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It was discovered that the isothermal equation of state for solids in compression is a simple, universal form. This single form accurately describes the pressure and bulk modulus as a function of volume for tonic, metallic, covalent, and rare gas solids.
The use of reduced variables to account for the time-temperature dependence of the relaxation modulus is a standard and universally adopted technique in the stress analysis of solid propellant grains. Recent work has suggested that the reduced variable technique can also be used to account for the dependence of the relaxation modulus on the crosslink density of an elastomer system. By combining variables, it is now possible to determine the relaxation modulus as a function of both mechanical and chemical parameters over a long period of time. The problems involved, the pitfalls to be avoided, and suggested techniques to be used in acquiring data are discussed.
A case bonded end burning solid propellant rocket motor is described. A propellant with sufficiently low modulus to avoid chamber buckling on cooling from cure and sufficiently high elongation to sustain the stresses induced without cracking is used. The propellant is zone cured within the motor case at high pressures equal to or approaching the pressure at which the motor will operate during combustion. A solid propellant motor with a burning time long enough that its spacecraft would be limited to a maximum acceleration of less than 1 g is provided by one version of the case bonded end burning solid propellant motor of the invention.
A technique has been developed for modeling solid films in rolling element bearings. For a given bearing geometry an effective viscosity can be calculated for a solid film as a function of the film shear modulus and ball-race friction coefficient. The calculated effective viscosity can subsequently be used as an input to a numerical model of cage motion and stability. Results from a sample calculation of effective viscosity and prediction of cage stability for a turbopump bearing are presented for films of molybdenum disulfide (MoS2) and polytetrafluoroethylene ()PTFE).
Monolithic metallic copper alloy and NiCrAlY coatings were fabricated by either the cold spray (CS) or the vacuum plasma spray (VPS) deposition processes. Dynamic elastic modulus property measurements were conducted on these monolithic coating specimens between 300 K and 1273 K using the impulse excitation technique. The Young's moduli decreased almost linearly with increasing temperature at all temperatures except in the case of the CS Cu-23%Cr-5%Al and VPS NiCrAlY, where deviations from linearity were observed above a critical temperature. It was observed that the Young's moduli for VPS Cu-8%Cr were larger than literature data compiled for Cu. The addition of 1%Al to Cu- 8%Cr significantly increased its Young's modulus by 12 to 17% presumably due to a solid solution effect. Comparisons of the Young s moduli data between two different measurements on the same CS Cu- 23%Cr-5%Al specimen revealed that the values measured in the first run were about 10% higher than those in the second run. It is suggested that this observation is due to annealing of the initial cold work microstructure resulting form the cold spray deposition process.
Direct characterization procedures were used to determine the relaxation modulus as a function of time, temperature, and state of strain. Using the quasi-elastic method of linearviscoelasticity, these properties were employed in a finite element computer code to analyze a thick-walled, nonlinear viscoelastic cylinder in the state of plane strain bonded to a thin (but stiff) elastic casing and subjected to slow thermal cooling. The viscoelastic solution is then expressed as a sequence of elastic finite element solutions. The strain-dependent character of the relaxation modulus is included by replacing the single relaxation curve used in the linear viscoelastic theory by a family of relaxation functions obtained at various strain levels. These functions may be regarded as a collection of stress histories or responses to specific loads (in this case, step strains) with which the cooldown solution is made to agree by iterations on the modulus and strain level.
The previous work of Schlosser and Ferrante (1988) on universality in solids is extended to the study of liquid metals. As in the case of solids, to a good approximation, in the absence of phase transitions, plots of the logarithm of the reduced-pressure function H, of the reduced-isothermal-bulk-modulus function b, and of the reduced-sound-velocity function v are all linear in 1-X. Finally, it is demonstrated that ln(Cp/C/v) is also linear in 1-X, where X = (V/V/0/)exp 1/3), and V(0) is the volume at zero pressure.
Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P=0) isothermal bulk modulus; (2)it P=0 pressure derivative; (3) the P=0 volume; and (4) the P=0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.
Recently it has been argued based on theoretical calculations and experimental data that there is a universal form for the equation of state of solids. This observation was restricted to the range of temperatures and pressures such that there are no phase transitions. The use of this universal relation to estimate pressure-volume relations (i.e., isotherms) required three input parameters at each fixed temperature. It is shown that for many solids the input data needed to predict high temperature thermodynamical properties can be dramatically reduced. In particular, only four numbers are needed: (1) the zero pressure (P = 0) isothermal bulk modulus; (2) its P = 0 pressure derivative; (3) the P = 0 volume; and (4) the P = 0 thermal expansion; all evaluated at a single (reference) temperature. Explicit predictions are made for the high temperature isotherms, the thermal expansion as a function of temperature, and the temperature variation of the isothermal bulk modulus and its pressure derivative. These predictions are tested using experimental data for three representative solids: gold, sodium chloride, and xenon. Good agreement between theory and experiment is found.
Novel transformation toughened ceramic compositions comprising finely divided Zr0 2 -Hf0 2 solid solution particles dispersed in a Al 2 0 3 -Cr 2 0 3 (alumina) or 3Al 2 0 3 .2Si0 2 -3Cr 2 0 3 .2Si0 2 (mullite) solid solution matrix phase. It is found that increased hardness and modulus associated with higher relative Cr 2 0 3 content (e.g. 20 mole % ) in the matrix phase and increased fracture toughness associated with higher relative Hf0 2 content ( e.g. 10 to 20 mole % ) in the disperse phase represent viable and improved ceramic compositions. Such transformation toughened ceramic compositions are considered useful in superhot light diesel engine applications, high temperature gas turbines and ultrahigh temperature ceramic heat exchangers.
The objective of this program is to develop an advanced high temperature oxide structural ceramic for application to the heavy duty diesel engine. The approach is to employ transformation toughening by additions of ZrO.5HfO.5O2 solid solution to the oxide ceramics, mullite (2Al2O3S2SiO2) and alumina (Al2O3). The study is planned for three phases, each 12 months in duration. This report covers Phase 1. During this period, processing techniques were developed to incorporate the ZrO.5HfO.5O2 solid solution in the matrices while retaining the necessary metastable tetragonal phase. Modulus of rupture and of elasticity, coefficient of thermal expansion, fracture toughness by indent technique and thermal diffusivity of representative specimens were measured. In Phase 2, the process will be improved to provide higher mechanical strength and to define the techniques for scale up to component size. In Phase 3, full scale component prototypes will be fabri-]cated.
A comprehensive survey of the elastic modulus of binary alloys as a function of the concentration is presented. Alloys that form continuous solid solutions, limited solid solutions, eutectic alloys, and alloys with intermetallic phases are investigated. Systems having the most important structures have been examined to obtain criteria for the relation between lattice structure, type of binding, and elastic behavior.
Protein crystals are so fragile that they often can not be handled by tweezers. Indeed, measurements of the Young modulus, E, of lysozyme crystals resulted in E approx. equals 0.1 - 1 GPa, the lower figures, 0.1 - 0.5 GPa, being obtained from triple point bending of as-grown and not cross-linked crystals sitting in solution. The bending strength was found to be approx.10(exp -2) E. On the other hand, ultrasound speed and Mandelstam-Raman-Brilloin light scattering experiments led to much higher figures, E approx. equals 2.7 GPa. The lower figures for E were found from static or low frequency crystal deformations measurements, while the higher moduli are based on high frequency lattice vibrations, 10(exp 7) - 10(exp 10) 1/s. The physical reason for the about an order of magnitude discrepancy is in different behavior of water filling space between protein molecules. At slow lattice deformation, the not-bound intermolecular water has enough time to flow from the compressed to expanded regions of the deformed crystal. At high deformation frequencies in the ultra- and hypersound waves, the water is confined in the intermolecular space and, on that scale, behaves like a solid, thus contributing to the elastic crystal moduli. In this case, the reciprocal crystal modulus is expected to be an average of the water protein and water compressibilities (reciprocal compressibilities): the bulk modulus for lysozyme is 26 GPa, for water it is 7 GPa. Anisotropy of the crystal moduli comes from intermolecular contacts within the lattice while the high frequency hardness comes from the bulk of protein molecules and water bulk moduli. These conclusions are based on the analysis of liquid flow in porous medium to be presented.
The effect of substituting the Mg metal in Mg-B composites by a Mg-14 wt pct Li solid solution on the ductility of the resulting composite was investigated using elastic modulus measurements on the P/M composite material prepared with a dispersion of B particles (in a vol pct range of 0-30) in a matrix of Mg-14 wt pct Li-1.5 wt pct Al. It was found that the elastic modulus of the composites increased rapidly with increasing boron, with specific stiffness values reaching about two times that of most structural materials. The values of the compression and tensile strengths increased significantly with boron additions. Good tensile ductility was achieved at the level of 10 vol pct B. However, at 20 vol pct B, the Mg-Li composite exhibited only limited tensile ductility (about 2 percent total elongation).
Recent accomplishments in our research efforts have included the successful measurement of the thermal mechanical properties of polymer materials exposed to the low-earth orbit environment. In particular, viscoelastic properties were recorded using the Rheometrics Solids Analyzer (RSA 2). Dynamic moduli (E', the storage component of the elastic modulus, and E'', the loss component of the elastic modulus) were recorded over three decades of frequency (0.1 to 100 rad/sec) for temperatures ranging from -150 to 150 C. Although this temperature range extends beyond the typical use range of the materials, measurements in this region are necessary in the development of complete viscoelastic constitutive models. The experimental results were used to provide the stress relaxation and creep compliance performance characteristics through viscoelastic correspondence principles. Our results quantify the differences between exposed and control polymer specimens. The characterization is specifically designed to elucidate a constitutive model that accurately predicts the change in behavior of these materials due to exposure. The constitutive model for viscoelastic behavior reflects the level of strain, the rate of strain, and the history of strain as well as the thermal history of the material.
The dynamic response properties of the space shuttle solid rocket moter (TP-H1148) propellant were characterized and the expected limits of propellant variability were established. Dynamic shear modulus tests conducted on six production batches of TP-H1148 at various static and dynamic strain levels over the temperature range from 40 F to 90 F. A heat conduction analysis and dynamic response analysis of the space shuttle solid rocket motor (SRM) were also conducted. The dynamic test results show significant dependence on static and dynamic strain levels and considerable batch-to-batch and within-batch variability. However, the results of the SRM dynamic response analyses clearly demonstrate that the stiffness of the propellant has no consequential on the overall SRM dynamic response. Only the mass of the propellant needs to be considered in the dynamic analysis of the space shuttle SRM.
This paper is concerned with verification of the applicability of the Vinet et al. (1987) universal equation of state to the liquid phase of the rare-gas elements under pressure. As previously observed in solids and liquids metals, to a good approximation, in the absence of phase transitions, plots of the logarithms of the reduced pressure function, of the reduced sound velocity, and of the reduced bulk modulus, are all linear functions of 1 - X over the entire experimental pressure range. The results obtained on the rare-gas liquids are comparable in accuracy to those obtained in previous work on solids and liquid metals.
Thermoelastic constitutive equations are derived for a material undergoing solidification or hardening as the result of a chemical reaction. The derivation is based upon a two component model whose composition is determined by the degree of hardening, and makes use of strain-energy considerations. Constitutive equations take the form of stress rate-strain rate relations, in which the coefficients are time-dependent functions of the composition. Specific results are developed for the case of a material of constant bulk modulus which undergoes a transition from an initial liquidlike state into an isotropic elastic solid. Potential applications are discussed.