Solid Propellant Rocket Grains Research Articles

Reliability of solid rocket propellant grain under simultaneous action of multiple types of loads

A case-bonded solid propellant rocket grain is subjected to many stress-inducing loads during the service life, due to temperature, extended polymerization, transportation, vibration, acceleration, aerodynamic heating etc. and finally due to the operating pressure in the rocket motor. Composite propellant is a viscoelastic material whose mechanical properties highly depend on temperature and strain rate and sometimes may vary in the range of use of rocket motors for several orders of magnitude. Relationships between stresses and strains are much more complex than for the elastic material. Therefore, the stress and strain analysis and estimation of safety factor under the action of each individual load is quite complex and sometimes impossible. An even greater problem occurs when multiple different types of loads act simultaneously. An extreme case occurs in the moment of rocket motor ignition. Then, the very fast load acts due to the pressure, at which the propellant tensile strength is high. At the same time, the very slow thermal load acts on the grain, and in these conditions the propellant tensile strength is low. The vector addition of the stresses and strains due to different loads is not possible. It is also not possible to define the equivalent or resultant values of tensile strength and allowable strain. The principle of adding the current damage is applied here, similar to the model of cumulative damage. In addition, due to the large variations in mechanical properties of the rocket propellant, it is necessary to apply the methods of mathematical statistics for assessing the propellant grain reliability and service life.

ПРИМЕНЕНИЕ МЕХАНИКИ РАЗРУШЕНИЯ К ОБОСНОВАНИЮ ВЫБОРА РАЦИОНАЛЬНЫХ ВАРИАНТОВ КОНСТРУКТИВНЫХ ЭЛЕМЕНТОВ ЗАРЯДОВ РДТТ

ПРИМЕНЕНИЕ МЕХАНИКИ РАЗРУШЕНИЯ К ОБОСНОВАНИЮ ВЫБОРА РАЦИОНАЛЬНЫХ ВАРИАНТОВ КОНСТРУКТИВНЫХ ЭЛЕМЕНТОВ ЗАРЯДОВ РДТТ

Use of Mueller matrices in the photoelastic determination of the stress distribution in a model for a solid propellant rocket grain

We introduce some basic optical rules dealing with Mueller matrices as phenomenological descriptors of optical devices. Specific simple examples illustrate how all the Stokes parameters of a beam passing through a system of several devices can be determined by the multiplication of the individual Mueller matrices of the respective system components and the Stokes vector of the incident beam. Two resulting families of interference fringes in the (visible) emerging field of the de- vices considered are separated from each other by the introduction of suitable additional system components. The ''isochromatic'' family of fringes can thus be isolated from the ''isoclinic'' family, and a natural application to photoelastic problems becomes evident. Thus, a second purpose is to use this technique and these fringes to photoelastically determine the stress distribution in a disk with a square perforation, when the disk is subjected to a uniformly distributed pressure, acting at its outside or at its inside periphery. This enables the visualization and quantification of the stresses developed during the burning of the grain. The size of the square hole and the radii of the fillets at the corners of the square are variables of the study. Results are given as stress concen- tration factors, in dimensionless form, and are of use to the designer of solid propellant rocket grains. An analogy is given to suggest another application at longer wavelengths to calibrate or discriminate between some radar signals in the microwave region. © 2003 Society of Photo-Optical

Numerical experiments on the solution of the Helmholtz equation in the case of domains of complicated boundary shape

Domains of complicated boundary shape are of great practical importance in several fields of technology and applied science; e.g. solid propellant rocket grains, electromagnetic and acoustic waveguides, and certain elements used in nuclear engineering. The technical literature contains very few comparative studies of analytical and numerical solutions when dealing with such rather complex geometries. The present study constitutes an effort in that direction.

Fracture of Rocket Grain Models Subjected to Cooldown: A Study of Temperature-Initiated Fractures of Two-Dimensional Rocket Grain Models

Abstract A method is presented for evaluating two-dimensional crack behavior resulting from thermal cooldown loading of rocket motor configurations in which the grain is bonded to a stiff case. The associated analytical solution used to quantitatively interpret the data is also presented. For three different grain geometries of a brittle epoxy tested, comparison was quite good between analytical predictions (using elastic fracture mechanics methods) and experimental observations. The results of this study can be applied to fracture analyses of solid propellant rocket grains and other structures containing cracks extending partially through the thicknesses of the structures.

Pressurized Crack Behavior in Two-Dimensional Rocket Motor Geometries

A method is presented for evaluating two-dimensional crack behavior in rocket motor geometries for pressure loadings in which the pressure is applied directly to the crack surfaces. The experimental requirements associated with pressurizing the crack necessitated the application of pressure over the two-dimensional plane surface of the specimen. Analytical solutions are developed which include the side pressure and relate the stress intensity factors to the classical unpressurized situation. Stress intensity factors for the complex cracked rocket motor geometries were evaluated using finite element computer techniques based on strain energy methods. Comparison between analytical predictions using elastic fracture mechanics and experimental observations of a brittle epoxy was quite good for the three different geometries tested. The work has application in fracture analysis of solid propellant rocket grains and in pressure vessels containing partial-thickness cracks which emanate from the inside.

A pseudo two-dimensional photoelastic method of testing axisymmetric geometries

Problems involving three-dimensional bodies which possess axial symmetry reduce to two-dimensional analytical problems. If a wedge-shaped portion of an axisymmetric body is tested subjected to the proper boundary condition, then a pseudo two-dimensional photoelastic method of testing may be used. This results in tremendous simplification in testing procedures, particularly when slight changes in model geometry are to be made during the course of testing. This method has been applied to axisymmetric solidpropellant rocket grains to conduct a parametric study of various conicyl geometries. Both pressure and thermal loads were considered for a case-bonded grain. Six parameters were required to define the geometry. The effects of these parameters and of the material properties of the grain were investigated, and parametric curves showing the variation of the maximum stress with those parameters are presented. The experimental results are compared with results obtained from a finite-element computer solution. Good agreement is obtained.

Some Pressure-Temperature Equivalences in Elasticity, With Applications to Case-Bonded Solid Propellant Rocket Grains

Some Pressure-Temperature Equivalences in Elasticity, With Applications to Case-Bonded Solid Propellant Rocket Grains

Stresses in hollow cylinders with conical ends bonded to shell and shrunk

This paper deals with, the three-dimensional photoelastic analysis of stresses and strains in two long, hollow circular cylinders with conical ends of 45° and 60°. The cylinders were bonded to a steel casing on the outer surface. The stresses and strains due to restrained shrinkage have been determined at the interface. The maximum stress for both geometries was found to occur at the end of the bond, and to be about 40% higher in the 60° cylinder than in the 45° cylinder. A study was also made at the opposite end of the two cylinders, where a natural meniscus was formed. The results should be of interest in the design of solidpropellant rocket grains.

Constant-acceleration stresses in a composite body

This paper is a contribution to the experimental stress analysis of composite structures subjected to gravitational forces. It is proved, generally, that the immersion analogy can be used to analyze these stresses in composite bodies provided all the materials of such bodies have the same weight per unit volume. Applications are described in two-dimensional problems immersing urethane-rubber models bonded to epoxy shells in a thallium-formate solution. Photoelasticity is used to determine stresses. The method increases the response obtained and will have application in the solution of problems where constant-acceleration stresses are important, as in dams and solid-propellant rocket grains.

STRESS CONCENTRATIONS IN A RECTANGULAR PLATE WITH CIRCULAR PERFORATIONS ALONG ITS TWO BONDED EDGES AND SUBJECTED TO RESTRAINED SHRINKAGE

Two‐dimensional photoelasticity is used for minimising stress concentration associated with a fillet present at the end of a solid propellant rocket grain subjected to restrained shrinkage. For this purpose, successive holes were added along the bonded interface of case and propellant, but no decrease was obtained. The photoelastic method used illustrates two uncommon techniques of interest to experimental stress analysts: (1) restrained shrinkage loading and (2) a parametric stress‐analysis solution obtained with a single model.

Maximum stress at the angular corners of long strips bonded on one side and shrunk

The value of the maximum stress, and its position, at the corner of long strips bonded on one side and shrunk, has been determined using photoelasticity. The angle of the strip end varies from zero (crack) to 180 deg (no corner). The radius at the corner varies from less than 0.0001 to 0.125 in. The solution obtained is an approximation to a plane-stress solution and will have application in composite-materials problems (coatings, solid-propellant rocket grains, etc.).

Gravitational Stresses Determined Using Immersion Techniques

This paper deals with a generalization of an immersion analogy suggested by Biot. A simple general proof of the analogy is given. Applications are described to two-dimensional problems (using urethane rubber specimens immersed in thallium formate) and to three-dimensional problems (using epoxy models immersed in mercury). Two and three-dimensional photoelasticity is used to determine stresses. The increase in response obtained by using the immersion technique permits the solution of a number of new problems where gravitational stresses play an important role; for example, in dams and in solid propellant rocket grains.

Some studies of gravitational loads on United Kingdom solid-propellant rocket grains.

Covers advancements in spacecraft and tactical and strategic missile systems, including subsystem design and application, mission design and analysis, materials and structures, developments in space sciences, space processing and manufacturing, space operations, and applications of space technologies to other fields.

Mathematical determination of stresses and displacements in star-perforated grains

A mathematical method is presented for determining stresses in solid propellant rocket grains due to pressurizatio n, steady thermal gradients, and uniform propellant shrinkage. The type of solid propellant grain considered is a long cylinder containing a longitudinal perforation with an arbitrary number of identical star points of general shape. The external boundary of the propellant grain is bonded to a circular-cylindrical motor case. The propellant has constant mechanical and thermal properties and is in a state of plane strain. Linear elasticity theory and complex variable methods are used to formulate a general stress problem for a doubly connected region that has a star-shaped internal boundary and a circular external boundary and is subjected to steady thermal gradients and uniform boundary pressures. This problem is solved approximately by considering a related problem for an infinite plane with a star-shaped hole. Effects of bonding the external boundary to an elastic case are deduced approximately by superposition. A general stress program for a digital computer is described, and example computations testing the validity of the assumed approximations are made. The method is found to provide a practical means of analyzing stresses in solid propellant grains.

PHOTOELASTIC DESIGN DATA FOR PRESSURE STRESSES IN SLOTTED ROCKET GRAINS

The preliminary photoelastic data of Ordahl and Williams for calculating the maximum stress in a family of slotted solid propellant rocket grains are amplified and improved in accuracy. The effect of changes in the shape of the inverse star point on the maximum stress at the star point also is investigated, and the experimental data are compared with Wilson's analytical results that used conformal mapping. Finally, an empirical formula covering the range of parameters tested is derived for possible use in integrated internal ballistics computations. The design data are useful in the elastic and viscoelastic stress analysis of free or case-bonded, internally or externally pressurized rocket grains.

Stresses Owing to Internal Pressure in Solid Propellant Rocket Grains

An analysis was made of the stresses and displacements in an elastic solid propellant grain perforated internally by a star shaped configuration, bonded peripherally to an elastic motor case, and loaded internally by pressure normal to the perforation. The analysis was performed under the assumption of plane strain using conformal mapping and the complex variable method of N. I. Muskhelishvili. The effects on stress concentration at the star tip owing to changes in star tip radius of curvature and web thickness of the grain were studied. The analysis was made specifically for a four-pointed, star shaped internal perforation but can be generalized to an n-pointed configuration.

Transient, Radial Heat Conduction in Hollow Circular Cylinders

A FREQUENT problem in rocket engineering is to compute the temperature distribution in a solid-propellant rocket grain some specified time after the temperature of its environment has been suddenly changed. For so-called cigarette-burning propellant configurations, this problem is satisfactorily solved by using the published charts or tables for heat conduction in a solid cylinder infinitely long when subjected to a heat flow at its surface that is governed by a constant conve3tion coefficient. Carslaw and Jaeger (l), pp. 176-177, discuss the analytical solution of the heat conduction equation for this case. Austin (2) and Heisler (3), among others, give tables and charts of the solution for practical use. In the case of internal-burning'' propellant configurations it is necessary to resort to graphical or numerical computations because tables or charts for even the simplest case of the hollow infinite cylinder have not been published. The heat conduction equation for this case is: