Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

Abstract

As a typical viscoelastic material, solid propellants have a large difference in mechanical properties under static and dynamic loading. This variability is manifested in the difference in values of the relaxation modulus and dynamic modulus, which serve as the entry point for studying the dynamic and static mechanical properties of propellants. The relaxation modulus and dynamic modulus have a clear integral relationship in theory, but their consistency in engineering practice has never been verified. In this paper, by introducing the “catch-up factor λ” and “waiting factor γ”, a method for the inter-conversion of the dynamic storage modulus and relaxation modulus of HTPB propellant is established, and the consistency between them is verified. The results show that the time region of the calculated conversion values of the relaxation modulus obtained by this method covers 10−8–104 s, spanning twelve orders of magnitude. Compared to that of the relaxation modulus (10−4–104 s, spanning eight orders of magnitude), an expansion of four orders of magnitude is achieved. This enhances the expression ability of the relaxation modulus on the mechanical properties of the propellant. Furthermore, when the conversion method is applied to the dynamic–static modulus conversion of the other two HTPB propellants, the results show that the correlation coefficient between the calculated and measured conversion values is R2 > 0.933. This proves the applicability of this method to the dynamic–static modulus conversion of other types of HTPB propellants. It was also found that λ and γ have the same universal optimal value for different HTPB propellants. As a bridge for static and dynamic modulus conversion, this method greatly expands the expression ability of the relaxation modulus and dynamic storage modulus on the mechanical properties of the HTPB propellant, which is of great significance in the research into the mechanical properties of the propellant.

Dynamic mechanical damping analysis of up/step-quenched Cu-Zn-Sn-based shape memory alloys

“…Storage modulus (E′) relates to the elastic responses of materials and determines the capacity of a material to absorb and store mechanical energy generated during periodic deformation or vibrations [40]. E′ is an important consideration when designing against structural instability such as the springback effect which involves dimensional alteration caused by residual stresses [41]. The loss modulus (E″) is proportional to the mechanical energy dissipated in the form of heat under static and dynamic loading conditions [9].…”

Numerical Analysis of Curing Residual Stress and Strain in NEPE Propellant Grain

“…[ 27 ] (831.1 × 10 3 ~868.3 × 10 3 Pa) is approximately equal to the equilibrium modulus (0.868 MPa). In view of the long-term stress relaxation time in the curing process, an empirical dynamic–static modulus conversion equation [ 15 ] was adopted to estimate the Young’s modulus of the propellant during the curing process. where is the Young’s modulus, is the storage modulus, is the frequency.…”

“…The final crosslinking structures present some new bonds and the molecular growth continues over time until a perceptible gel-like lump can be formed; this also resulted in volume shrinkage of the adhesive system [ 14 ]. The point at which the adhesive system is converted from the liquid phase to the solid phase is called the gel point [ 15 ]. Typically, most propellants begin to shrink before the gel point, but little or no stress is developed in the resin before the gel point, because modulus development is minimal at cure states below the gel point [ 16 , 17 ].…”

Interaction Mechanism of Composite Propellant Components under Heating Conditions

“…Hydroxyl-terminated polybutadiene (HTPB) propellant is currently the most important type of composite propellant and has been applied in various rocket motor models in China and abroad. HTPB not only improves the specific impulse of the propellant but also has a widely adjustable range of burning rates, good mechanical properties, a simple manufacturing process, and abundant raw materials [1][2][3][4][5][6]. Thus, it is one of the mainstream composite propellants in use.…”