Static Stresses

The mechanical properties of plastics enable them to perform in a wide variety of end uses and environments, often at lower cost than other design materials such as metal or wood. This section reviews the static property aspects that relate to short term loads. 

As reviewed thermoplastics (TPs) being viscoelastic respond to induced stress by two mechanisms viscous flow and elastic deformation. Viscous flow ultimately dissipates the applied mechanical energy as frictional heat and results in permanent material deformation. Elastic deformation stores the applied mechanical energy as completely recoverable material deformation. The extent to which one or the other of these mechanisms dominates the overall response of the material is determined 

With the longer duration of material stress or strain, the more time for viscous flow to occur that results in the likelihood of viscous flow and significant permanent deformation. As an example when a TP product is loaded or deformed beyond a certain point, it yields and immediate or eventually fails. Conversely, as the temperature or the duration or magnitude of material stress or strain decreases, viscous flow becomes less likely and less significant as a contributor to the overall response of the material and the essentially instantaneous elastic deformation mechanism becomes predominant. 

Changing the temperature or the strain rate of a TP may have a considerable effect on its observed stress-strain behavior. At lower temperatures or higher strain rates, the stress-strain curve of a TP may exhibit a steeper initial slope and a higher yield stress. In the extreme, the stress-strain curve may show the minor deviation from initial linearity and the lower failure strain characteristic of a britde material. 

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Static stress A stress whose magnitude remains at a constant value. Contrast with cyclic stress. 

Gray and Follansbee [44] quasi-statically tested OFE copper samples that had been shock loaded to 10 GPa and pulse durations of 0.1 fis, 1 /rs, and 2 fus. The quasi-static stress-strain curves are shown in Fig. 7.10 with the response of annealed starting copper included for comparison. The yield strength of shock-loaded copper is observed to increase with pulse duration, as the work-hardening rate is seen to systematically decrease. 

Sulfide Stress Cracking) on steels over Rockwell C 22. (4) static stresses. other equipment handling sour gas, oil and/or water wherein H2S and H2O (liquid phase) are present up to about 150 F, where sulfide stress cracking slows down perceptibly. stainless steels with Rockwell hardness over C 22. (4) into crystal structure, exact mechanism uncertain. Sulfur expedites absorption of atomic H into grain structure. (4) if feasible use inhibitors and/or resistant coatings where feasible time or heating up will permit H to diffuse out but will not relieve any areas when H2 has concentrated. 

Fracture mechanics has also been used to predict failure under static stresses. The basis of this is that observed crack growth rates have been found to be... 

Figure 4-70. Efficiencies of wire ropes bent around stationary sheaves (static stresses oniy) [11].

Bundy, K. J., Vogelbaum, M. A. and Desai, V. H., The Influence of Static Stress on the Corrosion Behaviour of 316L Stainless Steel in Ringer s Solution , Journal of Biomedical Materials Research, 20, 493-505 (1986)... 

The eccentric rotation of filler in virtue of the variant shear rates along the extrudate cross-section has been proposed as an alternative to the plug flow mechanism to explain this orientation pattern [355]. In [357] it was noted that the cross-wise orientation of fibers at the core of molded specimens was established only after the entire mold had been filled the authors assumed this orientation to be due to the quasi-static stresses arising in the material under pressure. 

Linear viscoelasticity Linear viscoelastic theory and its application to static stress analysis is now developed. According to this theory, material is linearly viscoelastic if, when it is stressed below some limiting stress (about half the short-time yield stress), small strains are at any time almost linearly proportional to the imposed stresses. Portions of the creep data typify such behavior and furnish the basis for fairly accurate predictions concerning the deformation of plastics when subjected to loads over long periods of time. It should be noted that linear behavior, as defined, does not always persist throughout the time span over which the data are acquired i.e., the theory is not valid in nonlinear regions and other prediction methods must be used in such cases. 

It is demonstrated in Figure 22.11 that the quasi-static stress-strain cycles at different prestrains of silica-filled rubbers can be well described in the scope of the above-mentioned dynamic flocculation model of stress softening and filler-induced hysteresis up to large strain. Thereby, the size distribution < ( ) has been chosen as an isotropic logarithmic normal distribution (< ( i) = 4> ) = A( 3)) ... 

Environmental Cracking The problem of environmental cracking of metals and their alloys is very important. Of all the failure mechanism tests, the test for stress corrosion cracking (SCC) is the most illusive. Stress corrosion is the acceleration of the rate of corrosion damage by static stress. SCC, the limiting case, is the spontaneous cracking that may result from combined effects of stress and corrosion. It is important to differentiate clearly between stress corrosion cracking and stress accelerated corrosion. Stress corro-... 

On poly(dimethylsiloxane) (PDMS) networks having comb-like crosslinks, torsional vibration experiments and static stress-strain measurements at small deformations were performed as a function of temperature, torsional vibrations also as a function of frequency. 

Dynamic properties are more relevant than the more usual quasi-static stress-strain tests for any application where the dynamic response is important. For example, the dynamic modulus at low strain may not undergo the same proportionate change as the quasi-static tensile modulus. Dynamic properties are not measured as frequently as they should be simply because of high apparatus costs. However, the introduction of dynamic thermomechanical analysis (DMTA) has greatly widened the availability of dynamic property measurement. 

Figure 3.38. Examples of dynamic stress leading to failure at approximately 1 000000 cycles at20°C versus quasi-static stress at yield...

Y. K. Vohra, Spectroscopic studies on diamond anvil under extremes static stress, in Recent Trends in High Pressure Research, A. K. Singh, ed., Oxford and IBH Pubhshing Co., New Dehh, 1992. 

The integral U((7m) represents the area under the engineering stress-strain master curve up to the maximum stress (7. The static stress is a function of the energy density function U([Pg.18]

A dynamic statistical approach is used to predict dynamic stresses in a hyperboloidal cooling tower due to earthquakes. It is shown that the configuration associated with one circumferential wave is the only one which is excitable by earthquake force and that the first mode of such configuration is dominant. An equivalent static load is calculated on this basis. Numerical data presented give coefficients for equivalent static loads, natural frequencies of cooling towers, and static stresses for a seismic load. 21 refs, cited. 

The fractures on a plane surface, created by the collisions of hard spherical particles at low-impact velocities, may form a conical crack according to the Hertzian quasi-static stress theory. In a multiple-impact situation, the conical cracks meet those extending from neighboring impact sites, and then the brittle material becomes detached. Once appreciable damage is done, the cracking mechanism may be altered because the particles no longer strike on a plane surface nevertheless the brittle removal continues by the successive formation and intersection of cracks. 

The onset of powder motion in a hopper is due to stress failure in powders. Hence, the study of a hopper flow is closely related to the understanding of stress distribution in a hopper. The cross-sectional averaged stress distribution of solids in a cylindrical column was first studied by Janssen (1895). Walker (1966) and Walters (1973) extended Janssen s analysis to conical hoppers. The local distributions of static stresses of powders can only be obtained by solving the equations of equilibrium. From stress analyses and suitable failure criteria, the rupture locations in granular materials can be predicted. As a result, the flowability of granular materials in a hopper depends on the internal stress distributions determined by the geometry of the hopper and the material properties of the solids. 

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