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Repository of works by Caltech published authors.
Group = Graduate Aeronautical Laboratories (Solid Mechanics)
Repository of works by Caltech published authors.
Group = Graduate Aeronautical Laboratories (Solid Mechanics)
Fung, Y. C.
[no abstract]
Williams, M. L.
During the past several years solid propellant power units have changed in many ways. Notwithstanding the increase in specific impulse, probably the most striking of all is the remarkable growth in its physical size. This past and probably future growth has been accompanied by a proportionate rise in the cost of propellant units. The point of reviewing these facts is to stress an obvious but important fact. Grains are not cheap. The corollary is that it behooves the rocket engineer to bend every effort to design a grain which will not abort. He should carefully consider the use of scale...
Williams, M. L.; Jessey, M. E.; Parmerter, R. R.
During the last three years the Guggenheim
Aeronautical Laboratory of the California Institute of
Technology (GALCIT) has been conducting a photoelastic
study of stress wave propagation in solids
using a high speed framing camera.
This paper presents a technical description of
the camera, now operating at 100,000 35 mm frames
per second at one tenth microsecond exposure time
for an elapsed time of approximately two milliseconds.
The design capability is expected to approach a half
million frames per second. This equipment has been
used to record dynamic photoelastic stress fringe
patterns in various specimens under impact loadings.
Typical experimental records of wave propagation in
cracked plates, layered media, compressed bars and
beams, and cross sections...
Blatz, P. J.; Knauss, W. G.; Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
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....
Schapery, R. A.; Stimpson, L. D.; Williams, M. L.
In continuing the investigation of analysis procedures to be used in studying the structural integrity of solid propellant grains, we amplify the content of the first progress report without at this time opening up any new areas. However it is perhaps appropriate to enumerate some of the specific subjects to be presented later. Following
the earlier pattern of (1) model representation and (2) tabulated elastic solutions, both of which are supplemented in this report, it is expected to include (3) heat transfer and temperature distributions, (4) engineering analysis, i.e. the practical combination of items (1), (2),
and possibly (3) above, (5) failure...
Schapery, R. A.; Stimpson, L. D.
In this report the groundwork is laid for the proposed work scope which stressed the need for a greater understanding of the solid mechanics of grains. Particular emphasis will be directed toward the multi-axial behavior of thick walled configurations. The work falls naturally into
three areas; (1) analysis procedures, (2) material properties, and (3) failure criteria.
As a necessary preliminary to treating specific designs, certain material of general applicability must be developed, collected, and summarized. The following sections therefore deal with a general
description of viscoelastic analysis and material representation, discussed by contrast with more conventional engineering analysis. By this means
a background is...
Blatz, P. J.; Ko, W. L.; Zak, A. R.
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...
Rosakis, A. J.; Samudrala, O.; Coker, D.
Classical dynamic fracture theories predict the Rayleigh surface wave speed to be the limiting speed for propagation of in-plane cracks in homogeneous, linear-elastic materials subjected to remote loading. However, in the present
study, experimental evidence to the contrary is reported, in which intersonic shear dominated crack growth is seen along weak planes in Homalite-100 under far-field asymmetric loading. It is seen that mode-II (in-plane shear) conditions are essential to attain intersonic crack-tip speeds. The stress field generated by
the intersonically propagating crack-tip is recorded using photoelasticity and high speed photography. Intersonic shear cracks, featuring shear shock waves
and large scale crack face frictional...
Blatz, P. J.; Levinson, M.
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...
Blatz, P. J.; Knauss, W. G.; Schapery, R. A.; Williams, M. L.
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...
Rosakis, A. J.; Mason, J. J.; Ravichandran, G.
Investigations of the temperature rise at a dynamically propagating crack tip using an infrared detector array are reported. Also, a measurement of the fraction of plastic work converted to heat using a split hopkinson bar apparatus in conjunction with an infrared detector array is summarized. For 4340 steel it is seen that ≈85% of the plastic work is converted to heat leading to a temperature rise of 300°C at a crack tip propagating 600 m/s in steel. This results is compared to earlier studies that report a 450°C temperature rise at a crack tip propagating 900 m/s in steel. In...
Ravichandran, G.; Tong, W.
