Studies on the Thermodynamic Properties of C/ph Irradiated by Intense Electron Beams

Abstract

The thermal shock wave and blow-off impulse are important phenomena of the thermodynamic effects produced in material bombarded by electron beams. The experimental results of the blow-off impulse in an improved carbon fiber-reinforced phenolic material (referred to, in short, as C/ph) exposed to intense electron beams are presented. Used to generate electron beams, the “FLASH II” accelerator has energy fluences ranging from 150 to 350 J·cm⁻², and average energies of 0.5 or 0.6 MeV. The experimental results showed that the coupling coefficient of the blow-off impulse of C/ph was 0.42 ± 0.02 Pa∙s/(J·cm⁻²). The thermal shock waves and the blow-off impulse were numerically calculated separately by using a one-dimensional elastic–plastic hydrodynamic model. Attenuating with propagating distances, the peak values of the thermal shock waves during experiments were 0.6~1.5 GPa at the location of x = 8 mm in targets. The results of the numerical calculations were in good agreement with experimental data. The results obtained provide a basis for nuclear hardness and survivability assessments of aerospace.

1. Introduction

When a pulsed beam (X-ray, laser or electron beam) that irradiates the outer layer of a structure is characterized by high energy density, and takes place over times of the order of a few nanoseconds to a few hundred nanoseconds, the nearly instantaneous deposition of energy in the material can produce various thermal-mechanical effects, such as thermal shock wave propagation and blow-off impulse [1,2,3,4,5]. Tensile stress may appear when the shock waves reflect from the rear surface. The tensile stress may lead to the spallation of the material when its strength exceeds the material’s tensile strength threshold. At sufficiently high dose levels, the front surface layer of the material melts, vaporizes or experiences blow-off, imparting momentum to the material. These processes may lead to severe structural damage in underlying materials. Many scholars have been attracted by the dynamic mechanical responses of materials under the radiation condition and have done much research in this field [6,7,8,9,10,11,12,13,14].

Carbon fiber-reinforced phenolic (C/ph) composite has been widely used in the heat shield parts of space vehicles as a functional ablation material, due to its low-cost, and its anti-heat and anti-ablation characteristics [15]. Due to its low mechanical properties, its application in the field of structural materials is limited. With the development of high-performance phenolic resin, the mechanical properties of phenolic composites have been greatly improved, and C/ph materials have been gradually applied as structural materials [16,17]. C/ph composites can not only maintain complete aerodynamic shape of the aircraft during flight, but also have the dual functions of heat protection and structure, so C/ph composites have become an ideal thermal protection material for interstellar reentry and ballistic reentry. Many studies have focused mainly on the ablation mechanism [18], mechanical properties and constitutive model of the C/ph composite [19,20,21]. In addition to high-speed aerodynamic heating and fuel heating, high energy density pulsed beam irradiation also causes ablation damage to materials [22]. The physical and mechanical properties of the improved C/ph materials, especially the thermal mechanical properties produced by pulse radiation, are hot issues, while having some concerns. It is of great significance for the fields of radiative hardening and laser weapons to study the radiative thermal shock wave and blow-off impulse of the improved C/ph materials [23,24,25,26].

The objectives of this paper were to measure the blow-off impulse of an improved C/ph material and numerically calculate the thermal shock wave and blow-off impulse under pulsed, high-energy, high-intensity electron beams. The results obtained provide a basis for judging the conservativeness of predictions of blow-off impulse loads used in hardness and survivability analyses and assessments of space crafts.

2. Experiment

2.1. Experimental Specimen

The improved C/ph material is a kind of laminated composite made of orthogonally woven carbon fiber layers and phenolic resin [21]. The composite with ablation and heat protection function was obtained by laminating with carbon fiber as reinforcement and phenolic resin as matrix. The direction of X1 is perpendicular to the fabric layers and is defined as off-layer direction. The directions of X2 and X3 are defined as in-layer directions (See Figure 1). The C/ph is an anisotropic composite, but the mechanical behaviors at X2 and X3 directions are the same for the identical material. This paper aimed to experimentally study the thermal mechanical properties of C/ph at X1 direction, with samples of nominally 30 mm (diameter) × 4 mm (thickness). The density of the C/ph material was 1430 kg/m³, lower than for metal materials, but its specific stiffness is large. The Young’s modulus in X1 direction was 7 GPa.

