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A Caltech Library Repository Feedhttp://www.rssboard.org/rss-specificationpython-feedgenenTue, 16 Apr 2024 16:14:34 +0000Castable Plastics in Photoelastics Stress Analysis
https://resolver.caltech.edu/CaltechETD:etd-02182009-112040
Authors: {'items': [{'id': 'Matzdorff-Roger-Edward', 'name': {'family': 'Matzdorff', 'given': 'Roger Edward'}, 'show_email': 'NO'}]}
Year: 1950
DOI: 10.7907/1CAZ-4A36
An investigation was begun on the feasibility of utilizing castable, thermosetting plastics in experimental stress analysis by means of either photoelasticity or electrical strain gages imbedded in the plastic.
The first phase of the study was the development of a casting technique that would give a stress free casting suitable for photoelastic work. This was considerably complicated by the inherent shrinkage which occurs during the polymerization of the plastic. A good method was found for casting solid models, and a workable method was devised for casting hollow section models.
The second phase constituted the development and evaluation of the optimum physical properties of a resin known as Castolite. The results were encouraging with the exception that the strain creep was excessive. The rate of creep, however, is slow and it is possible to use the material for two dimensional photoelasticity with results comparable to those obtained from other photo-elastic materials. The desirable features are a very low optical creep, stress-strain and stress-fringe number curves that are linear for constant loading time, no time-edge stress effects, chemical stability under high temperatures, modulus of elasticity of 600,000 psi, and a fringe value of 175 psi per in-fringe in tension.
An additional feature is the ability to bond two or more cured plastic pieces together with the liquid plastic itself. The strength of the bonded area is equal to the rest of the structure.
Three dimensional frozen stress properties were not determined, but there is evidence that the resin would be suitable.https://thesis.library.caltech.edu/id/eprint/676Transient Analysis Methods for Determining the Longitudinal Stability Derivatives of a Submerged Body from Free Flight Tests
https://resolver.caltech.edu/CaltechETD:etd-02052009-152837
Authors: {'items': [{'id': 'Geisberg-Ralph Lewis', 'name': {'family': 'Geisberg', 'given': 'Ralph Lewis'}, 'show_email': 'NO'}]}
Year: 1950
DOI: 10.7907/H9NV-2777
The stability derivatives obtainable from dynamic free flight tests are determined. Methods for reducing flight test data to the form of stability derivatives using the Fourier integral and the Laplace transform are developed.https://thesis.library.caltech.edu/id/eprint/513Fatigue Stress Concentration Studies on Aluminum Alloys
https://resolver.caltech.edu/CaltechETD:etd-03232009-161109
Authors: {'items': [{'id': 'Dervishyan-Aram-Ohannes', 'name': {'family': 'Dervishyan', 'given': 'Aram Ohannes'}, 'show_email': 'NO'}]}
Year: 1952
DOI: 10.7907/4BCE-M652
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Fatigue tests in reversed bending were conducted in 75S-T6 and 17S-T6 aluminum alloys to determine whether Neuber's theory on fatigue stress concentration factors in notches was applicable to these materials. The results of the tests indicate confirmation of the theory within engineering accuracy providing the value of […] (a material constant) is determined experimentally.
Material size effect was investigated and found to exist. This was an unexpected result since other sources (see References 3 and 4) indicated that no size effect existed for aluminum alloys.