A brief derivation of the expression is given for the effective bulk modulus of discontinuously
reinforced metal matrix composites (DMMCs) with damaged particles (either complete voids
as shattered particles or debonded particles). The analytical results are then compared with
elastic moduli determined from nondestructive ultrasonic wave speed measurements of SiC
particle-reinforced titanium matrix composites produced via shock wave consolidation. For
the shock consolidated Ti-SiC metal matrix composites compacts, the overall particle damage
mode is found to be similar to debonded particles and the effective volume fraction of
damaged particles is determined to be 39% based on the data of both Young's and bulk
moduli. Ultrasonic wave speed measurements...
Chu, Billie
In recent years there has been an increase in interest in the problems of strength and deformation of highly elastic materials. A number of simpler cases which have been solved indicate some markedly different characteristics from their counterparts in infinitesimal elasticity. References 1 and 2 discuss these cases in some detail. It seems natural therefore to ask whether in the problem areas of fracture in which the application of the infinitesimal theory of elasticity has met with some success in brittle elastic materials an equally marked difference in behavior would result if the possibility of large strains were included in...
Chai, H.; Babcock, C. D.; Knauss, W. G.
In a previous report a one dimensional model of buckling-delamination in a column was summarized. The main assumption made in that report was that the unbuckled portions of the column can be assumed to remain straight. The purpose of this report is to investigate the
more general problem in which bending effects are taken into account. We deal here with the case of a single off center delamination in a column. (The case of multi-delaminations in a column can be worked out too
under slight modifications.) Following the general procedure outlined in previous reports, consider the column of unit width shown in...
Schapery, R. A.
An easily applied collocation method is discussed for fitting the response of finite-element viscoelastic models to experimental stress-strain curves. It can be used with creep, relaxation, and steady-state oscillation data. The method is illustrated by means of two examples. As the first one, a model is obtained utilizing the dynamic shear compliance of polyisobutylene. In the second example we calculate a model from the tensile relaxation modulus of polymethyl methacrylate. With each case the model's response agreed with the experimental data within graphical accuracy over the entire frequency (or time) scale.
Schapery, R. A.
Two approximate methods of Laplace transform inversion are given which are simple to use and are particularly applicable to stress analysis problems in quasi-static linear viscoelasticity. Once an associated elastic
solution is known numerically or analytically, the time-dependent viscoelastic response can be easily calculated using realistic material properties,
regardless of how complex the property dependence of the elastic solution may be. The new feature of these methods is that it is necessary to know only 1) an elastic solution numerically for certain ranges of elastic constants and 2) numerical values of the operational moduli or compliances
for real, positive values of the transform...
Arbocz, J.; Babcock, C. D.
By expanding the response of a cylindrical shell in truncated Fourier series, the nonlinear Donnell type shell equations for imperfect stiffened shells were reduced to a set of linear equations in the correction terms by Newton's method of quasilinearization. Solutions
were obtained for isotropic and for ring and stringer stiffened shells. The amplitudes of the initial imperfections used in the analysis were
calculated from the corresponding Imbert-Donnell imperfection models. The free parameters in this imperfection model were obtained by
least square fitting the harmonics of the experimentally measured initial imperfections. It was possible in all cases to achieve satisfactory correlation using only a...
Ko, W. L.; Blatz, P. J.
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...
Williams, M. L.; Zak, A. R.
The mathematical procedure for analyzing stress singularities in infinite wedges has been developed in References (1) and (2) and has been successfully applied to the analysis of stress distribution in the vicinity of a tip of a crack (3) (4). As a continuation of this study, the results presented in this note relate to the symmetrical stress field about a crack point perpendicular to a bi-material interface, and hence complement earlier results (4) wherein the crack lay along the interface.
Zak, A. R.; Williams, M. L.
A continuing study of plane stress singularities at
corners and cracks has been extended to the case of a crack in.
a hard (soft) material ending normal to a continuous interface
with a soft (hard) material. The increase (decrease) in stress
singularity over the homogeneous material case. which is of the
characteristic inverse square root of distance from the crack
point, is given for all relative rigidities between zero and
infinity. Associated changes in the principal stress and
distortion strain energy density distribution are also discussed,
along with indications of application to such situations as
microcrack growth near grain boundaries and earth faults in
layered strata.