2.2. The Measuring Method of Impulse

An electron beam was used to rapidly deposit energy at the front surface of improved C/ph samples. At sufficiently high dose level, the components of the front surface of the C/ph were melted or vaporized, imparting momentum to the sample. Using a translation cart with an infrared light velocity measurement system, the blow-off impulse of the material was determined. Figure 2 shows the schematic diagram of the probe [9,25]. The translation bar featured a flat target attached on one end and a shape of rings with a constant spacing on the other end. Moreover, on the two sides of the bar were infrared luminous tubes and photoelectric triodes. When the bar moved forward, the ring blocked the light and turned off the signal, and, then, the signal went on. The digital oscilloscope recorded the time interval “Δt” while the bar moved through the spacing “L” between two rings. Thus, the average velocity “V” was obtained by [9]:

$$V=\frac{L}{(1-\xi )\Delta t}$$

(1)

where, ξ is the friction adjusting factor (less than 4.5%), which was calibrated by a light gas gun. V is the average velocity of the target. According to the law of momentum conservation, the blow-off impulse “I” is represented by [9]:

$$I=\frac{mV}{A}$$

(2)

where, m is the total mass of the target and bar, A is the irradiated area on the target. I is the momentum obtained per unit area. The experimental uncertainty of impulse is less than 10%. With the energy fluence “Φ” of electron beam on the target, the coupling coefficient of blow-off impulse “β” was determined [9]:

$$\beta =I/\Phi$$

(3)

Φ represents radiation energy per unit area. β represents the potential for generating blow-off impulse with unit energy fluence of the electron beam.

2.3. Experimental Installation

Experiments were carried out on the “Flash-II” accelerator to measure the blow-off impulse of the C/ph material. The “Flash II” electron beam accelerator is a low-energy, high-current pulsed relativistic electron beam accelerator, which is used to simulate the thermo-mechanical effects caused by the interaction between X-rays and materials in nuclear explosions. Four impulse probes are mounted on the bracket in the drift tube. As shown in Figure 3, several different materials were radiated in one shot and the fluence of the electron beam was measured by a graphite energy probe. Different energy fluence could be obtained by adjusting the position of the probe in the magnetic field.

2.4. Experimental Results

The graphite cathode discharge of the accelerator emitted an electron beam. The electron beam was concentrated in the drift tube magnetic field and irradiated to the experimental target. The incident electron collided inelastically with the electron in the atom of the material to deposit energy. Under electron beam irradiation, the specific internal energy of the phenolic resin matrix and other substances in the material increased, and, subsequently, part of pyrolysis gas was produced, and the pyrolysis gas gushed to the boundary. At the same time, the phenolic resin matrix and other materials formed a “carbonized layer”. When the specific internal energy was high enough, the carbonized layer erupted. Figure 4 shows the scheme of ablation mechanism of the C/ph material [18].

Figure 5 shows the ablation of the material surface before and after irradiation. After the front surface of the material was irradiated by the electron beam, a large amount of energy was deposited on the thin surface layer, phenolic resin heated up, pyrolysis occurred, gas was removed, and the rest was carbonized. In the experiment, a Tektronix 4104B oscilloscope was used to record the probe’s measurement signal. Figure 6 shows a typical waveform recorded by the blow-off impulse probe. The distances of straight-line motion, corresponding to the time interval between any two peak voltage signals, were 6 mm, so the velocity of the target and rod system could be calculated from the waveform. The radiated area of the specimen, A, was 3.14 cm². The total mass and fluence of every shot were known. The blow-off impulse and impulse coupling coefficients could be obtained according to Formulas (2) and (3).

