Stress Induced Anisotropy in Pressurized Thick Walled Cylinders

The most important mechanical features of propellants arise from the presence of a highly packed array of granular particles (filler), and a distribution of adhesive strengths between the rubbery binder and these particles. The first factor leads to dilatation and the formation of voids in any stress field other than pure hydrostatic compression. The second factor virtually guarantees that the pullaway of the binder from the filler is nonuniform, leading in extreme cases to the so-called "zebra-stripe" effect, or localized dewetting. This factor also is associated with stress relaxation due to the slow flow of the binder from regions of high strain concentration into regions of low concentration or into voids. Finally, because the binder is incompressible, and the filler is for all practical purposes infinitely rigid, most of the macroscopically applied load is concentrated as large strains near the binder-filler interfaces leading to non-linear behavior. At ambient temperature or thereabouts, viscoelasticity as associated with polymer chain uncoiling plays no role in the mechanical behavior of the propellant. Summarizing, the important mechanical features to be expected are 1. Dilatation with void formation when the stress is tensile. 2. Localized dilatation because of nonuniformity of adhesion strengths. 3. Stress relaxation due to binder flow and perhaps due to particle movement at a very slow rate determined by frictional and adhesive effects . 4. Nonlinear stress-strain relations due to high local strains at binder-filler interfaces

Application of Finite Viscoelastic Theory to the Deformation of Rubberlike Materials I. Uniaxial Stress Relaxation Data

In this report the constitutive equation for finite viscoelastic materials will be postulated as the sum of equilibrium terms and integral terms which describe the viscoelastic behavior of the materials and vanish when the equilibrium state is reached or when the materials have always been at rest. It is also our purpose i) to show how the twelve relaxation functions are reduced to two independent ones in the case that the material has Mooney-Rivlin elastic behavior and that all the relaxation functions depend only on time, ii) to display the mechanics of evaluating the two non-zero relaxation functions from data obtained from uniaxial stress relaxation tests

Studies of the mechanical behavior of ammonium perchlorate particles, a glass-bead filled polyurethane binder, and a typical continuum binder

Experimental studies were carried out on a continuum Neoprene binder, a glass bead-filled-polyurethane binder, and unbound micro-pulverized ammonium perchlorate particles. As a result of stress relaxation and creep experiments, it is concluded that the large deformation behavior of the filled binder can be described in part in terms of the large deformation behavior of the continuum binder. The time scale of relaxation of stress in the filled binder is much longer than that of the unfilled binder. It is determined by frictional processes between the filler and binder and also among the filler particles. As a result of relaxation and creep studies on ammonium perchlorate particles, it is found that the time scale of relaxation is of the same order of magnitude as that of the filled binder. In addition, it is believed that the static indeterminacy of the unbound particles helps to explain much of the strain variation at given stress level that is observed in tensile experiments of composite propellants

The effective compressibility of a hollow sphere

The problem of determining the effective compressibility of a hollow sphere is practically important because it relates to the problem of compacting a real material containing voids. For example, the void content in propellants is such that the initial slope of the P-V curve is three-to-ten times lower than the limiting slope obtained after all the voids have been collapsed. The phenomenon of compaction-decompaction is extremely important in determining the mechanical properties of propellants since it accounts for much of the batch-to-batch variability and also is a function of the stress-time-temperature history of the material. In this memo we consider only a very special type of compaction, but it is believed that this will pave the way for further analysis along these lines

Physicomechanical Behavior of Rubberlike Materials

During the past year, further progress was made in understanding both the molecular nature of the strain energy function of a homogeneous, nearly incompressible rubberlike material. The importance of non-affinity of deformation, chain stiffness, and volume exclusion in modifying the basic statistical model of Kuhn, Grün, James and Guth are discussed. A phenomenological theory for predicting the distribution of times- to-break arising in creep failure in terms of the growth of defects in rubber was proposed and showed good agreement with experimental data. Batches of thermoelastic rubber filled with glass beads are being prepared prior to evaluation in terms of sedimentation theory

