Research on the influence of loading rate on the dynamic initiation fracture toughness of CMDB propellant

Abstract

In the field of gun launched missile extended range rocket, the propellant grain in the rocket needs to withstand significant launch loads during their firing phase, and also bear the high pressure caused by ignition, and the impact of launch overloads and ignition shocks on the structural integrity of propellants becomes very important. So this work investigated the dynamic initiation fracture toughness of the composite modified double-base (CMDB) propellant by both experiments and numerical simulations. The dynamic mechanical properties test of the cracked straight through flattened Brazilian disc (CSTFBD) specimens were conducted using a modified Split Hopkinson pressure bar (SHPB). By comparing the results of quasi static and dynamic numerical simulations, it was found that dynamic fracture initiation toughness can be determined by time-to-fracture using the quasi-static theory. The numerical simulation results combined with the ZWT constitutive model agree well with the experimental results, indicating that ZWT constitutive model is suitable for numerical simulation calculation of propellant structural integrity under dynamic load, and provides a theoretical basis for propellant structural integrity analysis under dynamic load. During the measurement of the mechanical response, the fracture surfaces of the dynamic test specimens were observed by electron microscopy scanning. Then the evolution of the microstructure synchronously was obtained. The scanning electron microscope (SEM) results revealed that fracture modes and breakage of the ammonium perchlorate (AP) particles in the surface layer played an important role in determining the failure mechanism, which revealed the failure mechanism of the propellant under dynamic load. The result of experimental measurement showed the influence of loading rate on the dynamic fracture initiation toughness of CMDB propellant.

Introduction

Impact loads are usually associated with high amplitude and short duration stress pulses¹. In modern aerospace engineering, impact related problems have been one of the most crucial issues of structural failure^2,3. Information regarding mechanical properties of solid propellant material is of considerable importance in accessing the stability of structure under dynamic loads⁴. Especially in the field of gun launched missile extended range rocket engines, since extended range rockets need to withstand significant launch loads during their firing phase, and also bear the high pressure caused by ignition during engine ignition, the impact of launch overloads and ignition shocks on the structural integrity of propellants becomes very important⁵. Fully understanding and investigating the structural failure performance and mechanisms under impact loading is important for aerospace/aeronautical applications of solid propellants.

Propellant grain is the main energy source for the solid rocket motor (SRM), its structural integrity is the essential guarantee that the SRM works normally. During the service life of solid propellant for an SRM, there are many kinds of loading conditions inducing structural failure. Quite a few number of aerospace explosion accidents directly caused by the propellant structural failure. Studies have found that the propellant grain undertaken typical blast impact loading at the moment of being ignited. Many researchers have put great effort into making a thorough inquiry of failure mechanism of solid propellant under impact loading^6,7. Fong et al.⁸ developed a model to describe the effect of strain rate and temperature on the fracture behavior of propellant with impact loading. Ho et al.^9,10 extended a constitutive model that incorporates mechanical damage effects for solid propellant under impact loading. Fong et al.¹¹ applied linear elastic fracture mechanics to research the effect of AP particle size and orientation on the fracture toughness of solid propellant, and he found the dynamic fracture toughness was virtually independent of strain rate over the range from 3 to 90s^− 1. Duan et al.^12–14 proposed experimental methods for investigating fracture characterization of solid propellants, a tensile split Hopkinson bar device was set up and fitted to experiments up to strain rate of 300 s^− 1, and significant influence of loading rate on JIC was observed. Ho et al.¹⁵ investigated the dynamic fracture behavior of solid propellant per-formed on a modified Hopkinson bar. He revealed that fracture properties depended on filler-binder interactions and impact temperature. Chyuan et al.¹⁶ developed a numerical modeling based on transient analysis of solid propellant grains under impact loading, and results showed that the dynamic effect is of great importance for structural integrity of solid propellant grains.