The experimental results are listed in

Table 1. The experimental results of the C/ph and Ly12 Aluminum.

Shot No.	Material	Ea /MeV	Φ /J·cm−2	I /Pa·s	β /Pas/(J·cm−2)
1	C/ph	0.6	315	117	0.37
2	C/ph	0.6	316	114	0.36
3	C/ph	0.5	341	138	0.41
4	C/ph	0.5	201	88.0	0.44
5	C/ph	0.5	210	102	0.48
6	C/ph	0.5	205	84.0	0.41
7	C/ph	0.6	350	163	0.47
8	C/ph	0.5	158	58.4	0.37
9	C/ph	0.5	182	99.3	0.55
10	C/ph	0.5	171	68.0	0.40
11	C/ph	0.5	171	62.0	0.36
12	Ly12 Al	0.6	200	229	1.15
13	Ly12 Al	0.6	202	235	1.17

. The value I denotes the blow-off impulse. E_a is the average energy of the electron beam. β is the coupling coefficient of blow-off impulse. Φ is the energy fluence. From the Table 1, it can be concluded that the blow-off impulse of the C/ph increased with energy fluence. The average coupling coefficient of the blow-off impulse of C/ph was 0.42 ± 0.02 Pa∙s/(J·cm⁻²). Under the same conditions, the coupling coefficient of C/ph was less than that of Ly12 aluminum. The former was about 1/3 of the latter. The density of Ly12 aluminum was 2785 kg/m³, and its vaporization energy was 11 kJ/g.

3. Numerical Simulation

3.1. Energy Deposition

The Monte-Carlo method is generally considered to be a more accurate method in the calculation of electron beam energy deposition [27,28]. Considering that the electron mass is very small and has a unit charge, it collides with matter atoms a large number of times, so it is impossible to simulate each collision process of an electron, because the amount of calculation would be daunting. Therefore, the method of condensing history, proposed by Berger, was adopted [29,30]. The electron random walk path length is determined by the energy steps. For a single step, the electron energy loss is the total amount of the nonradiative (collisional) energy loss and radiative (bremsstrahlung) energy loss. The nonradiative energy loss in each step is sampled from the Landau formulation, and the radiative energy loss and the production of bremsstrahlung photon is sampled from the Bethe formulation. The direction of the electron at the end of each step is sampled from the Gouddsmit-Saunderson multiple scattering formulation [31]. The Moller cross section is used for the sampling of the electron-electron scattering.

The electron angle has a dramatic effect on the shape of the energy profile [32,33]. For small angles (less than 30 degrees), the normalized peak dose of the energy profile barely changes, but begins to balloon as the electron angle increases above 30 degrees. With the assumption of a mono-energetic, mono-angle electron spectrum, the average incident angle of the electron beam is about 40 degrees, and the deposition profiles are generated with Monte Carlo transport codes. Figure 7 shows the profiles of several single energy electrons. When the incident angle of the electron was 40°, the peak of energy deposition was not on the surface. When the incident angle of the electron was 75°, the peak of energy deposition was on the surface of the material, similar to that of X-rays.

3.2. Theoretical Model

A one-dimensional elastic–plastic hydrodynamic model was used to simulate the thermodynamic effects of the C/ph composite exposed to an electron beam. The equations in uniaxial strain configurations are expressed as follows [34,35]

$$\frac{\partial u}{\partial t}+\frac{1}{{\rho }_0}\frac{\partial (\sigma +q)}{\partial r}=0$$

(4)

$$\begin{array}{c}u=\frac{\partial R}{\partial t},\end{array}V=\frac{1}{{\rho }_0}\frac{\partial R}{\partial r}$$

(5)

$$\frac{\partial E}{\partial t}+(\sigma +q)\frac{\partial V}{\partial t}=E_R(R,t)$$

(6)

$$\sigma =p+S_D,\begin{array}{cc}& p=f(V,E)\end{array}$$

(7)

where,

$$S_D=\left\{\begin{array}{ll}\frac{2}{3}{Y}_0{S}_x/\left|S_x\right|,& \left|S_x\right|\ge \frac{2}{3}{Y}_0\\ S_x,& \left|S_x\right|<\frac{2}{3}{Y}_0\end{array}\right.$$

(8)

$$\frac{\partial S_x}{\partial t}=2G(\frac{1}{3V}\frac{\partial V}{\partial t}-\frac{\partial u}{\partial r})$$

(9)

$$q=\left\{\begin{array}{ll}{a}_1{}^2\rho {\left|\Delta u\right|}^2+a_2\rho c\left|\Delta u\right|,& \frac{\partial u}{\partial r}<0\\ 0,& \frac{\partial u}{\partial r}\ge 0\end{array}\right.$$

(10)

where R and r are, respectively, Eulerian and Lagrange coordinates (unit is m), and t time (unit is second), The other variables are as follows: ρ₀ is the initial mass density (unit is kg/m³), V is the specific volume (unit is m³/kg), u is the particle velocity (unit is m/s), SD is the partial stress, P is the pressure (unit is Pa), Y₀ is the dynamic yield strength (unit is Pa), q is the artificial viscous force, a₁ and a₂ are the viscosity coefficient, c is the local sound speed (unit is m/s), G is the shear modulus (unit is Pa), σ is the total stress (unit is Pa), E is the specific energy (unit is J/kg), E_R(R, t) is the deposited specific energy rate (unit is J/(kg·s)), which reflects the contribution of pulsed beam radiation to internal energy.

Under the conditions of strong pulsed X-ray and electron beam radiation, vapor, liquid and solid states may occur in the material. For this complex material state under radiation, we used the following state equation to describe it.

In the compression region, ρ > ρ₀, the shock Hugoniot equation was adopted by:

$$p=p_H+{\rho }_0{\Gamma }_0(E-E_H)$$

(11)

where:

$$p_H=\frac{C_0^2(V_0-V)}{{[V_0-S(V_0-V)]}^2}$$

(12)

$$E_H=\frac{1}{2}{p}_H(V_0-V)$$

(13)

In the expansion zone, $\rho \le {\rho }_0$, using Puff equation of state:

$$\begin{array}{ll}p=& \rho [\gamma -1+({\Gamma }_0-\gamma +1){(\frac{\rho }{{\rho }_0})}^{1/2}]\\ & [E-E_s\{1-\exp [\frac{N{\rho }_0}{\rho }(1-\frac{{\rho }_0}{\rho })]\}]\end{array}$$

(14)

In the vaporization zone, Equation (14) automatically transitioned to the ideal gas equation of state. Where E_s is the specific sublimation energy, C₀ is the initial speed of sound, S is the material constant, Γ₀ is the normal Gruneisen coefficient, γ is the specific heat rate, N = C₀²/Γ₀E_s.

In the numerical calculation, the blow-off impulse is the sum of the momentum of all the matters flying away from the target surface.

$$I={\displaystyle \sum _{u_i<0}{m}_i\left|u_i\right|}$$

(15)

where u_i and m_i are the velocity and mass of the cell, respectively.

3.3. Results of Numerical Simulation

The parameters of the C/ph are listed in

Table 2. Material parameters of the new type C/ph.

ρ0/g·cm−3	1.430	Γ0	1.2	Es/kJ/g	5.14
c0/m·s−1	3069	G/GPa	6.0	H	0.5
s	1.578	Y0/GPa	0.05	N	1.53

. The value ρ₀ is the density of the C/ph. Γ₀ is the normal Gruneisen coefficient, indicating the partial derivative of pressure to internal energy at a constant volume. E_s represents the equivalent eruption energy of the composite, which is related to impulse calculation. G is the shear modulus of the material. Y₀ is the yield threshold. N is the material constant. H = γ − 1. Figure 8 shows the relationship of impulse with energy fluence, i.e., the blow-off impulse increased with the energy fluence. There were some small differences in the uniformity of the C/ph composite. In the experiment, the relative uncertainty of electron beam energy fluence was about 15%, and the relative uncertainty of impulse measurement was less than 10%. In the numerical simulation, the selection of material parameters also affected the results. The relative uncertainty of experimental results and numerical calculation was less than 20%. The numerical simulation agreed well with the experimental results.

The experiments of thermal shock waves in this improved C/ph irradiated by electron beam were carried out in the Reference [25]. According to the experimental conditions, the thermal shock waves were numerically simulated. Figure 9 shows the attenuation of the thermal shock waves, the peak values of which attenuated with propagating distances. When Φ = 531 J·cm⁻² and x = 10 mm, σ = 1.33 GPa in C/ph. However, when Φ = 509 J·cm⁻² and x = 10 mm, σ = 2.16 GPa in Ly12 aluminum, as shown in Reference [25].

The maximum stress did not appear on the irradiated surface. The maximum peak value of the thermal shock wave appeared in the front part of the energy deposition zone. Outside the deposition area, the thermal shock wave decreased with increase of distance. Figure 10 shows the energy deposition profile induced by different fluences. When the energy fluence was 531 J·cm⁻², the peak value of specific energy and stress appeared at x = 0.24 mm and at x = 0.36 mm. In the process of irradiation, the propagation of the thermal shock wave was a dynamic process, so the position of the maximum stress was slightly larger than that of the peak value of specific energy.

Figure 11 and Figure 12 show that thermal shock waves were in a triangular pulse shape. With the increase of propagation distance, the waveform broadened and the peak value of the compressive stress decreased.

According to the weak-shock theory [7], the stress wave attenuation relationship is shown as:

$$\frac{\sigma }{{\sigma }_0}={[1+2s(\frac{{\sigma }_0}{k})(\frac{x}{{\delta }_0})]}^{-1/2}$$

(16)

where k is the bulk modulus (k = ρc²), k = 13.5 GPa for C/ph, k = 81.2 GPa for Ly12 aluminum. s is the constant of material. δ₀ is the initial pule width. Assume that δ₀ = 0.4 mm, σ₀ = 0.1 and 0.5 GPa respectively, the normalized stress attenuation curves in C/ph and Ly12 aluminum are shown in Figure 13. It shows that the wave attenuation performance of C/ph was better than that of aluminum.

4. Conclusions

C/ph composite is a kind of thermal protection material with integrated thermal insulation, and has been widely used in the aerospace field. The thermodynamic response of C/ph composites under intense pulse irradiation is a hot spot. Experimental measurements of blow-off impulses were carried out on one improved C/ph composite exposed to intense electron beams. A one-dimensional elastic–plastic hydrodynamic model was used to simulate the thermodynamic properties (blow-off impulse and thermal shock wave) of this composite. Through experimental research and analysis, the conclusions could be drawn as follows:

(1)

When the energy fluences of the electron beam were in the range of 100 to 400 J·cm⁻², the average coupling coefficient of the blow-off impulse of C/ph was 0.42 ± 0.02 Pa·s/(J·cm⁻²).

(2)

When the electron beam with the same energy flux irradiated carbon phenolic and Ly-12 aluminum targets, respectively, the peak value of the thermal shock wave in C/ph was lower than that in Ly-12 aluminum at the same position. This improved C/ph composite had excellent attenuation performance of thermal shock wave. The experimental results were consistent with the theoretical results.

(3)

Under the same conditions, the coupling coefficient of C/ph was less than that of Ly12 aluminum, at about 1/3 of the Ly12 aluminum.

(4)

According to the incident energy fluence on the C/ph, the impulse load and wave propagation characteristics could be easily understood. The results obtained provide a basis for anti-radiation hardness and survivability assessments of aerospace.