Physicomechanical Behavior of Rubberlike Materials

During the past year, further progress was made in understanding both the molecular nature of the strain energy function of a homogeneous, nearly incompressible rubberlike material. The importance of non-affinity of deformation, chain stiffness, and volume exclusion in modifying the basic statistical model of Kuhn, Grün, James and Guth are discussed. A phenomenological theory for predicting the distribution of times- to-break arising in creep failure in terms of the growth of defects in rubber was proposed and showed good agreement with experimental data. Batches of thermoelastic rubber filled with glass beads are being prepared prior to evaluation in terms of sedimentation theory

Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors

During the past three years, the mechanical testing of solid propellants, solid rocket grains, and solid rocket motors under idealized conditions has been receiving increased attention. Today it is not uncommon to see a multitude of new techniques and analyses being investigated. One may expect to see dummy propellant prepared with glass bead filler to observe its dilatation to rupture; to ink circles, rectangular g rids at various critical areas on a grain surface, and to observe the distortion of these grids as a result of thermal cycling and/or slump; to subj e ct rectangular parallel-opipedal-shaped specimens to both torsion and biaxial tension as well as hydrostatic compression and parallel-plate tension; to apply theories of large elastic strain, and non-linear viscoelasticity; to search for an isotropic failure criterion as well as a crack propagation criterion. In short the mechanics of propellant behavior from small deformation all the way to fracture initiation and propagation has become quite sophisticated. Gradually the results of this testing and their thinking are being integrated in a logical scheme of analysis which is being passed along to the engineer and being used in predicting performance of rocket motors. This particular program will pertain to four areas: 1) The characterization of polyurethane propellant behavior out to fracture initiation in terms of large strain theory. 2) The development of a failure criterion and crack propagation criteria for said materials. 3) The generation, where possible, of macroscopic mechanical parameters in terms of molecular parameters. 4} The solution of certain stress problems, in both linear and non-linear theory, which are prerequisite to engineering applications. As such it is part of a continuing research study of structural integrity problems in solid propellant rocket motors being conducted under the general direction of Dr. M. L. Williams in the Guggenheim Aeronautical Laboratory. This preliminary report is intended as an interim working document to be circulated for the purpose of stimulating discussion

Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors

The former reports provided considerable information about foam and continuum rubbers under three types of tensile loading (i.e. uniaxial, strip-biaxial and homogeneous-biaxial tension). Since continuum rubbers are almost incompressible it is extremely difficult to determine the strain energy function beyond the linear term. On the other hand the highly dilatable foam rubber enables one to determine the functional form of the strain energy valid up to higher order terms. Special attention is being paid to foam rubber, since it represents .the limiting case of completely dewetted propellant. The present report will (i) furnish the method of determination of strain energy function and the associated constitutive stress-strain law for large deformations out to fracture and (ii) present the triaxial tensile test data needed to double check item (i)

On the Simple Tensile Deformation of an Incompressible Rubber Matrix Filled with Non-Adherent Rigid Spheres of Uniform Size Distribution

Two striking features revealed in a photograph (cf Figure 1) of a thin film of rubber binder highly filled with glass beads are: a) that the growth of voids around particles increases with increasing strain and b) that the preferred direction of the void growth seems to be in the direction of the applied macroscopic strain. It is obvious that the local stress field around particles in a deformed composite is not as high as it would be if the binder did not pull away from the filler particles. On the other hand, because of the high rigidity of the particles relative to the binder, the local stress field in the binder will still be significantly higher than the average macroscopic stress field. It is of interest to define both this stress field and the associated dilatation in terms of a simple model

Fundamental Studies Relating to Systems Analysis of Solid Propellants

As in the previous progress reports, the contents in this report have been categorized so as to present a clear picture of their role in contributing to the problem of mechanical failure analysis. The subject of material representation by mechanical failure analysis. The subject of material representation by mechanical models is discussed in Section I, while Section II contains additions to the subject of Elastic Solutions for cylinders. The Engineering Analysis section includes an example of the strain response of an internal star grain to pressure. A damped sinusoid has been assumed for the pressure rise, and the use of stress concentration factors for a star grain is demonstrated. Section V on failure includes some preliminary test results which indicate the feasibility of the cumulative damage concept for composite (polyurethane) propellants, at least in the limited range tested. Recommendations are given which would expand this testing to show how damage accumulates under other conditions such as low temperatures, high strain-rates and with other types of propellant