Most previously proposed researches only focused on the effects of strain rate and stress states or temperature on the fracture with dynamic loading. However, very few study focuses on characterizing the failure micro-mechanism of the solid propellant dynamic fracture over higher and wider range of loading rate. The investigation of dynamic fracture in CMDB propellant at the microscale is rarely documented. Understanding the strain rate or loading rate dependence of underlying failure mechanisms is important for aerospace applications of these solid propellants. CMDB propellant contains ammonium perchlorate (AP, as an oxidizer), aluminum (as fuel), nitrocellulose and nitroglycerine (as a binder) and various additives¹⁷. It is inhomogeneous on the microscale. Adding particles inside the material are rigid relative to the binder. There is a considerable volume big-particle-diameter AP within the matrix. As the strain gradually increases, the voids around the particles will then grow larger and even coalesce¹⁸. The ignition impact loads may cause these voids evolve to visible cracks wherein the solid propellant, which will have a nonignorable influence on the motor’s ballistic performance. It also can cause catastrophic structural failure. Therefore, research of dynamic fracture micro-mechanisms in CMDB propellant under impact loads is necessary.

It has been recognized that the topography of fracture surface reveals inherent details of deformation and the associated energy dissipation mechanisms that govern the process of fracturing^19–22. A large effort has been devoted to perform reliable microscopic observations on fracture surfaces and it is well-established that fracture surfaces satisfy a scaling invariance known as fractal dimension or self-affinity^23–25. However, most of the existing research results only focus on the mechanical response test results and simulation results of propellant materials under dynamic loads, or only study the microstructure failure mechanism of propellants under dynamic loads, ignoring the impact of changes in the microstructure of propellants under different dynamic loads on their macroscopic mechanical response. It is rarely reported that the mechanical response characteristics of propellants under dynamic loads are systematically studied by means of numerical simulation, SHPB test and SEM.

In order to obtain the mechanical response characteristics of CMDB propellant under high strain rate and establish the design method of the extended range rocket engine launched by artillery, the dynamic initiation fracture toughness of CMDB propellant under different loading rates was studied in this paper, and the fracture fracture of the propellant was analyzed by SEM to reveal the changes of microstructure under different dynamic loads. This is the key to understand the mechanical properties of materials at the macro level, and provides a reference for the study of the structural integrity of propellants.

Materials and methods

Materials and specimens

The solid propellant material investigated is manufactured by the casting method and provided by the manufacturer of North Industries Group Corporation in China²⁴. There is no obvious flaw in the material. Details of the formulation of the CMDB propellant is as shown in Table 1. The mass fractions represent the filler contents.

Table 1.

Ingredients composition of CMDB propellant.

Ingredient	CMDB binder	RDX	AP	Al	Others
Mass fraction (%)	41.5	21	33.6	2.2	1.7

The behavior of solid propellants has been studied by a series of experimental investigation. In addition, relevant rate-dependent composites have been extensively investigated and well described by Zhu-Wang-Tang (ZWT) constitutive equations^28–30. In this work, the mechanical properties of CMDB propellant in a strain rate range from 10^− 4 to 10³ are described employing a modified ZWT model. By means of quasi-static and dynamic tests and by using least square method, the parameters of the model are determined. The modified ZWT model parameters at 20 °C are illustrated in Table 2 contains. The function is given as:

1

Table 2.

The modified ZWT model parameters of CMDB propellant at 20 °C.

E0/MPa	α/MPa	β/MPa	E1/MPa	θ1/s	E2/MPa	θ2/µs
828.7	-8927.5	-34538.6	251.8	4.78	1341.3	72.5

Dynamic fracture performed on a CSTFBD configuration in a modified SHPB³¹. The geometry of specimen is shown in Fig. 1. It was cut from propellant slabs. Table 3 demonstrates its parameters for geometrically similar specimens. CSTFBD specimen is sandwiched between the bars. With the flat ends before impact as shown in Fig. 1(b), a satisfied contact is achieved. Since the propellant specimen is cut from the propellant slabs, there is residual stress in the crack tip of the specimen, which affects the subsequent SHPB test results³². Therefore, to eliminate the residual stress that located at the tip of the crack-tip, all the specimens are placed into a thermostatic cabinet varying the temperature from 50 °C to 20 °C for 24 h, respectively³³. Besides, the bar/specimen interfaces are lubricated with the molybdenum grease in order to mini-mize the friction caused by the impact rigidly.

Fig. 1.

Sketch and loading method of CSTFBD. (a) CSTFBD schematic diagram; (b) CSTFBD sandwiched by bars with perfect contact before impact.

Table 3.

Geometric parameters of CSTFBD specimens.

