Stress and dynamics

De Witt T., Mezner. W. A rheological equation of state which predicts non-Newtonian viscosity, normal stresses and dynamics module. J. Appl.Phys., 1985, v. 26, p. 889-892. 

The static moduli failure stresses and dynamic moduli of both filled and unfilled polyurethanes are measured over a range of equihbrium water contents and these results are compared with those obtained from dry controls. The degradation of mechanical properties in the presence of water, and the hydrolytic disruption of filler/matrix adhesion is assessed. A quantitative relationship between the water content and mechanical properties is established and the mechanics of the water/polymer/filler interaction are considered. 4 refs. 

The static moduli, failure stresses and dynamic moduli of an unfilled and filled polyether-urethane were measured over a range of equilibrium water contents and the results obtained compared with those for dry controls. Fillers employed were barytes (and small amounts of fumed silica and carbon black) or iron oxide. A quantitative relationship between water content and mechanical properties was established and the mechanics of the water/ polymer/filler interaction assessed. (Tenth Annual Meeting of the Adhesion Society Inc., Williamsburg, Virginia, USA, 22-27 Feb. 1987). 4 refs. 

As discussed above, the nonlinear material response, P f) is the most connnonly encountered nonlinear tenn since vanishes in an isotropic medium. Because of the special importance of P we will discuss it in some detail. We will now focus on a few examples ofP spectroscopy where just one or two of the 48 double-sided Feymnan diagrams are important, and will stress the dynamical interpretation of the signal. A pictorial interpretation of all the different resonant diagrams in temis of wavepacket dynamics is given in [41]. 

The relaxation and creep experiments that were described in the preceding sections are known as transient experiments. They begin, run their course, and end. A different experimental approach, called a dynamic experiment, involves stresses and strains that vary periodically. Our concern will be with sinusoidal oscillations of frequency v in cycles per second (Hz) or co in radians per second. Remember that there are 2ir radians in a full cycle, so co = 2nv. The reciprocal of CO gives the period of the oscillation and defines the time scale of the experiment. In connection with the relaxation and creep experiments, we observed that the maximum viscoelastic effect was observed when the time scale of the experiment is close to r. At a fixed temperature and for a specific sample, r or the spectrum of r values is fixed. If it does not correspond to the time scale of a transient experiment, we will lose a considerable amount of information about the viscoelastic response of the system. In a dynamic experiment it may... 

The Weissenberg Rheogoniometer (49) is a complex dynamic viscometer that can measure elastic behavior as well as viscosity. It was the first rheometer designed to measure both shear and normal stresses and can be used for complete characteri2ation of viscoelastic materials. Its capabiUties include measurement of steady-state rotational shear within a viscosity range of 10 — mPa-s at shear rates of, of normal forces (elastic... 

The Imass Dynastat (283) is a mechanical spectrometer noted for its rapid response, stable electronics, and exact control over long periods of time. It is capable of making both transient experiments (creep and stress relaxation) and dynamic frequency sweeps with specimen geometries that include tension-compression, three-point flexure, and sandwich shear. The frequency range is 0.01—100 H2 (0.1—200 H2 optional), the temperature range is —150 to 250°C (extendable to 380°C), and the modulus range is 10" —10 Pa. 

G.T. Gray III and P.S. Follansbee, Influence of Peak Pressure and Pulse Duration on the Substructure Development and Threshold Stress Measurements in Shock-loaded Copper, in Impact Loading and Dynamic Behavior of Materials (edited by C.Y. Chiem, H.-D. Kunze, and L.W. Meyer), Deutsche Gesellschaft fuer Metall-kunde, Germany, 1988, 541 pp. 

More general dynamic loading conditions can lead to more complex domains of tensile stress and spall. For example, in a Taylor impact experiment (Kipp and Davison, 1981), where a short cylinder of material is caused to undergo symmetric normal impact on the flat surface of a large block of material, a roughly spherical region within the cylinder is carried into dynamic tension and can undergo spall. 

Note that this product of the spall stress and time is a constant provided F itself is constant. This relation is also useful for estimating fracture energy from dynamic spall data. Also, from (8.30) and (8.31) a relation for the fragment size... 

Numerical simulation of a complex dynamic fracture application can be illustrated by calculations of impact induced damage in a ceramic cylinder. The computer model used was originally developed for oil shale explosive fragmentation (Grady and Kipp, 1980), with various extended applications considered by Boade et al. (1981) and Chen et al. (1983). In this model, stress and strain are related through... 

The parameters for the model were originally evaluated for oil shale, a material for which substantial fracture stress and fragment size data depending on strain rate were available (see Fig. 8.11). In the case of a less well-characterized brittle material, the parameters may be inferred from the shear-wave velocity and a dynamic fracture or spall stress at a known strain rate. In particular, is approximately one-third the shear-wave velocity, m has been shown to be about 6 for various brittle materials (Grady and Lipkin, 1980), and k can then be determined from a known dynamic fracture stress using an analytic solution of (8.65), (8.66) and (8.68) in one dimension for constant strain rate. 

The effect of ozone is complicated in so far as its effect is largely at or near the surface and is of greatest consequence in lightly stressed rubbers. Cracks are formed with an axis perpendicular to the applied stress and the number of cracks increases with the extent of stress. The greatest effect occurs when there are only a few cracks which grow in size without the interference of neighbouring cracks and this may lead to catastrophic failure. Under static conditions of service the use of hydrocarbon waxes which bloom to the surface because of their crystalline nature give some protection but where dynamic conditions are encountered the saturated hydrocarbon waxes are usually used in conjunction with an antiozonant. To date the most effective of these are secondary alkyl-aryl-p-phenylenediamines such as /V-isopropyl-jV-phenyl-p-phenylenediamine (IPPD). 

The simplest dynamic system to analyse is one in which the stress and strain are changing in a sinusoidal fashion. Fortunately this is probably the most common type of loading which occurs in practice and it is also the basic deformation mode used in dynamic mechanical testing of plastics. 

In dynamic mechanical analysis of plastics, the material is subjected to a sinusoidal variation of stress and the strain is recorded so that 1, 2 and S can be determined. The classical variation of these parameters is illustrated in Fig. 2.55. 

Irrespective of the analysis approach, the representative volume element must be carefully defined and used. In fact, the representative volume element is crucial to the analysis and is the micromechanics analog of the free-body diagram in statics and dynamics. The representative volume element is of higher order than the free-body diagram because deformations and stresses are addressed in addition to forces. 

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