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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenThu, 30 Nov 2023 19:02:09 +0000Application of Finite Elastic Theory to the Deformation of Rubbery Materials
https://resolver.caltech.edu/CaltechAUTHORS:20120920-102757157
Authors: Blatz, Paul J.; Ko, William L.
Year: 1962
DOI: 10.1122/1.548937
The purpose of this discussion, then, is to show how the nature of
the strain energy function can be deduced from experiments on rubbery materials.https://authors.library.caltech.edu/records/1yrya-20y92The effective compressibility of a hollow sphere
https://resolver.caltech.edu/CaltechAUTHORS:20100518-093521955
Authors: Blatz, P. J.
Year: 1963
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.https://authors.library.caltech.edu/records/bgx4b-w6572Studies of the mechanical behavior of ammonium perchlorate particles, a glass-bead filled polyurethane binder, and a typical continuum binder
https://resolver.caltech.edu/CaltechAUTHORS:20100518-094619158
Authors: Blatz, P. J.
Year: 1963
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.https://authors.library.caltech.edu/records/0a323-32v45The Finite Elastic Plane Strain Deformation of a Mooney-Rivlin Body
https://resolver.caltech.edu/CaltechAUTHORS:20151207-171424371
Authors: Blatz, P. J.
Year: 1964
DOI: 10.1016/0020-7225(64)90018-7
The problem of developing a general systematic method for obtaining solutions to boundary value problems in finite elasticity is still unsolved, although of paramount importance in many applications where geometrical nonlinearity cannot be neglected. This paper does not present such a method, but nevertheless,
calls attention to the nature of the compatibility equation, for plane-strain deformation, which is
cast in terms of a stress function. Some special solutions are recorded, at which time some interesting comments
about the existence of singular stress fields are made. It is hoped that this paper may stimulate
further investigations which might lead to more general solutions of the compatibility equation than are
presented below.https://authors.library.caltech.edu/records/bf99p-kg777On the Simple Tensile Deformation of an Incompressible Rubber Matrix Filled with Non-Adherent Rigid Spheres of Uniform Size Distribution
https://resolver.caltech.edu/CaltechAUTHORS:20151125-113442516
Authors: Blatz, P. J.; McQuarrie, D. A.; Shen, M. C.
Year: 1966
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.https://authors.library.caltech.edu/records/y35ab-vw284A new elastic potential function for rubbery materials
https://resolver.caltech.edu/CaltechAUTHORS:BLApnas73
Authors: Blatz, P. J.; Sharda, S. C.; Tschoegl, N. W.
Year: 1973
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.https://authors.library.caltech.edu/records/9n5hv-qwz72Application of the BST Strain Energy Function to Torsion of a Circular Cylinder
https://resolver.caltech.edu/CaltechAUTHORS:20151130-160819754
Authors: Sharda, S. C.; Blatz, P. J.; Tschoegl, N. W.
Year: 1974
The problem of torsion of a circular cylinder is solved with the aid of a new strain energy density function. The results obtained are used to predict data of Rivlin and Saunders on natural rubber in simple torsion and torsion with extension. It is shown that the new
s train energy function correctly describes the torsional couple and the normal load data from parameters obtained in simple tension.https://authors.library.caltech.edu/records/t3rxm-3ve84Application of Finite Viscoelastic Theory to the Deformation of Rubberlike Materials I. Uniaxial Stress Relaxation Data
https://resolver.caltech.edu/CaltechAUTHORS:20141015-104600512
Authors: Ko, W. L.; Blatz, P. J.
Year: 2014
DOI: 10.7907/jt41-1v03
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.https://authors.library.caltech.edu/records/0yere-m2y28Fundamental Studies Relating to Systems Analysis of Solid Propellants, January 1, 1960-May 31, 1960
https://resolver.caltech.edu/CaltechAUTHORS:20150604-135847602
Authors: Blatz, P. J.; Knauss, W. G.; Schapery, R. A.; Williams, M. L.
Year: 2015
DOI: 10.7907/6wsw-zw77
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.https://authors.library.caltech.edu/records/5dasw-zyj96Stress Induced Anisotropy in Pressurized Thick Walled Cylinders
https://resolver.caltech.edu/CaltechAUTHORS:20151111-140758116
Authors: Blatz, P. J.; Levinson, M.
Year: 2015
DOI: 10.7907/25x3-0y40
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.https://authors.library.caltech.edu/records/wqg0c-vsv06Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors
https://resolver.caltech.edu/CaltechAUTHORS:20151202-162838780
Authors: Blatz, P. J.; Ko, W. L.; Zak, A. R.
Year: 2015
In the previous report the isothermal strain energy function
and the associated constitutive stress and strain law for a 47 volume % voided polyurethane foam were presented. This function involves three parameters--the shear modulus, the £-factor, and the Blatz-Poisson ratio, all of which are constants of the material for deformations
up to fracture. Based on experimental data obtained in three
different stress fields, experimental values were assigned to each of these parameters. Some thought is being given to an analysis which will predict these parameters from a knowledge of the properties of the continuum binder and the void content and void size.
In addition, a failure criterion was proposed for this foam.