Diameter 2R/mm	Thickness B/mm	Crack length 2a /mm	Crack width b/mm	Load angle φ/°
25	8	14	0.75	20

Experimental setup

The 14 mm diameter modified SHPB system is shown in Fig. 2. It is composed of a striker (300 mm in length), an incident bar (1400 mm in length), a transmitted bar (1400 mm in length), a momentum bar (400 mm in length), made of high strength LC4 aluminum alloy with a nominal modulus of 74GPa^34–36. Strain gauges are mounted at 700 mm away from the bar/specimen interfaces on the incident bar and transmitted bar connecting to a 12-bits digital oscilloscope. Through a Wheatstone bridge and a differential amplifier (CS-1D dynamic strain meter), incident pulse ε_i(t) and transmitted pulse ε_t(t) are monitored, respectively. What’s more, two another strain gauges (SG1, SG2) are mounted at both sides of specimen crack tip. Then, by taking the derivative of the strain at the crack tip with respect to time, the maximum value is defined as the crack initiation time t_f.

Fig. 2.

Schematic diagram of the SHPB system.

Dynamic fracture test is conducted. The striker generates an incident pulse of an approximately duration of 250µs by launching the gas gun. Using a time counter and a data acquisition unit measurement system, the striking velocity was measured. A low-pass filter with a cutoff frequency of 10 MHz is applied to the raw data just as observed on digital oscilloscope. Then, the recorded pulses are converted into strains. Finally, the normal force history of the specimen is calculated. Forces and velocities at both faces of specimen are then given by the following³⁷:

2

3

where P_L(t), P_R(t), V_i(t), V_t(t) are forces and particle velocities at corresponding interfaces. ε_i(t), ε_r(t), ε_t(t) are the strain signals at the bar-specimen interface. A, E and C₀ are the cross-sectional area, Young’s modulus and the longitudinal stress wave speed in the pressure bars, respectively.

However, it should be noted that specimen under stress or dynamic force balances is the key and fundamental guarantee in dynamic tests. In SHPB tests, it is difficult to achieve the dynamic stress equilibrium in material without proper pulse shaping. Because the specimen may fail immediately from its end in contact with the incident bar when it is impacted by the incident bar³⁸. The pulse-shaper technique in SHPB is especially useful and crucial for investigating dynamic response of materials³⁹. This work develops a new composite pulse-shaper which is a combination of a thin rubber shim and a C11000 copper. It is applied by sticking a pulse shaper on the impact end of the incident bar, which prevents the sudden hit by the striker bar.

Figure 3(a) represents a typical set of incident, reflected, transmitted, SG1and SG2 waves in the test. It can be observed from Fig. 3(b) that high frequency oscillating components disappear and the rising front of the stress pulse is not steep due to the pulse shaper technique. During the dynamic test, the dynamic force balances. The stress equilibrium in the CSTFDB specimen is clearly achieved, as P_L≈P_R. Results with a striking velocity 10 m/s calculated using Eq. (2) is illustrated in Fig. 3(c). It is evident that no significant variations in same striking velocity with pulse-shaper technique in five dynamic tests, which demonstrated the test results had a good reliability and repeatability.

Fig. 3.

(a) Raw data of CSTFDB test at a 10 m/s; (b) Axial force at left and back end of CSTFDB specimen; (c) Typical results of five specimens at a striking velocity of 10 m/s; (d) Two strain gauges near the crack tip.

For the two SGs (SG1, SG2), the sudden decrease of strain as a function of time indicated the crack initiation. Then, an unloading stress wave was generated and traveled to the strain gauges. As indicated in Fig. 3(d), the time-to-fracture of SG1 (t_f) is about 42µs, the time shift is approximately 8µs. What’s more, it is worth to notice that the crack propagation was unstable due to the very high compressive stress at the side of the incident bar, resulting in unusual results of increase rate of two strain gauges. Therefore, experimental results were invalid when the striking velocity exceeded 25 m/s.

Comparison between simulation and experimental test

The dynamic test is considered credible with assumptions as following: (1) the stress distribution in both load ends shows the same behavior as in the quasi-static test (i.e., P_L≈P_R, as in Fig. 3(b)); (2) the indirect tensile failure occurs after the stress distribution is developed.