Ignoring the correction due to size effect a value of the Neuber's constant […] of approximately 0.05" gave reasonable checks with the experimental data for both 75S-T6 and 17S-T6 aluminum alloys. This may indicate that this value of […] is the correct material constant for aluminum alloys but additional data on other alloys is needed to confirm this conclusion.https://thesis.library.caltech.edu/id/eprint/1082A New Approach to the Analysis of Large Deflections of Plates
https://resolver.caltech.edu/CaltechETD:etd-12042003-163054
Authors: {'items': [{'id': 'Berger-Howard-Martin', 'name': {'family': 'Berger', 'given': 'Howard Martin'}, 'show_email': 'NO'}]}
Year: 1954
DOI: 10.7907/FA0E-1X79
As a result of the assumption that the strain energy due to the second invariant of the middle surface strains can be neglected when deriving the differential equations for a flat plate with large deflections, simplified equations are derived that can be solved readily. Computations using the solution of these simplified equations are carried out for the deflection of uniformly loaded circular and rectangular plates with various boundary conditions. Comparisons are made with available numerical solutions of the exact equations. The deflections found by this approach are then used to obtain the stresses, and the resulting stresses are compared with existing solutions. In all the cases where comparisons could be made, the deflections and stresses agree with the exact solutions within the accuracy required for engineering purposes.https://thesis.library.caltech.edu/id/eprint/4772Pressurized Fuselage Stress Analysis
https://resolver.caltech.edu/CaltechETD:etd-12022003-161233
Authors: {'items': [{'id': 'Chase-Robert-Apperson', 'name': {'family': 'Chase', 'given': 'Robert Apperson'}, 'show_email': 'NO'}]}
Year: 1955
DOI: 10.7907/ZCGR-N460
Theoretical methods for obtaining the complete stress analysis of a pressurized, stiffened circular cylinder of special geometry are presented. In certain limiting cases, the exact solutions are tractable, but in general the solutions lead to approximate results. There are practical cases for which none of the solutions is applicable. Accompanying the theoretical analysis is a short experimental program consisting of the strain gage instrumentation and testing of a Lucite and cellulose acetate model of typical aircraft structural geometry. The results compare favorably with the theoretical analysis.https://thesis.library.caltech.edu/id/eprint/4711Some Radiation Problems in Elastodynamics
https://resolver.caltech.edu/CaltechETD:etd-10072004-092112
Authors: {'items': [{'id': 'Ang-Dang-Dinh', 'name': {'family': 'Ang', 'given': 'Dang Dinh'}, 'show_email': 'NO'}]}
Year: 1958
DOI: 10.7907/TF74-2977
Three elastodynamic problems are studied. The first deals with waves generated by instantaneous and uniform closure of a semi-infinite crack, while in the second, a semi-infinite crack is suddenly initiated in a continuous medium initially subjected to uniform tension. The last of the three deals with a force moving at uniform velocity along a semi-infinite crack, starting from the edge. The problems are solved by means of the Wiener-Hopf integral methods. The characteristic wave patterns and stress singularities are discussed.https://thesis.library.caltech.edu/id/eprint/3959Exact and Approximate Solutions to the Pressure-Loaded Plate Strip with Temperature Distribution
https://resolver.caltech.edu/CaltechETD:etd-12072005-131831
Authors: {'items': [{'id': 'Lindquist-David-Max-Wadsworth', 'name': {'family': 'Lindquist', 'given': 'David Max Wadsworth'}, 'show_email': 'NO'}]}
Year: 1960
DOI: 10.7907/G7PZ-8898
The large deflection analysis for a plate strip under uniform pressure and temperature loading is extended to include spanwise variation of temperature. An exact temperature distribution is derived and stress and deflection equations are developed for the fundamental mode thereof. A parabolic approximation to the fundamental mode is shown to be reasonably accurate. Using this approximation, a direct analogy to the case of uniform temperature distribution can be demonstrated in terms of "effective" pressure, temperature moment, and average temperature. The equilibrium equations are formally identical, permitting the use of design charts based on spanwise constant loadings.https://thesis.library.caltech.edu/id/eprint/4829Irreversible Thermodynamics and Variational Principles with Applications to Viscoelasticity
https://resolver.caltech.edu/CaltechTHESIS:08092011-111909246
Authors: {'items': [{'id': 'Schapery-Richard-Allan', 'name': {'family': 'Schapery', 'given': 'Richard Allan'}, 'show_email': 'NO'}]}
Year: 1962
DOI: 10.7907/QEB0-N308
A unified theory of the thermo-mechanical behavior of
viscoelastic media is developed from studying the thermodynamics of irreversible processes, and includes discussions of the general equations of motion, crack propagation, variational principles, and approximate methods of stress analysis.
The equations of motion in terms of generalized coordinates
and forces are derived for systems in the neighborhood of a stable equilibrium state. They represent a modification of Biot's theory in that they contain explicit temperature dependence, and a thermodynamically consistent inclusion of the time-temperature superposition principle for treating media with temperature-dependent viscosity coefficients. The stress-strain-temperature and energy equations for viscoelastic solids follow immediately from the general
equations and, along with equilibrium and strain-displacement relations, they form a complete set for the description of the thermomechanical behavior of media with temperature-dependent viscosity. In addition, an energy equation for crack propagation is derived and examined briefly for its essential features by applying it to a specific problem.
The thermodynamic equations of motion are then used to
deduce new variational principles for generalized coordinates and forces, employing convolution-type functionals. Anticipating various engineering applications, the formulation is phrased alternately in terms of mechanical displacement, stresses, entropy displacement, and temperature in thermally and mechanically linear solids. Some special variational principles are also suggested for applications wherein the nonlinear thermal effects of temperature dependent viscosity and dissipation may be important.