In order to check further the invariance of the proposed criterion over the failure surface, additional data in a triaxial stress field were obtained. On the basis of these data and an inference based on thermodynamic consideration, which suggests that all carpets of the surface must be non-concave, it looks like the failure surface is
the frustum of a triangular pyramid, the frust rated facet being the carpet of the hydrostatic plane. The sides of the frustum are then the carpets of the planes of maximum principal strain. Thus it looks like a dual criterion obtains: each criterion controls one of
two subsets of failure modes.
In order to confirm the universality of the function, law and definition mentioned above, the triaxial tensile test was performed and reported in the previous report. Because of unsatisfactory bonding of the specimens, the test points were scattered a round the theoretical curves.
The present report furnishes i) more triaxial data obtained
with improved bonding of the specimens, and depicts more clearly the ii) failure surface based on the averaged experimental values of ultimate stresses in the normal stress space.https://authors.library.caltech.edu/records/pnhfh-6r293Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors
https://resolver.caltech.edu/CaltechAUTHORS:20151202-163931753
Authors: Blatz, P. J.; Ko, W. L.; Zak, A.
Year: 2015
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.https://authors.library.caltech.edu/records/gbyt1-0p392Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors
https://resolver.caltech.edu/CaltechAUTHORS:20151202-161615987
Authors: Blatz, P. J.; Ko, W. L.; Zak, A.
Year: 2015
In the earlier report the information obtained from both uniaxial and biaxial tension on foam and continuum rubbers was presented. The biaxial data of foam was comparable to the uniaxial data, but it was not so for the continuum rubbers. Namely, the continuum rubbers were found
dilating enormously in biaxial tension in which the thickness change was measured by the travelling microscope at the edge of specimens.
Due to the above unusual result, further strip-biaxial tension tests as well as homogeneous - biaxial tension tests were performed, on the same materials SBR - 500 (1. 75 percent S), SBR - 1500 (3 percent S)
and polyurethane foam with an improved technique for measurement of thickness change at the center of the specimens in order to check the dependability of earlier data.
The purpose of this report is to furnish complete set of data to supplement the earlier ones from which the nature of the parameters (W_1, W_2, dJ_3/dλ, μ, etc.) can be more definitely clarified. Following it the effective Poisson's ratio can be found through which the failure criterion
could be established.https://authors.library.caltech.edu/records/16ghz-64p64Fundamental Studies Relating to Systems Analysis of Solid Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20151202-160659665
Authors: Blatz, P. J.; Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
Year: 2015
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.https://authors.library.caltech.edu/records/qav8g-b8e97Fundamental Studies Relating to the Mechanical Behavior of Solid Propellants, Rocket Grains and Rocket Motors
https://resolver.caltech.edu/CaltechAUTHORS:20151203-152918001
Authors: Blatz, P. J.; Ko, W. L.; Zak, A. R.
Year: 2015
DOI: 10.7907/exmn-em08
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).https://authors.library.caltech.edu/records/yk5gg-rfh60Fundamental Studies Relating to Systems Analysis of Solid Propellants, October l, 1959-December 31, 1959
https://resolver.caltech.edu/CaltechAUTHORS:20151203-165233805
Authors: Blatz, P. J.; Knauss, W. G.; Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
Year: 2015
DOI: 10.7907/0sxn-1k84
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.https://authors.library.caltech.edu/records/ge1wj-66q37On the Microstructure of Composite Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20151207-103048945
Authors: Blatz, Paul J.
Year: 2015
The term composite propellant as commonly used in the solid
rocket industry refers to a heterogeneous mixture of several phases of solid particles entrained in a rubberlike binder. The two principal solid phases are aluminum fuel and ammonium perchlorate oxidizer; together with a small amount of additives which control adhesive and ballistic
properties, they constitute the filler. Either a branched polyurethane or crosslinked polybutadiene network serves as a typical binder. Performance calculations based on the assumption that the enthalpy of the composite balances
the enthalpy of the combustion products at their flame temperature lead to the demand for a composite filled with slightly more than 88 wt. % of solid phases, about 25% of which is aluminum. At this point a little arithmetic is in order.https://authors.library.caltech.edu/records/4adwe-fg842Physicomechanical Behavior of Rubberlike Materials
https://resolver.caltech.edu/CaltechAUTHORS:20160111-105851222
Authors: Blatz, P. J.
Year: 2018
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.https://authors.library.caltech.edu/records/1jkm1-mp662Fundamental Studies Relating to the Mechanical Behavior to the Mechanical Behavior of Solid Propellants Rocket Grains and Rocket Motors
https://resolver.caltech.edu/CaltechAUTHORS:20160111-102302934
Authors: Blatz, P. J.; Ko, W. L.; Zak, A.
Year: 2018https://authors.library.caltech.edu/records/dszww-vnp65Fundamental Studies Relating to Sytems Analysis of Solid Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20160111-090438298
Authors: Blatz, P. J.; Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
Year: 2018https://authors.library.caltech.edu/records/ptrz5-9fd19Fundamental Studies Relating to Systems Analysis of Solid Propellants
https://resolver.caltech.edu/CaltechAUTHORS:20160108-114541765
Authors: Blatz, P. J.; Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
Year: 2018https://authors.library.caltech.edu/records/epdqx-0na88A Research Program on Solid Propellant Physical Behavior
https://resolver.caltech.edu/CaltechAUTHORS:20160111-114236933
Authors: Blatz, P. J.; Tschoegl, N. W.; Landel, R. F.
Year: 2018https://authors.library.caltech.edu/records/gpqsw-ytv68