Aiming at validating the experimental test, numerical study is conducted. By using the commercial finite element code ABAQUS/Explicit solver, the tensile stress states of the specimen are captured. Comparing with the corresponding experimental data and numerical calculations, stress distribution in CSTFBD specimen is verified.

The finite element model and its mesh used in the numerical simulation are shown in Fig. 4(a). Element type of both compression bars and the specimen is C3D8R, the number of grids is 14,362 and the number of cells is 18,517. Instead of directly modelling the striker bar and the pulse shaper, the incident stress wave is created artificially. This is implemented by specifying a pressure boundary condition on the incident compression bar to closely match the experimental incident stress pulse⁴⁰. By this way, the computation time is reduced. By using the kinematics hard contact formulation, the contact between the compression bars and the sample is modeled. With the forward increment Lagrange multiplier method, contact constraints are imposed. Friction is neglected in the simulation. In addition, the numerical simulation of crack propagation in CSTFDB specimen adopts the extended finite element method (XFEM), which introduces a discontinuous displacement mode. In the XFEM, the description of the discontinuous displacement field no longer depends on the element boundary, so the mesh at the crack does not need to be densified.

Fig. 4.

(a) Finite element 3D model of CSTFBD; (b) Experimental results of CSTFBD incident dynamic force (200 mm impact rod, velocity 10 m/s) and its piecework linear fitting; (c) Comparison of simulation and experimental results of CSTFBD dynamic contact force P_R.

The finite element 3D model for dynamic analysis of the CSTFBD is built. The initial velocity of the shorter striker bar (300 mm) is set to be 10 m/s. To determine the specimen fails before or after reaching dynamic force equilibrium, an objective of the simulation process is conducted. Since the expression used to calculate the dynamic initiation fracture toughness only valid when the stress distribution in the specimen is similar to that of the quasi-static tests⁴¹, this factor is critical.

The piecewise linear approximation in the simulation and the incident stress pulse in the experiment are shown in Fig. 4(b). Figure 4(c) shows the simulated dynamic contact force P_R curves and experimental results. It can be seen from the results in Fig. 4(c) that the numerical load agrees well with measured results.

The stress distribution in the quasi-static and dynamic conditions is simulated. Images of the stress distribution before waves arriving at the specimen at seven different moments are shown in Fig. 5. It is clearly to see that the stress wave does not reach the other end in the first instants. In the next moment just a little bit later, the stress tends to distribute among the whole specimen. The stress distributions are approximately symmetric after a certain interval from the initial impact, here is 45.6µs, indicating a status of dynamic stress equilibrium. What’s more, it is noticed from Fig. 5 that the maximum contours of the vertical strain field are concentrated around the tip of pre-notched crack. With the increasing applied loads, the localized strain is propagating and evolving along the pre-notch direction.

Fig. 5.

Finite element simulation of various CSTFBD specimens reveals the time to reach equilibrium and the pattern of stress distribution.

Results and analysis

Failure mode

Figure 6(a) shows the broken CSTFDB specimen recovered after a dynamic test. It is evident that there is an axial crack, dividing the specimen into two pieces due to brittle crushing cracking. It also can be found that the main crack orientation is parallel to the impact direction, it is a typical mode I fracture. The fracture surface was also investigated, Fig. 6(b) shows a typical fracture surface, and the red arrow was the micro-cracking zones or fracture process zones within the green circle of Fig. 6(a). Figure 6(c) presents a high magnification of the surface morphology within the red circle of Fig. 6(b).

Fig. 6.

(a) Typical failure patterns of CSTFDB specimen under dynamic load; (b) Magnified fracture surface image using optical microscope (Pre-crack is indicated as a green arrow.); (c) A high magnification of the surface morphology.

Determination of the dynamic initiation fracture toughness

Dynamic initiation fracture toughness (K_Id) at the time-to-fracture (t_f) is defined as the critical stress intensity factor value at the crack tip at the instant of crack initiation. For mode I fracture, it is approximated as:

4

The crack initiation time t_f is also called the fracture time, and determined by the maximum value for the derivative of the strain at the crack tip with respect to time⁴⁰, this is demonstrated in Fig. 3(d). This is interpreted as the strain reading increased abruptly when the strain gauge is extended very fast, it is natural that when the strain rate is reaching its maximum overtime value, the critical point is also reaching⁴², since the crack opening displacement when crack is initiated must be much larger than the CMDB propellant deformation at the same point without crack.