Building upon the basic variational formulation, it is next
shown that when these convolution functionals are Laplace-transformed with respect to time, some convenient minimum principles result which can be employed for the approximate calculation of transformed, viscoelastic responses. The characteristic time dependence of exact and approximate solutions is then derived and used in relating error
in approximate viscoelastic solutions to error in the associated elastic solutions.
The dissertation is concluded with a study of some approximate methods of viscoelastic analysis. First, the important problem of inverting complicated Laplace transforms to physical time-dependent solutions is resolved by advancing two easily applied, approximate methods of transform inversion. These inversion methods and
variational principles are then used in some illustrative, numerical, examples of stress and heat conduction analysis.
https://thesis.library.caltech.edu/id/eprint/6576Application of Finite Elastic Theory to the Behavior of Rubber-Like Materials
https://resolver.caltech.edu/CaltechETD:etd-03012004-143718
Authors: {'items': [{'id': 'Ko-William-L', 'name': {'family': 'Ko', 'given': 'William L.'}, 'show_email': 'NO'}]}
Year: 1963
DOI: 10.7907/WMS4-A521
In Part I, methods for determining the strain energy function and the associated constitutive stress-deformation law for rubber-like materials is undertaken and the mechanics of data reduction needed to determine some parameters of the theory are displayed. Experiments were performed in four different stress fields on a foamed polyurethane rubber (dilatable rubber) and on several kinds of continuum rubbers. A new strain energy function and the associated stress-deformation law for a foamed rubber are generated which correlate most of the data to a high degree of accuracy. A parameter appearing in the functional expression for a foam rubber has the same significance as Poisson's ratio in infinitesimal elastic theory. For continuum rubbers, the isotropic Neo-Hookean representations of quasi-static behavior is found to be sufficient over most of the whole range of extension.
In Part II, geometrical representations of an isotropic failure surface based on various criteria are depicted both in principal stress and principal stretch spaces for elastic materials. The experimental data are compared with all criteria and the results are discussed.
In Part III, finite elastic theory is used to determine the stress and deformation fields around the base of a radial crack in an infinitely long rubber log opened by a facially bonded rigid wedge-shaped bellow.
In the last Part, the topology of interstices idealized as closest packed spherical holes (idealized foam structure) is investigated. Equivalent elastic constants are calculated for rubbery interstices of both hexagonal and face-centered cubic closest packings under small displacement.https://thesis.library.caltech.edu/id/eprint/816Rupture Phenomena in Viscoelastic Materials
https://resolver.caltech.edu/CaltechETD:etd-11052003-091542
Authors: {'items': [{'id': 'Knauss-Wolfgang-Gustav', 'name': {'family': 'Knauss', 'given': 'Wolfgang Gustav'}, 'show_email': 'NO'}]}
Year: 1963
DOI: 10.7907/KZSV-0Y32
A failure theory for high polymers is developed from the hypothesis that weak regions exist in the material. Defects nucleate in these regions through bond rupture until the defects reach a size which is critical for the applied boundary loading. This critical condition is based on energy balance considerations.
By considering the relaxation of the polymer chain in terms of the phenomenological stress-strain behavior and the rupture of chemical bonds in terms of an Arrhenius type rate law, the theory is able to accommodate an arbitrary stress or strain history, and shows reasonably good agreement with experiments which cover a large range of conditions.
In addition the stress analysis of a special crack geometry is presented. The geometry consists of a thin infinite strip containing a semi-infinite crack. For a uniform separation of the infinite boundaries an infinitesimal elasticity solution is obtained with the help of the Fourier transform and Wiener-Hopf techniques. The effect of large strains on the stresses near the crack tip is studied experimentally and a surprising correlation with the infinitesimal elasticity solution is found.https://thesis.library.caltech.edu/id/eprint/4409The Stresses in a Spherical Shell Containing a Crack
https://resolver.caltech.edu/CaltechETD:etd-09132002-104440
Authors: {'items': [{'id': 'Folias-Efthymios-Stefanos', 'name': {'family': 'Folias', 'given': 'Efthymios Stefanos'}, 'show_email': 'NO'}]}
Year: 1964
DOI: 10.7907/N4ST-K607
NOTE: There is a 3-page Notation Eqivalency Chart preceding the Introduction.
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Introduction is included in .pdf document.
Chapter I
Introduction
One of the problems in fracture mechanics which apparently has not received extensive theoretical treatment is that concerning the effect of initial curvature upon the stress distribution in a thin sheet containing a crack. Considerable work has been carried out on initially flat sheets subjected to either extensional or bending stresses, and for small deformations the superposition of these separate effects [1] is permissible. On the other hand, if a thin sheet is initially curved, a bending load will generally produce both bending and extensional stresses, and similarly a stretching load will also induce both bending and extensional stresses. The subject of eventual concern therefore is that of the simultaneous stress fields produced in an initially curved sheet containing a crack.
Two geometries immediately come to mind: a spherical shell, and a cylindrical shell. In the latter case one of the principal radii of curvature is infinite and the other constant. It might appear therefore that this geometric simplicity leads to a rather straightforward analytical solution. However, the fact that the curvature varies between zero and a constant as one considers different angular positions - say around the point of a crack which is aligned parallel to the cylinder axis - more than obviates the initial geometric simplification. For this reason a spherical section of a large radius of curvature constant in all directions is chosen for consideration.
It is of some practical value to be able to correlate flat sheet behavior with that of initially curved specimens. In experimental work, for example, considerable time could be saved if a reliable prediction of curved sheet response behavior could be made from flat sheet tests. For this reason an exploratory study was undertaken to assess analytically how the two problems might be related. Although it is recognized that elastic analysis is not directly applicable to fracture prediction because of the plastic flow near the crack tip, considerable information can be obtained.
Chapter II lists the basic assumptions and equations of shallow spherical shells. Then the complementary problem of a cracked spherical shell is formulated in terms of Reissner's shallow shell equations in Chapter III where the problem is separated into two parts, symmetric and antisymmetric. In Chapters IV and V the solutions to the symmetric and antisymmetric parts respectively are expressed in integral form. They are then reduced to the solution of a pair of coupled singular integral equations, which are solved by successive approximations for small values of the characteristic shell parameter [...]. No effort was made to convert the pair of singular integral equations to a corresponding Fredholm type, however Appendix II shows that the two methods are equivalent.
The particular example of a clamped segment of a thin shallow spherical shell is considered in Chapter VI which serves to illustrate how the local solution may be combined in a particular case. Then in Chapter VII, Griffith's criterion is extended to the local region of an initially spherical curved sheet and an expression for its critical crack length is obtained.
Finally, Chapter VIII compares the experimental and theoretical results for the particular problem described in Chapter VI.https://thesis.library.caltech.edu/id/eprint/3509Theoretical and Experimental Studies of Wave Propagation in Viscoelastic Materials
https://resolver.caltech.edu/CaltechETD:etd-09072002-150755
Authors: {'items': [{'id': 'Arenz-Robert-James', 'name': {'family': 'Arenz', 'given': 'Robert James'}, 'show_email': 'NO'}]}
Year: 1964
DOI: 10.7907/E8KM-6M98
The phenomenon of wave propagation in viscoelastic materials is investigated both theoretically and experimentally, with attention directed to two areas. First, analytical methods of solution are developed for certain wave propagation problems in one and two dimensions utilizing realistic material properties. This is accomplished by use of time-dependent material property characterization through a Dirichlet series representation to overcome the limitations of the widely-used simple spring and dashpot models involving two or three elements. The Laplace transformed solutions are then inverted by an extension of the Schapery collocation method to dynamic situations.
The second topic deals with dynamic photoelasticity applied to viscoelastic materials. It is shown that the relationships between stress optic and strain optic coefficients for linearly viscoelastic materials can be formulated. Then the time-dependent birefringence characteristics of a typical low modulus polymer material are determined from constant strain rate tests for a full range of dynamic loading rates by taking advantage of the time-temperature shift phenomenon. Much recent work in dynamic photoviscoelasticity has been based on static calibrations only. Hence to put the technique on a firm foundation and indicate the general necessity of including the time dependency in treatment of material properties, a comparison is made of predicted fringe patterns with experimental results for both one- and two-dimensional situations. The cases considered are the rod and semi-infinite plate geometries under quasistep pressure inputs, for which viscoelastic solutions are obtained from the wave propagation analysis in the first part of the thesis. The results indicate the feasibility of quantitative photoviscoelasticity for dynamic stress analysis.https://thesis.library.caltech.edu/id/eprint/3368The thickness effect and plastic flow in cracked plates
https://resolver.caltech.edu/CaltechETD:etd-12122003-100109
Authors: {'items': [{'id': 'Swedlow-J-L', 'name': {'family': 'Swedlow', 'given': 'Jerold Lindsay'}, 'show_email': 'NO'}]}
Year: 1965
DOI: 10.7907/0WVE-W364
Over a range of plate thickness, it is well known that the fracture behavior of flat plates is substantially different from that predicted by classical fracture analyses. Finiteness of the plate thickness causes a variety of failure mechanisms to occur, and qualitative features of the associated stress and strain fields may be deduced. It is indicated that both the three-dimensional nature of the stress field and the plastic deformations will be needed for an accurate prediction of the thickness effect.
As a contribution to the three-dimensional analysis, an appropriate elastic boundary value problem is given limited consideration. It is observed that the three in-plane stresses can be singular, in accord with the two-dimensional results, but the transverse components appear to be bounded at the crack tip.
Equations which include plastic behavior are outlined, and a plane stress problem is solved using numerical methods. Comparison with analytical and experimental results is made and found to be satisfactory. One important result indicates that, compared to the elastic solution, the intensity of stress at the crack point decreases with load, while that for strain increases.
The results do not include determination of a fracture stress, as this further step requires the development of an elastoplastic fracture criterion. Comments on this extension are included, together with other aspects of future work.https://thesis.library.caltech.edu/id/eprint/4958Hydrostatic Tensile Fracture of a Polyurethane Elastomer
https://resolver.caltech.edu/CaltechETD:etd-11232005-113650
Authors: {'items': [{'id': 'Lindsey-Gerald-Herbert', 'name': {'family': 'Lindsey', 'given': 'Gerald Herbert'}, 'show_email': 'NO'}]}
Year: 1966
DOI: 10.7907/K12J-X907
The investigation of fracture of polymeric materials in hydrostatic tensile fields constitutes an avenue of approach to the study of fracture in more general three-dimensional environments. The advantages created by the symmetry of the stress field are considerable and, in one of the cases studied, facilitates a theoretical treatment that includes large deformations, which are characteristic of this class of materials.
The analysis is developed through the concept of fracture originating from a flaw, which in this instance is taken to be a spherical cavity. Through the application of energy principles, a theoretical prediction of ultimate strength is made for hydrostatic tensile fields.
Experiments were conducted to demonstrate the existence of such flaws and to evaluate the theory. Results of the tests on specimens containing both residual flaws and artificially inserted ones indicate a fundamental difference in behavior as contrasted with cracks.
An explanation is given linking experimental results and theoretical predictions. It is based on the concept that a flaw "grows" in the material under load using the cavity as a nucleating point. Upon this hypothesis is built a theory of rupture in which planar cracks grow radially from the center of the cavity in the form of Saturn-ring cracks.https://thesis.library.caltech.edu/id/eprint/4643An Experimental Investigation of Dynamic Crack Propagation in Plastic and Metals
https://resolver.caltech.edu/CaltechETD:etd-09262005-152806
Authors: {'items': [{'id': 'Beebe-Wayne-Metcalf', 'name': {'family': 'Beebe', 'given': 'Wayne Metcalf'}, 'show_email': 'NO'}]}
Year: 1966
DOI: 10.7907/PC0B-4P13
NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document.
Crack propagation experiments were conducted in polyester resin sheets containing a central crack. Uniaxial tension loading at several loading rates was applied perpendicular to the crack direction. Two types of experiments were conducted: (1) High loading rate tests at 24°C and -45°C, with a constant loading rate to study the acceleration characteristics of cracks running in a glassy material, and (2) high temperature-low loading rate tests to study slow crack propagation when appreciable viscous dissipation could occur.
During crack propagation, full frame photographs were taken of the photoviscoelastic isochromatic patterns and crack tip position at framing rates from 250 to 100,000 frames per second. The principal conclusions were as follows:
1. Even at loading rates exceeding [...] psi per sec, isochromatic patterns prior to crack propagation compare closely with static patterns.
2. Constant crack velocities were achieved in the high loading rate tests and it was found that the isochromatic patterns compare closely with the theoretical solution of Broberg.
3. During the crack acceleration period, the experimental data could not be represented adequately by the Berry elastic theory.
4. For the early phase of the slow (viscous) crack growth period, the crack length could be predicted using a simple theory proposed by Schapery and Williams.
Several tests were conducted on silicon-iron metal sheets; it was concluded that the same testing technique can be applied to the study of crack growth in metals.https://thesis.library.caltech.edu/id/eprint/3786