Stress relaxation, plastics

Testing of plastics - Stress relaxation test (withdrawn)... 

The test of relaxation behaviour is described in (outdated) DIN 53441 1984 Testing of Plastics, Stress Relaxation Test. The principle of the test method is that an elongation is imposed on the test specimen by a uniaxial tensile force which is then kept constant. The force necessary to... 

Tensile, Compressive, and Flexural Creep and Creep-Rupture of Plastics Stress Relaxation of Plastics... 

Another aspect of plasticity is the time dependent progressive deformation under constant load, known as creep. This process occurs when a fiber is loaded above the yield value and continues over several logarithmic decades of time. The extension under fixed load, or creep, is analogous to the relaxation of stress under fixed extension. Stress relaxation is the process whereby the stress that is generated as a result of a deformation is dissipated as a function of time. Both of these time dependent processes are reflections of plastic flow resulting from various molecular motions in the fiber. As a direct consequence of creep and stress relaxation, the shape of a stress—strain curve is in many cases strongly dependent on the rate of deformation, as is illustrated in Figure 6. 

Measurements of stress relaxation on tempering indicate that, in a plain carbon steel, residual stresses are significantly lowered by heating to temperatures as low as 150°C, but that temperatures of 480°C and above are required to reduce these stresses to adequately low values. The times and temperatures required for stress reUef depend on the high temperature yield strength of the steel, because stress reUef results from the localized plastic flow that occurs when the steel is heated to a temperature where its yield strength is less than the internal stress. This phenomenon may be affected markedly by composition, and particularly by alloy additions. 

Stress-relaxation measurements, where stress decay is measured as a function of time at a constant strain, have also been used extensively to predict the long-term behavior of styrene-based plastics (9,12). These tests have also been adapted to measurements in aggressive environments (13). Stress-relaxation measurements are further used to obtain modulus data over a wide temperature range (14). 

Romanchenko and Stepanov (1981) recognized that spall in an elastic-plastic material can involve plastic release to the tensile failure stress followed by elastic recovery as stress relaxation at the spall plane proceeds. Thus, the... 

Stress Relaxation. Another important consequence of the viscoelastic nature of plastics is that if they are subjected to a particular strain and this strain is held constant it is found that as time progresses, the stress necessary to maintain this strain decreases. This is termed stress relaxation and is of vital importance in the design of gaskets, seals, springs and snap-fit assemblies. This subject will also be considered in greater detail in the next chapter. 

The thorough and persistent work on precursor decay (the dependence of Hugoniot elastic limit on propagation distance) of Duvall s Washington State University group was successful in demonstrating that precursor attenuation was due to both stress relaxation and hydrodynamic attenuation. Typical data on crystalline LiF is shown in Fig. 2.7. Observed plastic strain... 

Object in this section is to review how rheological knowledge combined with laboratory data can be used to predict stresses developed in plastics undergoing strains at different rates and at different temperatures. The procedure of using laboratory experimental data for the prediction of mechanical behavior under a prescribed use condition involves two principles that are familiar to rheologists one is Boltzmann s superposition principle which enables one to utilize basic experimental data such as a stress relaxation modulus in predicting stresses under any strain history the other is the principle of reduced variables which by a temperature-log time shift allows the time scale of such a prediction to be extended substantially beyond the limits of the time scale of the original experiment. 

The stress-relaxation behavior of a material is normally determined in either the tensile or the flexural mode. In these experiments, a material specimen is rapidly elongated or compressed to produce a specified strain level and the load exerted by the specimen on the test apparatus is measured as a function of time. Specimens of certain plastics may fail during tensile or flexural stress-relaxation experiments. 

The rate of creep and stress relaxation of TPs increases considerably with temperature those of the TSs (thermoset plastics) remain relatively unaffected up to fairly high temperatures. The rate of viscoelastic creep and stress relaxation at a given temperature may also vary significantly from one TP to an-... 

Basics Creep data can be very useful to the designer. In the interest of sound design-procedure, the necessary long-term creep information should be obtained on the perspective specific plastic, under the conditions of product usage (Chapter 5, MECHANICAL PROPERTY, Long-Term Stress Relaxation/Creep). In addition to the creep data, a stress-strain diagram under similar conditions should be obtained. The combined information will provide the basis for calculating the predictability of the plastic performance. 

Stress relaxation. In a stress-relaxation test a plastic is deformed by a fixed amount and the stress required to maintain this deformation is measured over a period of time (Fig. 2-33) where (a) recovery after creep, (b) strain increment caused by a stress step function, and (c) strain with stress applied (1) continuously and (2) intermittently. The maximum stress occurs as soon as the deformation takes place and decreases gradually with time from this value. From a practical standpoint, creep measurements are generally considered more important than stress-relaxation tests and are also easier to conduct. 