For the equilibrium state of the dynamic stress is reached in the propellant specimen, the dynamic stress distributions achieves well approximation with quasi-static condition, which is demonstrated in Sect. 2.3. For CSTFBD specimens, K_I is given as⁴¹:

5

where P(t) is the applied impact load, t represents time, B is the thickness, R is the radius. Y(φ,α) is determined by the geometry of CSTFBD specimen, namely, the mode-I fracture geometry factor. It is relevant to the crack length a/R ratio and loading angle φ (20° is studied in this paper, as in Fig. 1(a)), which can be pre-calibrated according to Eq. (6):

6

In order to determine the dynamic initiation fracture toughness, finite element method is employed to achieve accurate Y(φ,α) values. The results are plotted in Fig. 7(a) and compared to the values obtained by Wang et al.⁴³. It shows good consistency. The maximum error less than 0.5%. It indicates that the results are highly satisfactory.

Fig. 7.

(a) Normalized stress intensity factors for CSTFBD with ABAQUS model; (b) Normalized dynamic fracture initiation toughness.

Dynamic fracture initiation toughness is determined by time-to-fracture using the quasi-static theory²² when the requirement of stress equilibrium in the specimen is satisfied. The calculation in this work illustrates a reasonable value with the accurate normalized stress intensity factor Y(φ,α) in Fig. 7(b), and dynamic loading rate is calculated by the average value of K_Id and t_f. Figure 7(b) shows that within a range of normalized loading rates from 5.89 × 10⁴MPa⋅m^1/2⋅s⁻¹ to 10.01 × 10⁴MPa⋅m^1/2⋅s⁻¹, the normalized dynamic fracture initiation toughness increases linearly with the loading rate. A reasonable assumption could be that the process of fracturing at different loading rates is governed by the inherent details deformation and fracture morphology of particles within propellant matrix. In other words, the microstructure of the material and its evolution when deformed is of great importance to gain insights of the underlying deformation and dynamic fracture mechanisms.

SEM analysis

From a microstructure point of view, a scanning electron microscope (SEM) is adopted for investigation of the underlying mechanism of the significant rate sensitivity. It enables an evaluation of the micro-structural mechanisms, which is a vital to understand the mechanical properties at a macroscopic level of the material. To evaluate the microstructure of the solid propellant material, micrographs are obtained from a non-deformed specimen. This is also a reference for the brittle fracture morphology. In this paper, the SEM images were obtained by SEM SU3500, its main parameters are: magnification: 7 ~ 800,000 times, continuous adjustable; Secondary electronic image resolution: 30 kV in high vacuum mode is better than 3 nm, 3 kV is better than 7 nm; Acceleration voltage: 0.3 ~ 30 kV, continuously adjustable. Figure 8 presents a high magnification of the surface morphology. It indicates that the AP particles do not fracture. Cavities and voids are also can be observed.

Fig. 8.

Surface morphology of non-deformed sample.

The fracture morphology of specimens fractured within a range of normalized loading rates from 5.89 × 10⁴ MPa⋅m^1/2⋅s⁻¹ to 10.01 × 10⁴ MPa⋅m^1/2⋅s⁻¹ is shown in Fig. 9. It is worth to note that the fracture surfaces differ clearly from a non-deformed specimen. These AP particles structure is characteristic of the interaction existing between cavities and the propellant matrix³⁴. A close-up look of the AP particles structure of a specimen fractured at a loading rate around 5.89 × 10⁴ MPa⋅m^1/2⋅s⁻¹ is shown in Fig. 9(a). Here, voids are initiated by AP particles debonding from the matrix. What’s more, we can see a very clear damage surface of AP particles in this field of SEM view. During tensile deformation around crack tip, an explanation could be formation of micro-necks. The visible AP particles are damaged with stress wave in dynamic condition.

Fig. 9.

Typical SEM images of fracture surfaces from dynamic CSTFBD tests at various striking velocities. (a) 5 m/s; (b) 10 m/s; (c) 15 m/s; (d) 20 m/s.

