244 research outputs found
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
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)
A new elastic potential function for rubbery materials
A new four-parameter elastic potential function is proposed which represents data on the elastic deformation of rubbery materials with the same parameters in various deformation fields up to break
Fundamental Studies Relating to Systems Analysis of Solid Propellants : Progress Report No. 6 - GALCIT 101, Subcontract No. R 69752, January 1, 1960-May 31, 1960
Previous reports of this series have attempted to
define some of the important parameters affecting structural
integrity of solid propellant rocket grains. Three general
areas have been discussed, namely material properties,
analytical procedures, and criteria for mechanical failure.
This particular report is devoted to failure criteria,
including both limiting deformation and fracture. First of all, the characteristic material properties of filled and unfilled elastomers are described, followed by a brief description of current and proposed tests which can be conducted to obtain experimental information relating to these characteristics in such a form that they can be incorporated in structural integrity analyses. In particular, the necessity for multi-axial
tests is stressed in conjunction with minor requirements
for new experimental equipment.
The selection of appropriate fracture criteria is discussed.
Most progress, however, can be reported only in criteria for
unfilled elastomers for small and large strains where it appears a distortion strain energy density may be used. It is necessary to delay any really definitive remarks upon filled elastomers or actual grain composites, and subsequent use with cumulative
damage analyses, until additional experimental data for propellants is forthcoming
Student-Athletes with Learning Disabilities: Unique Problems, Unique Solutions
This paper explored the issues/acing student-athletes with learning disabilities and their academic counselors. Understanding the nature of learning disabilities and their effects can enhance the counselor's ability to address the complex needs of the student-athlete with a learning disability. The increasing numbers of college student-athletes who have diagnosed learning disabilities demands notice. This paper provided an explanation of the problems of diagnosis and treatment. Suggestions for academic counselors were provided, as well
Fundamental Studies Relating to Systems Analysis of Solid Propellants : Progress Report No. 5 - GALCIT 101, Subcontract No. RU- 293, October l, 1959-December 31, 1959
Previous reports of this series have attempted to define some of the important parameters affecting the structural integrity of solid propellant rocket grains. Three general areas have been discussed, namely material properties, analytical procedures, and criteria for mechanical
failure.
This particular report is devoted to a more detailed examination of the properties of a filled viscoelastic resin, and their representation by appropriate mechanical models. In addition, a comparison of two methods of computing viscoelastic strains in a pressurized cylinder is
presented.
In the category of material properties, linear viscoelastic model theory is reviewed, and certain important relations among sets of experimental data are deduced. A justification for the application of this theory is provided by the analytic representation of available dynamic
data in terms of a well-known distribution function. Since the inception of this work additional experimental data on propellants has become available.
In the category of analytical procedures, the usual approach of representing material properties by a four-element model, as determined from the dynamic data in a limited frequency range, is compared with the
more sophisticated Fourier transform method in which the entire frequency range is utilized. The two approaches are applied to calculate the viscoelastic hoop strain at the inner boundary of an internally pressurized infinitely
long hollow cylinder subjected to a ramp-type pressure pulse. In this example, the dilatation is assumed elastic or frequency independent and the distortion viscoelastic.
In the following quarter, primary effort will be devoted to the determination of a criterion for mechanical failure of propellants. Two steps are involved. One is the analytical representation of ultimate strain as a function of temperature on strain rate by means of a mechanical model. In addition to the usual distribution of relaxation (or retardation) times, this model will be supplied with a distribution of ultimate strain. Step two involves
the choice of a suitable criterion for compounding ultimate strain or ultimate stress components into a single parameter, which, when exceeded at a given
rate and temperature, denotes the onset of fracture or mechanical failure
Borderline Aggregation Kinetics in ``Dry'' and ``Wet'' Environments
We investigate the kinetics of constant-kernel aggregation which is augmented
by either: (a) evaporation of monomers from finite-mass clusters, or (b)
continuous cluster growth -- \ie, condensation. The rate equations for these
two processes are analyzed using both exact and asymptotic methods. In
aggregation-evaporation, if the evaporation is mass conserving, \ie, the
monomers which evaporate remain in the system and continue to be reactive, the
competition between evaporation and aggregation leads to several asymptotic
outcomes. For weak evaporation, the kinetics is similar to that of aggregation
with no evaporation, while equilibrium is quickly reached in the opposite case.
At a critical evaporation rate, the cluster mass distribution decays as
, where is the mass, while the typical cluster mass grows with
time as . In aggregation-condensation, we consider the process with a
growth rate for clusters of mass , , which is: (i) independent of ,
(ii) proportional to , and (iii) proportional to , with . In
the first case, the mass distribution attains a conventional scaling form, but
with the typical cluster mass growing as . When , the
typical mass grows exponentially in time, while the mass distribution again
scales. In the intermediate case of , scaling generally
applies, with the typical mass growing as . We also give an
exact solution for the linear growth model, , in one dimension.Comment: plain TeX, 17 pages, no figures, macro file prepende
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