Short-time stresses

For high frequencies uj > 1 /tq, there are no relaxation modes in the Rouse model. The storage modulus becomes independent of frequency, and equal to the short time stress relaxation modulus, which is kT per monomer G uj) (pkTjb. This high-frequency saturation is not included in Eqs (8.49) and (8.50). At low frequencies a < 1/tr, the storage modulus is proportional to the square of frequency and the loss modulus is pro-portional to frequency, as is the case for the terminal response of any viscoelastic liquid. 

Fig. 2-3. Uniaxial tension creep and short-time stress-strain diagram for polymethylmethacrylate at 73.4 2 F. (From Engineering Design for Plastics, Eric Baer, Reinhold, 1964)...

The stress relaxation time in such polymers is long, consequently an intense, short time stress will not permit the macromolecule accommodation with the stress, so that they will finally split. 

A material tends to show elastic behavior at low temperatures or for a short time stress application ... 

Relaxation and recovery of the original state are total for short-time stresses entailing a fully reversible deformation. 

An experimental activity on the stress measurement of a pressure vessel using the SPATE technique was carried out. It was demontrated that this approach allows to define the distribution of stress level on the vessel surface with a quite good accuracy. The most significant advantage in using this technique rather than others is to provide a true fine map of stresses in a short time even if a preliminary meticolous calibration of the equipment has to be performed. 

Mechanical Properties Mechanical properties of wide interest include creep, rupture, short-time strengths, and various forms of ductihty, as well as resistance to impact and fatigue stresses. Creep strength and stress rupture are usually of greatest interest to designers of stationary equipment such as vessels and furnaces. 

Metals Successful applications of metals in high-temperature process service depend on an appreciation of certain engineering factors. The important alloys for service up to I,I00°C (2,000°F) are shown in Table 28-35. Among the most important properties are creep, rupture, and short-time strengths (see Figs. 28-23 and 28-24). Creep relates initially applied stress to rate of plastic flow. Stress... 

Pressure Vessels. Refineries have many pressure vessels, e.g., hydrocracker reactors, cokers, and catalytic cracking regenerators, that operate within the creep range, i.e., above 650°F. However, the phenomenon of creep does not become an important factor until temperatures are over 800°F. Below this temperature, the design stresses are usually based on the short-time, elevated temperature, tensile test. 

In Section 4.2.2 the central role of atomic diffusion in many aspects of materials science was underlined. This is equally true for polymers, but the nature of diffusion is quite different in these materials, because polymer chains get mutually entangled and one chain cannot cross another. An important aspect of viscoelastic behavior of polymer melts is memory such a material can be deformed by hundreds of per cent and still recover its original shape almost completely if the stress is removed after a short time (Ferry 1980). This underlies the use of shrink-fit cling-film in supermarkets. On the other hand, because of diffusion, if the original stress is maintained for a long time, the memory of the original shape fades. 

Internal or external defect in a plastic caused by tensile stresses below its short-time mechanical strength. 

A rod of polypropylene, 10 mm in diameter, is clamped between two rigid fixed supports so that there is no stress in the rod at 20°C. If the assembly is then heated quickly to 60°C estimate the initial force on the supports and the force after 1 year. The tensile creep curves should be used and the effect of temperature may be allowed for by making a 56% shift in the creep curves at short times and a 40% shift at long times. The coefficient of thermal expansion for polypropylene is 1.35 x 10 °C in this temperature range. 

Both time-related failure rates and demand-related failure rates can apply to and be reported for many pieces of equipment. Both types of rates are included in some of the data tables in Chapter 5. If a piece of equipment is in continuous service, such as a transformer, the failure rate is dominated by time-related stresses compared to demand-related stresses. Other failure rates may be dominated by demands. Take a piece of wire and repeatedly bend it. With each bend its probability of catastrophic failure increases. In a relatively short time, if the bending is continued, the wire will fail. On the other hand, the same wire could be installed in a manner that would prevent mechanical bending demands. In this case, the occurrence of catastrophic wire breakage would be remote. In the first instance, the failure rate is dominated by demand stresses and in the second by time-related stresses, such as corrosion. 

Where these valves are used, the time available to warm up the pipe work will be known, as it is set on the valve control. In other cases, details of the start-up procedure must be known so that the time may be estimated. Thus boilers started from cold may be fired for a short time, shut off for a period while temperatures equalize, and then fired again. Boilers may be protected from undue stress by these short bursts of firing, which extend the warm-up time and reduce the rate at which the condensate in the mains must be discharged at the traps. 

Fig. 2-23 Viscoelastic creep behavior typical of many TPs trader short-term stress (a) input stress vs. time profile and (b) output strain vs. time profile.

Fig. 2-50 Guide to maximum short-time tensile stress vs. temperature.

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. 

After obtaining the prototypes, tests must be made to determine the utility. Generally these include a short time destructive test to determine the strength and to check out the basic design. Another test that is done is to use the product in the projected environment with stress levels increased in a rational manner to make for an accelerated life test. Other tests may include consumer acceptance tests to determine what instructions in proper use are required, tests for potential safety hazards, electrical tests, self-extinguishing tests, and any others that the product requires. In the case of high risk products, the test program is continued even after the product enters service. 

Effect of UV on Productivity of the Southern Ocean. Has ozone depletion over Antarctica affected the productivity of the Southern Ocean There is no easy answer. First, one has to take into account the fact that the drastic decrease of ozone over Antarctica has been reported as recently as 1976, a relatively short time in the evolution of the organisms to develop mechanisms to cope with elevated UV. One of the most vexing problems in studying the effects of UV radiation on productivity, is a dearth of historical data on the level of UV. Without these baselines, normal fluctuations could easily be interpreted as decline in productivity. Second, there is a host of biotic and abiotic factors that play significant roles in governing the productivity of the Southern Ocean (40). Ultraviolet radiation is but one more complicating factor to be considered in an already stressful environment. 

In Equation 1, t is a thermal vibration frequency, U and P are, respectively activation energy and volume whereas c is a local stress. The physical significance and values for these parameters are discussed in Reference 1. Processes (a)-(c) are performed with the help of a Monte-Carlo procedure which, at regular short time intervals, also relaxes the entanglement network to its minimum energy configuration (for more details, see Reference 1). 

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