Showing papers by "Rensselaer Polytechnic Institute published in 1974"

Static Fatigue in Glass

Abstract: The decrease in the strength of glass under load results from reaction of the glass with water in the surrounding atmosphere. Hillig and Charles have proposed a model to explain the static fatigue of glass in which this reaction is enhanced by the concentration of stress at crack tips in the glass. This stress-enhanced corrosion leads to a sharpening of the crack tip, a still higher stress there, and ultimately failure when the theoretical cohesive stress of the glass is reached. This theory can explain some experimental results on delayed failure in glass but other results, such as the effect of surface treatment on delayed failure, are inconsistent with the theory.

Algebraic decision procedures for local testability

Abstract: 1. The Notion of Local Testability. A locally testable event is a set of words over an alphabet, membership in which is determined simply by the presence and absence of segments of a certain fixed length. The order in which these segments occur and their frequency are immaterial; however, the left-end segment and the right-end segment are allowed to play special roles. The alphabet Y~ is always finite and it turns out that the locally testable events constitute a subfamily of the family of regular events. Some notation is needed to make this concept precise. Assuming W is a word of'length k or more, let ~k(W) be the left-end segment of W of length k; let OJk(W) be the right-end length-k segment of W; and let ilk(W) be the set of interior length-k segments of W. (Thus if W has length k or k + l, ilk(W) = ~, the empty set.) Let Z k be the set of all words over Z of length k, and Z* be the set of all words of any length over Z, including A, the empty word, which has length zero. Thus zkz * is the set of all words over ~ whose length is at least k. I W} = k means W has length k. An event ~ (i.e., set of words) over a finite alphabet Z is k-testable when, for all words W, W ' c EkE *, ~k(W) = O~k(m\"), i lk(W) = i lk(mr) and ~Ok(W ) = ~k(W') imply that either both WeV and W' eV, or both W ¢ V and W' ¢7. (An event that is k-testable, according to this definition, can be arbitrary about words of length k 1 and less.) An event is locally testable if it is k-testable, for some k. Where [W 1 > k, the ordered triple (~k(W), ilk(W), ~Ok(W)) will be called the k-test vector of W. For a given k and Z, there are only finitely many k-test vectors, and only finitely many words of length less than k. A k-testable event can be completely characterized by the k-test vectors of words in it of length >k, and by the words in it of length < k + 1. Hence there are only finitely many k-testable events over a given Y~. (For further elucidation, see Chapter 2 of [4].) It is clear that local testability is a significant notion for the theoretical

A Thermal, Thermoelastic, and Wear Simulation of a High-Energy Sliding Contact Problem

Abstract: This paper describes an investigation of the sliding contact problem encountered in high-energy disk brakes. The analysis includes a simulation modeling, using the finite element method, of the thermoelastic instabilities that cause transient changes in contact to occur on the friction surface. In order to include the effect of wear of the concentrated contacts on the friction surface, a wear criterion is proposed that results in prediction of wear rates for disk brakes that are quite close to experimentally determined wear rates. The thermal analysis shows that the transient temperature distribution in a disk brake can be determined more accurately by use of this thermomechanical analysis than by a more conventional analysis that assumes constant contact conditions. It is also shown that lower, more desirable, temperatures in disk brakes can be attained by increasing the volume, the thermal conductivity, and especially, the heat capacity of the brake components.

Initially Stressed Mindlin Plates

Abstract: Equations of motion for a transversely isotropic plate in a general state of nonuniform initial stress where the effects of transverse shear and rotary inertia are included are derived by two methods. The first method is to perturb the nonlinear equations of elasticity by an incremental deformation. The resulting equations are linearized and integrated through the thickness of the plate to obtain the plate equations. The second method is to derive nonlinear equations of motion for a thick plate variationally by Hamilton's principle. These equations are then perturbed and suitably linearized to obtain the same equations as were obtained by the first method. A reduced set of equations for a thin plate are also given. Finally, the thick plate equations are solved for a simply supported rectangular plate in a state of uniform compressive stress plus a uniform bending stress both acting in the same direction.

Thermal analysis and dilatometry of glasses formed under elevated pressure

Abstract: Densified glasses, formed from the liquid state by cooling at 5°C/hr under elevated pressures of up to 517 MN/m2, were studied by thermal analysis and dilatometry at ambient pressure. The materials studied were polystyrene, poly(methyl methacrylate), phenolphthalein, sucrose, and a 1 : 1 mixture by weight of potassium and calcium nitrate. Enthalpies of the densified glasses were found to be up to 2–6 J/g greater than the enthalpies of the glasses formed at atmospheric pressure. The major enthalpy and volume relaxation on heating the densified glasses was found to be not correlated The upper temperature limit of the glass-transition region remained constant for all glasses cooled at various pressures, while the lower temperature limit of the polymeric glasses decreased up to 55°C with increasing pressure. The interpretation of the data suggests that an additional, significant volume relaxation occurred on depressurization at room temperature for all glasses analyzed.

Some properties of inn films prepared by reactive evaporation

Abstract: Some optical and electrical properties of degenerate InN films prepared by a reactive evaporation technique are presented. Thermal stability of these easily dissociated samples is discussed and evidence is presented indicating that the partial pressure of atomic nitrogen rather than diatomic nitrogen is a more fundamental parameter for describing thermal equilibrium. This has important implications for the growth of all group III-nitrides.

On the Focusing of Gravitational Radiation

Abstract: We investigate the gain in intensity that can be achieved by using a massive object as a ‘lens’ to focus gravitational radiation incident on the object from a point-like source. An object of massM produces a gain in intensity of the order ofαGM/λc2 whereα is a numerical factor which depends on the mass distribution andλ is the wavelength of the radiation. For large mass, the gain is large, but occurs only in a beam of small angular width.

Elasto-Plastic Indentation of a Layered Medium

Abstract: H. A. FRANCIS. The development of numerical finite-element models is undoubtedly the most fruitful theoretical approach for predicting and analyzing the complex strain field produced by plastic indentation. The authors' model for spherical indentation of an elastic-plastic semi-infinite layered body has yielded many interesting results. I t is felt: that some of these results can be enhanced by clarification of several points. The results have been presented as functions of the independent geometric variable D/H (indentation depth/layer thickness). However, the ratio D/H alone does not completely define the contact. The deformation mechanics must also depend on the geometry of the spherical segment of material displaced by the indenter (radius R), as specified by the ratio D/R. For Fig. 9, R/H = 20; was this value used for the other results as well? Fig. 8, which purports to show that the shape of the plastic boundary under load is strongly dependent on Yz/Yi, in fact represents a contradiction. As long as (1) the substrate is not softer than the layer (F2 > Y{), (2) the stress invariant J? decreases with depth z (which seems intuitively reasonable, considering the geometry of the plastic boundary), and (3) the plastic boundary does not extend to the layer-substrate interface, the solution must be independent of the substrate yield stress Y2. It can therefore be concluded solely from the loaded plastic boundary for Yi/Y\\ = 4.75 in Fig. 8 that during loading up to this load the solution is the same as for a homogeneous body (Ei = Ei, Y\\ = Y2). Thus, the two plastic boundaries shown for Y2/Y\\ = 1.0, 4.75 are mutually inconsistent. The surface profiles shown in Fig, 9 demonstrate that the deformation depends on the rigidity of the substrate and the fractional characteristics of the layer-substrate interface. I t is well known that the nature of the irreversible changes in surface shape outside the contact also depends on the strain-hardening rate Er. For plastic spherical indentation, the residual normal surface displacement sir) (measured positive outward) always has a positive maximum which for low ET is near or at r = a and whose distance from r = a in general increases with ET [I, 2]. For low ET, s(a) > 0 (\"piling up\"), and for high ET, s(a) < 0 (\"sinking in\") [3, 4, 5]. Thus the residual displacement field is strongly dependent on the flow stress gradient in the plastic, zone. For Y/E = 0.00084, the value ET/E = 0.244 given in Fig. 3 gives, practically speaking, a very high strainhardening rate: at a uniaxial plastic strain of 0.01, the uniaxial flow stress is 4.8 F. Assuming ET/E = 0.244 for Fig. 9, it is, therefore, realistic that, the unloaded contact perimeter lies below the original surface level. Did the authors investigate the nonstrain-hardening case Er = 0, and, if so, did it give the expected \"piling u p \" behavior (s(n) > 0)? Were any other results of the model found to be dependent on ET/E? For example, the di-

An Information Theory Measure for Television Programming

Abstract: A content-free measure of television program form is developed. This measure is created from a rigorous general theory construction viewpoint. The basic terms of the theoretical measure are created from iconic aspects of programming. These terms are mapped into variables by considering their human information-processing implications. The definitions of the variables are in information theory entropy terms. The variables are used to score 168 television programs, and the results used to factor analyze the variables, creating two independent dimensions called Dynamics and Unfamiliarity. As a validation, the viewing patterns of 149 adolescents on these two dimensions are compared to two other measures of programming content. The information theory dimensions of form are found to detect nonrandom viewing patterns as well or better than either of the other measures of content.

Electronic relaxation in the PbOSiO2Fe2O3 glass system

Abstract: The a.c. and d.c. conductivities of PbOSiO 2 glass with 0–10 mole% Fe 2 O 3 additions were measured in the temperature range 77–700 K. Two relaxation processes were noted. The relaxation mechanism at lower temperatures is due to polaron hopping between ferric-ferrous ion pairs with a distribution of relaxation times which is energy independent. The second relaxation phenomenon, at higher temperatures is polaron hopping along iron ion chains in the glass of which the pairs responsible for the first process are a part. A theoreticalmodel is proposed and additional evidence for this model is presented in the form of magnetic susceptibility and electron spin resonance (esr) data.

Fracture strength of soda-lime glass after etching

Abstract: The strength of soda-lime glass at liquid nitrogen temperature after various amounts of etching was measured. A median crack length of 6 μm was calculated from the results and a model of the etching process. It was found that the rate of etching at the crack tip was much lower than on the external surface. Measured distributions of strength for samples etched different depths were also in reasonable agreement with calculated distributions. The etching process itself was found to cause some weakening of the glass.

The Influence of State of Stress on Low-Cycle Fatigue of Structural Materials. A Literature Survey and Interpretive Report

Abstract: A literature survey was made on the influence of state of stress on the deformation and fracture behavior during low-cycle fatigue Only the phenomenological aspects of fracture and deformation in the low-cycle range (< 10 5 cycles) are considered Most of the materials investigated are shown or are assumed to have isotropic fatigue properties so that anisotropy was generally not considered For the isotropic case correlation formulas between uniaxial and multiaxial states of stress (strain) are stated in Appendix 1 Individual papers are reviewed to see which formula can best correlate uniaxial and multiaxial data No single criterion was found which consistently correlates the data Of all the correlation formulas the von Mises or distortion energy or octahedral shear stress criterion showed the highest degree of acceptance However, some papers show no good correlation on the basis of this criterion and serious objections are voiced against this criterion on principal grounds- The von Mises criterion gives the same value for two states of stress which differ only by a hydrostatic pressure, it is pressure insensitive Fatigue fracture is shown to be affected by the superposition of a hydrostatic pressure and therefore a preassure sensitive criterion should be used for correlation In future work a clear distinction of the influence of multiaxial states of stress (strain) on crack initiation and crack growth is necessary Crack initiation and propagation studies are urgently needed For isotropic fatigue properties pressure sensitive criteria should be incorporated into the constants of a generalized Coffin-Manson law In the case of anisotropic fatigue properties, new correlation procedures have to be developed

Thermal expansion, Debye temperature and Gruneisen constant of carbides and nitrides

Abstract: The experimental data on the thermal expansion of the carbides and nitrides of the early transition metals (with B 1 structure) have been collected and evaluated, and average curves of α against temperature and composition have been determined. Some of the difficulties encountered in making good thermal expansion measurements peculiar to this class of compounds are briefly discussed. The resultant values of α, together with the experimental specific heat and elastic constants, are used to determine the temperature dependence on the Debye temperature and the Gruneisen constant.