Engineering topics
Publications and source records attributed to Peng, S. T. J..
Solid propellants under tension loading dilate significantly, Therefore, they may be aptly called dilatable materials.
In the present treatment of a viscoplastic composite wafer formed from a viscoplastic matrix that is reinforced by elastic or viscoplastic fibers attached to its plane surfaces, one constitutive equation is established by considering the viscoplastic behavior of the matrix as determined by an integral-type constitutive law whose intrinsic time-measure is pertinent to endochronic viscoplasticity. Attention is given to asymptotic cases where fiber stiffnesses and the hydrostatic modulus of the wafer are much larger than the latter's shear modulus. An explicit calculation is used when the stress field is uniaxial.
The cell theory has been previously employed to compute the equation of state of a disordered condensed system. It is now generalized to include anisotropic stresses. The condition of affine deformation is adopted, transforming an orginally spherical into an ellipsoidal cell. With a Lennard-Jones n-m potential between nonbonded centers, the formal expression for the deformational free energy is derived. It is to be evaluated in the limit of the linear elastic range. Since the bulk modulus in this limit is already known, it is convenient to consider a uniaxial deformation. To begin with, restrictions are made to the low-temperature limit in the absence of entropy contributions. Young's modulus and Poisson's ratio then follow.
Theoretical paper presents solutions of equations that describe polymeric aging. Solutions apply under such loading conditions as constant strain (stress relaxation), constant strain rate, and stress relaxation with sudden change of cross-link density. Theoretical models form framework for predicting chemomechanical aging behavior of elastomers and polymers.
The constitutive equation for the relaxation behavior of time-dependent, chemically unstable materials developed by Valanis and Peng (1983), which used the irreversible thermodynamics of internal variables in Eyring's absolute reaction theory and yielded a theoretical expression for the effect of chemical crosslink density on the relaxation rate, is presently applied to the creep behavior of a network polymer which is undergoing a scission process. In particular, two equations are derived which may for the first time show the relations between mechanical models and internal variables in the creep expressions, using a three-element model with a Maxwell element.
The rheological behavior of progressively shear thickening FM-9 solutions, a time-dependent shear thickening material with characteristics of threshold behavior, is investigated as part of a study of the rheological properties of antimisting jet fuel. Flammability test results and test configurations from various sources are evaluated. A correlation is obtained between the rheological behavior and the flammability tests such that, for a given system, such as a fixed solvent system and the FM-9 polymer system, the flammability criterion can be applied to a wide range of concentrations and temperatures.
New theory calculates anisotropies induced by large deformations in polymers. Theory was developed primarily for calculating anistropy of thermal expansivity, but is also applicable to thermal conductivity, elastic moduli and other properties. Theory assumes that in isotropic state, long polymer chains are randomly coiled and not oriented in particular direction. They acquire an orientation when material is deformed. As average molecular orientation increases with deformation, properties of bulk material exhibit averaging of the microscopic anistropies of the oriented molecular segments.
The rheological behavior of the recently developed polymer FM-9 in Jet A fuel and JP 8 fuel is reported. In aqueous solution, FM 9 is found to exhibit strong time-dependent shear thickening behavior. Induction time necessary for the onset of thickening is found to depend on shear rate, solvent, concentration, and molecular weight. Altering the nature of the solvent results in effects similar to those obtained by changing the concentration or molecular weight. A critical shear rate is derived, and is inversely proportional to the zero shear rate viscosity of the solution for the temperature and concentrations observed. The onset of shear thickening behavior appears to be related to the onset of viscoelastic response, and thus the time scale follows reduced variable behavior.
Simultaneous effects of temperature and concentration on tensile viscosity are investigated using a semi-empirical scaling law established to relate the concentration, temperature and deformation rate by a reduced deformation rate variable. Results show the onset of high viscosity occurring in the vicinity of the onset of non-Newtonian viscosity observed in a simple shear flow experiment. High viscosity is also compared with steady and dynamic shear data. Finally, the asymptotic solution of Hassager's kinetic theory of a bead-rod model for macromolecular solutions is compared with the data, indicating that tensile viscosity depends strongly on the molecular weight, the higher the molecular weight, the more sensitive the tensile viscosity in terms of the deformation rate.
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Tubeless siphon technique offers practical viscosity parameter for accurately determining non-Newtonian liquid tensile viscosity.
Solid propellants, sand-asphalt concrete and hard plastics showed rate sensitive mechanical behavior which, in addition, indicated that these materials have a permanent memory of the strain (or loading) path by which their present state was attained. A constitutive equation was formulated in general three dimensional tensorial form by means of irreversible thermodynamics. By using a very simple analytical form, it was shown that the mechanical behavior of solid propellants and sand-asphalt concrete can be readily described.
In the light of a three-chain model of statistical network theories of rubberlike elastic models, it is assumed that the free energy function of incompressible viscoelastic polymer solids is a separable, symmetric function of the principle stretch ratios and the hidden thermodynamic coordinates along the same directions. This assumption leads to a characterization of those viscoelastic polymer solids which exhibit the property of factorizability between the time and strain functions.
A tubeless siphon apparatus has been set up to measure extensional flow. In this apparatus, the liquid is continuously drawn into a capillary and, after steady flow has been established, the tube is raised above the liquid surface. With viscoelastic liquids, the flow continues and a column can be lifted from the reservoir. At the capillary entrance, an oscillating bead of excess liquid collects which interferes with both the flow and the measurements. This can be minimized by careful control of the liquid-column height. For homogeneous solutions, the column is symmetrical and tapers steadily from the liquid surface to the capillary entrance, with no bulging. Preliminary results show tensile viscosities 1000 times that of the Trouton coefficient and having a very strong dependence on deformation rate. A concentration-stretch rate-reduced variable scheme is proposed.
It is shown that by employing a torsion-tension test, it is possible to have a complete mapping near the origin of the two principal strain invariants associated with the rate of change of the strain energy function. However, the mathematical representation of the twist moment and normal forces vs strain and the strain energy function are complex. This problem is solved by using a set of solid cylindrical bars with different diameters such that the difference in diameter of two successive bars is small. The stress-strain equations can be grossly oversimplified by considering differences in twist moment and normal force as a function of difference in radius.
By using new invariants in the theory of finite elasticity an expression is obtained for the stored energy function of slightly compressible materials in which the effects of the distortional change (change of shape) and of the volume change are clearly separated. The volume-related terms are expressed as a function of the third invariant, the classical compressibility, and an induced anisotropy of the effective compressibility which is due to the large deformations. After evaluating the terms, using data on pressure, volume, uniaxial strain, and fractional volume change vs strain data on natural rubber from the literature, it is shown that the volume change contribution to the total stress observed in a simple tensile experiment can be clearly separated from the distortional contribution, even at finite strains.
A simple analytical form of induced anisotropy of heat conductivity of initially isotropic polymer solids results from employing the simplified theory of the three-chain model of the non-Gaussian network. The analytical form appears to be valid up to a stretch ratio of 2.65, which is the limit of existing experimental data. The effect of induced anisotropy on the temperature distribution, due to the large deformations, is illustrated for a highly expanded spherical shell and a cylindrical tube under a steady-state heat flow using the derived analytical form of the strain-dependent heat conductivity.