Figure 9(b) shows the appearance fracture surface of the specimen at a loading rate around 7.51 × 10⁴ MPa⋅m^1/2⋅s⁻¹. It is evident that the trans-granular (TG) fracture major cracking form in the fracture surface. TG fracture becomes the dominant mode and there is little intact or unbroken AP particle with the increase of loading rate.

Moreover, Fig. 9(c) shows apparent crushing AP particles in fracture surface of the specimen with loading rates increasing to 9.24 × 10⁴ MPa⋅m^1/2⋅s⁻¹, it clearly differs the previous fracture mode, that is some AP particles seems to burst into pieces like. Another interesting observation from Fig. 9(d) is that, with loading rates increasing to 9.96 × 10⁴ MPa⋅m^1/2⋅s⁻¹, most of the AP particles completely broken into pieces and fragmented, and it is notable that the fracture surface gets worse, which is characteristic of typical brittle fracture.

It is evident that the damage and crack growth mechanism appears to include AP particles fracture. The perspective of the microscopic observation reveals the underlying mechanism. An explanation could be that the significant rate sensitivity is related to the microstructure and breakage of AP particles. Another possibility is that the roughness of the fracture surfaces is basically associated with fracture modes or failure mechanisms²², which is in turn dependent on the microstructures and loading conditions.

In general, AP particles debonding from the matrix and apparent damage occurred in AP particles surface induces a rougher fracture surface. Thus, the roughness of the TG fracture is flatter. During the fracture process as the loading rate increased, it is coupled with more energy absorption.

However, the cavities do not have enough time to grow at higher strain rates or loading rates, as they would do under slow test conditions. Instead, the AP particles breaks immediately at a lower deformation, as it can be seen in cleavage higher magnification morphology in Fig. 10. Is it also can be observed, the fracture surface of a single visible AP particle is clean and bright like. The failure mode of AP particles is corresponding to the rapid brittle propagation of the crack, which maybe contribute to the propellant becomes more brittle with the loading rate increased.

Fig. 10.

High-magnification morphology of a single visible AP particle.

In addition, thermo-mechanical coupling during deformation and significant adiabatic self-heating of the material at higher strain rate is another aspect to be considered. It has been observed by^{44 and 45}, which may result in increased resistance and hence larger observed stress or fracture toughness. This point remains to be confirmed. More investigations, e.g. using digital infrared thermography, are necessary to establish the underlying mechanisms.

Conclusions

The effect of loading rate on the dynamic initiation fracture toughness and microstructure evolution mechanisms of CMDB propellant has been investigated with the SHPB apparatus and SEM. The conclusions presented in this paper can provide reference for other composite solid propellants. Conclusions are drawn as following:

1. The SHPB experimental of viscoelastic materials such as propellants can be implemented to obtain more accurate and credible wave shape results with pulse-shaper technique.

2. By comparing the results of quasi static and dynamic numerical simulations, it is found that dynamic fracture initiation toughness can be determined by time-to-fracture using the quasi-static theory. The numerical simulation results combined with the ZWT constitutive model agree well with the experimental results.

3. The initiation toughness in the dynamic fracture test of CMDB propellant is found to be dependent on loading rate from normalized loading rates 5.89 × 10⁴ MPa⋅m^1/2·s⁻¹ to 10.01 × 10⁴ MPa⋅m^1/2·s⁻¹. The relation between the loading rate and the dynamic fracture initiation toughness is discussed.

4. The relations between the significant loading rate sensitivity and the micro-structure of the material is obtained by SEM analysis. The micrographs of fracture surfaces are observed. It reveals the underlying mechanism that AP particles fracture modes and breakage that govern the process of fracturing. What’s more, some significant self-heating of the material may exist due to the adiabatic regime at high loading rates. This remains to be studied by using of infrared thermography technique in future works.

Author contributions

Jian Zheng: Data curation (lead); investigation (lead); writing original draft (lead); Visualization (lead); Validation (lead). Xuan Wu: Methodology(supporting). Zheng-wei Sun: Resources (supporting). Zong-tao Guo: Methodology (supporting); resources(supporting); supervision (supporting). Meng-long Zhang: Conceptualization(supporting); methodology (supporting); resources(supporting); supervision (supporting). Xiong Chen: Methodology (supporting); resources(supporting); supervision (supporting).

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.