With crystalline plastics, the main effect of the crystallinity is to broaden the distribution of the relaxation times and extend the relaxation stress too much longer periods. This pattern holds true at both the higher and low extremes of crystallinity (Chapter 6). With some plastics, their degree of crystallinity can change during the course of a stress-relaxation test. This behavior tends to make the Boltzmann superposition principle difficult to apply. 

Many designs incorporate the phenomenon of stress-relaxation. For example, in many products, when plastics are assembled they are placed into a permanently deflected condition, as for instance press fits, bolted assemblies, and some plastic springs. In time, with the strain kept constant the stress level will decrease, from the same internal molecular movement that produces creep. This gradual decay in stress at a constant strain (stress-relaxation) becomes important in applications such as preloaded bolts and springs where there is concern for retaining the load. The amount of relaxation can be measured by applying a fixed strain to a sample and then measuring the load with time. 

Failure can be considered as an actual rupture (stress-rupture) or an excessive creep deformation. Correlation of stress relaxation and creep data has been covered as well as a brief treatment of the equivalent elastic problem. The method of the equivalent elastic problem is of major assistance to designers of plastic products since, by knowing the elastic solution to a problem, the viscoelastic solution can be readily deduced by simply replacing elastic physical constants with viscoelastic constants. 

Creep and stress relation Creep and stress relaxation behavior for plastics are closely related to each other and one can be predicted from knowledge of the other. Therefore, such deformations in plastics can be predicted by the use of standard elastic stress analysis formulas where the elastic constants E and y can be replaced by their viscoelastic equivalents given in Eqs. 2-19 and 2-20. 

The trend of this factor is generally consistent with plastics behaviors. However, stress-relaxation information has to be interrelated with the individual behavior of the plastics, as derived from the relaxation-test data (Chapter 2). 

The time/temperature-dependent change in mechanical properties results from stress relaxation and other viscoelastic phenomena that are typical of these plastics. When the change is an unwanted limitation it is called creep. When the change is skillfully adapted to use in the overall design, it is referred to as plastic memory. 

The mechanical concepts of stress are outlined in Fig. 1, with the axes reversed from that employed by mechanical engineers. The three salient features of a stress-strain response curve are shown in Fig. la. Initial increases in stress cause small strains but beyond a threshold, the yield stress, increasing stress causes ever increasing strains until the ultimate stress, at which point fracture occurs. The concept of the yield stress is more clearly realised when material is subjected to a stress and then relaxed to zero stress (Fig. Ih). In this case a strain is developed but is reversed perfectly - elastically - to zero strain at zero stress. In contrast, when the applied stress exceeds the yield stress (Fig. Ic) and the stress relaxes to zero, the strain does not return to zero. The material has irreversibly -plastically - extended. The extent of this plastic strain defines the residual strain. 

This paper describes application of mathematical modeling to three specific problems warpage of layered composite panels, stress relaxation during a post-forming cooling, and buckling of a plastic column. Information provided here is focused on identification of basic physical mechanisms and their incorporation into the models. Mathematical details and systematic analysis of these models can be found in references to the paper. 

Unlike other aqueous dental cements, the zinc polycarboxylate retains plastic characteristics even when aged and shows significant stress relaxation after four weeks (Paddon Wilson, 1976). It creeps under static load. Wilson Lewis (1980) found that the 24-hour creep value for one cement, under a load of 4-6 MPa, was 0-7 % in 24 hours, which was more than that of a zinc phosphate cement (0-13 %) and a glass-ionomer cement (0-32%), but far less than that of the zinc oxide eugenol cement (2-2%). 

Figure 5.18 This figure shows how the properties of a glass polyalkenoate cement change as it ages. S is the compressive strength, E the modulus, a a stress-relaxation function, and c a strain-conversion function from elastic to plastic strain (Paddon Wilson, 1976).

Water is a natural plasticizer for many polar polymers such as the nylons (23K). polyester resins (239), and cellulosic polymers (240). It strongly shifts in epoxies (241.242). Thus the creep and stress-relaxation behavior of such polymers can be strongly dependent on the relative humidity or the atmosphere. 

Crystallinity—about.i to 15% (213,232). The creep of plasticized poly(vinyl chloride) polymers as a function of temperature, concentration, and kind of plasticizer has been studied by many workers, including Aiken et ai. (232), