concrete target

Fig. 3.

Finite element model of the projectile

2.3 Unit and Algorithm Selection

The simulation software selected for this simulation calculation is ANSYS/LS-DYNA program, due to the need to establish a three-dimensional finite element model of the 76 mm bullet oblique impact C60 concrete target, so the choice of three-dimensional 8-node solid cell SOLID164 solid mesh division, the unit has eight nodes, each node has six degrees of freedom. The following Fig. 4 describes the geometric properties, node positions and coordinate system of SOLID164 cell.

Fig. 4.

SOLID164 solid cell geometry characteristics

2.4 Load and Constraint Setting

According to the actual working conditions of the simulation calculation of the 76 mm projectile hitting the C60 concrete target obliquely, a series of specific solution conditions are set up in the simulation calculation process, specifically in the following aspects:

• (1) Because of the huge number of units and nodes in the calculation model, the solver selects LS-DYNA software and sets up multi-node parallel calculation;

• (2) In order to ensure the energy conservation of the system as a whole, the hourglass control of the calculation system is carried out, and viscous damping is added to reduce the energy loss;

• (3) The contact between the concrete target and the elastomer is set as erosion contact.

2.5 Selection of Material Constitutive Model

In the calculation process, the elastic body of the principal model selection of viscoplastic damage principal model (*MAT_JOHNSON_COOK), the elastic body in the process of invasion are embodied in the strain rate effect, the commonly used viscoplastic damage model that can take into account both the strain rate effect and the temperature effect is the JOHNSON COOK model, the model consists of two main parts. The first part only involves stress:

$$\sigma =\left[A+B{\left({\overline{\varepsilon }}^{P}\right)}^{n}\right]\left[1+C\text{ln}{\dot{\varepsilon }}^{*}\right]\left[1-{\left({T}^{*}\right)}^{m}\right]$$

(1)

where: $\upsigma$ is the VON MISES flow stress, A, B, C, n, and m are the input constants associated with the material, ${\overline{\upvarepsilon } }^{\text{P}}$ is the equivalent plastic strain, and ${\dot{\upvarepsilon }}^{*}$ is the relative equivalent plastic strain rate. T* = (T − Tr)/(Tm − Tr) is the dimensionless temperature, and Tm and Tr are the melting point and room temperature of the material.

The first factor n of the above equation represents the flow stress as a function of equivalent plastic strain (${\dot{\upvarepsilon }}^{*}$ = 1.0, T* = 0); the second factor C represents the strain rate effect; and the third factor m represents the temperature effect.

The second part deals with strain:

$${\varepsilon }^{f}=\left[{D}_{1}+{D}_{2}exp{D}_{3}{\sigma }^{*}\right]\left[1+{D}_{4}\text{ln}{\varepsilon }^{*}\right]\left[1+{D}_{5}{T}^{*}\right]$$

(2)

where ${\upvarepsilon }^{\text{f}}$ is the fracture strain, ${\upsigma }^{*}$ is the ratio of the pressure to the equivalent force of VON MISES; D1, D2, D3, D4, and D5 are the damage coefficients. Fracture occurs when $\text{D}=\sum \frac{\Delta\upvarepsilon }{{\upvarepsilon }^{\text{f}}}=1$ ($\Delta\upvarepsilon$ is the equivalent plastic strain increment during the integration cycle).

The JOHNSON COOK model is generally used in conjunction with the GRUNEISEN equation of state, which is expressed as follows:

$$p=\frac{{\rho }_{0}{C}^{2}\mu [1+(1-\frac{{\gamma }_{0}}{2})\mu -\frac{a}{2}{\mu }^{2}]}{[1-\left({S}_{1}-1\right)\mu -{S}_{2}\frac{{\mu }^{2}}{\mu +1}-{S}_{3}\frac{{\mu }^{3}}{(\mu +1{)}^{2}}{]}^{2}}+\left({\gamma }_{0}+a\mu \right)E$$

(3)

where C is the intercept of the vs-vp curve; S1, S2, and S3 are the slope coefficients of the vs-vp curve; ${\upgamma }_{0}$ is the GRUNEISEN constant; and a is the first-order volumetric correction for ${\upgamma }_{0}$ and $\upmu =\frac{\uprho }{{\uprho }_{0}}-1$.

Concrete materials, available material models are more abundant. At present, the concrete material models applicable to impact conditions include HJC model, RHT model, TCK model, etc. From the numerical simulation of a large number of projectile penetration conditions and the comparison of test results, the HJC model (Holmquist-Johnson-Cook Concrete mode) is more advantageous in describing the dynamic mechanical behavior of concrete under high strain rate and high pressure conditions. The HJC model has been clearly defined in the LS-DYNA program and is divided into three aspects: equation of state, strength model, and damage model.

The equation of state is as follows:

Resilience phase:

$$p={k}_{e}\mu $$

(4)

Plastic loading stage:

$$p={p}_{1}+\frac{\left({p}_{1}-{p}_{c}\right)\left({\mu }_{1}-{\mu }_{c}\right)}{\mu -{\mu }_{1}} {p}_{c}\le p\le {p}_{1}$$

(5)

Plastic unloading stage:

$$p-{p}_{max}=\left[\left(1-\frac{{\mu }_{max}-{\mu }_{c}}{{\mu }_{1}-{\mu }_{c}}\right){K}_{e}+\frac{{\mu }_{max}-{\mu }_{c}}{{\mu }_{1}-{\mu }_{c}}{K}_{1}\right]\left({\mu }_{1}-{\mu }_{max}\right) {p}_{c}\le p\le {p}_{1}$$

(6)

Fully compacted loaded section:

$$p={k}_{1}\frac{\mu -{\mu }_{1}}{1+{\mu }_{1}}+{k}_{2}{\left(\frac{\mu -{\mu }_{1}}{1+{\mu }_{1}}\right)}^{2}+{k}_{3}{\left(\frac{\mu -{\mu }_{1}}{1+{\mu }_{1}}\right)}^{3} p>{p}_{1}$$

(7)

Fully compacted unloading section.

$$p-{p}_{max}={k}_{1}\left(\frac{\mu -{\mu }_{1}}{1+{\mu }_{1}}-{\left(\frac{\mu -{\mu }_{1}}{1+{\mu }_{1}}\right)}_{max}\right) p>{p}_{1}$$

(8)

At this stage the concrete is non-porous and dense and the material is completely destroyed.

Yield equation:

$${\sigma }^{*}=\left[A\left(1-D\right)+B{P}^{*N}\right]\left(1-C\,\text{ln}\,{\varepsilon }^{*}\right)$$

(9)

where: ${\upsigma }^{*}$ is the normative equivalent stress, ${\upsigma }^{*}=\upsigma /{\text{f}}_{\text{c}}$, $\upsigma$ is really the equivalent stress, ${\text{f}}_{\text{c}}$ is the quasi-static uniaxial compressive strength; ${\text{P}}^{*}$ is the normative pressure, ${\text{P}}^{*}=\text{P}/{\text{f}}_{\text{c}}$; D is the damage parameter; ${\upvarepsilon }^{*}$ is the dimensionless strain rate.

Injury Equation:

$$D=\sum \frac{\Delta {\varepsilon }_{P}+\Delta {\mu }_{P}}{{D}_{1}{\left({P}^{*}+{T}^{*}\right)}^{{D}_{2}}}$$

(10)

where: $\Delta {\upvarepsilon }_{\text{P}}$ is the equivalent plastic strain; $\Delta {\upmu }_{\text{P}}$ is the equivalent plastic bulk strain; D1 and D2 are material constants; ${\text{T}}^{*}$ is the standardized maximum tensile hydrostatic pressure, ${\text{T}}^{*}=\text{T}/{\text{f}}_{\text{c}}$.

Destructive strength:

$$ DS = f_{c}^{\prime } min\left[ {SFMAX,A\left( {1 - D} \right) + BP^{{{*}N}} } \right]\left[ {1 + C\ln \varepsilon^{*} } \right]{ }P^{*} > 0 $$

(11)

$$ DS = f_{c}^{\prime } max\left[ {0,A\left( {1 - D} \right) + A\left( {\frac{{P^{*} }}{T}} \right)} \right]\left[ {1 + C\ln \varepsilon^{*} } \right]{ }P^{*} < 0 $$

(12)

3 Simulation Results

The simulation results for four different working conditions corresponding to the oblique impact on the C60 concrete target plate at projectile speeds of 400, 500, and 600 m/s and angles of 45° and 60° are shown in Fig. 5. The stress distribution of the projectile at different times is shown in Fig. 6.

Fig. 5.

Results of oblique penetration of projectile into concrete target

Fig. 6.

Stress Distribution Cloud Map of Projectile Penetrating Concrete Target

The results show that in Case 1, the slanting impact of the projectile on the concrete target produces a ricochet, the deflection angle of the projectile is 123°; the depth of penetration of the projectile is 198.8 mm; the diameter of the concrete target pit is 1098.2 mm; the head of the projectile has been eroded and the projectile body is deformed obviously. Case 2: oblique penetration of the projectile into the concrete target, resulting in ricochet, the deflection angle of the projectile is 71°; the depth of penetration of the projectile is 71.4 mm; the diameter of the concrete target pit is 928 mm; the head of the projectile has been eroded, and the body of the projectile has obvious deformation. Case 3: oblique penetration of the projectile into the concrete target, resulting in ricochet, the deflection angle of the projectile is 89°; the depth of penetration of the projectile is 98.6 mm; the diameter of the concrete target pit is 941.5 mm; the head of the projectile has been eroded, and the body of the projectile has been deformed significantly. In Case 4, the slanting penetration of the projectile into the concrete target produces ricochet, the deflection angle of the projectile is 117°; the penetration depth of the projectile is 139.2 mm; the diameter of the concrete target pit is 942.3 mm; the head of the projectile has been eroded, and the body of the projectile has obvious deformation.

4 Analysis of Simulation Results

4.1 Analysis of Projectile Deflection and Target Damage

According to the requirements of the working conditions, the finite element model of the 76 mm projectile impacting obliquely on the C60 concrete target was established, and a total of four working conditions were calculated, as shown in Table 3 below. Through the calculation of different projectile velocity and different projectile incidence angle conditions, the 76 mm projectile oblique impact C60 concrete target ricochet, as well as the damage of the projectile and the target plate.

Based on the simulation results, the following conclusions can be obtained:

• (1) From the calculation results, it can be concluded that for the same projectile and under the same velocity conditions, a larger angle of incidence leads to a smaller projectile deflection angle, shallower penetration depth, and smaller crater diameter.

• (2) From the calculation results, it can be concluded that for the same projectile and under the same angle of incidence, a higher velocity leads to a larger projectile deflection angle and greater penetration depth.

• (3) Compared with the vertical penetration of concrete armor-piercing structures under the same conditions, the advantage of concrete structures against penetration is more pronounced under oblique impact conditions. The design of new concrete armor-piercing structures should fully utilize the advantage of concrete structures in causing projectile deviation under oblique impact conditions.

Table 3. Summary of numerical simulation results

4.2 Comparison Results with Vertical Penetration of Concrete Structures

Using the same numerical model to calculate the 76 mm projectile with 400 m/s vertical penetration of C60 concrete structure, the results are shown in Fig. 7, penetration depth of 0.68 m. Penetration according to the penetration formula proposed by Forrestal [11] can be calculated 76 mm projectile penetration of C60 concrete depth of about 0.7 m, and the numerical simulation results coincide with the 76 mm projectile in large angle In the four working conditions under the condition of oblique impact on C60 concrete structure, the effective depth of penetration is about 0.07 m, which is much smaller than the vertical penetration depth of the projectile, compared with the anti-invasion effect is very obvious, which proves that the large-angle oblique impact of the projectile target can be effective in deflecting the projectile to achieve the purpose of protection at the same time.

Fig. 7.

Schematic diagram of vertical penetration results

5 Conclusion

This article focuses on the numerical simulation of the oblique impact of a 76 mm projectile on a C60 concrete target, and a total of 4 working conditions were selected for calculation. The simulation results were used to obtain the skipping behavior of the 76 mm projectile and the damage to the projectile and the target plate under different projectile velocities and oblique impact angles.

• (1) The calculation results show that the oblique penetration of the projectile into the concrete target can be divided into the formation of a projectile pit, sliding zone, and tunnel. This is due to the loosening and shedding of the surface concrete when the projectile impacts the concrete target, resulting in minimal resistance to the projectile’s movement. As the penetration continues, an asymmetrical resistance force causes the projectile to deviate laterally. With increasing penetration depth, the resistance force becomes approximately uniform, resulting in the formation of a tunnel. When the tunnel length reduces to zero, skipping of the projectile occurs.

• (2) From the calculation results, it can be observed that for the same type of projectile and the same velocity, a larger oblique impact angle leads to a smaller deviation angle, shallower penetration, and smaller pit diameter.

• (3) Similarly, for the same type of projectile and oblique impact angle, a higher velocity results in a larger deviation angle and deeper penetration.

• (4) Compared to the vertical penetration of the projectile into the concrete, the concrete structure exhibits a more significant advantage in resisting penetration under oblique impact conditions. The design of new concrete shielding structures should fully exploit the advantage of deflecting projectiles under oblique impact conditions.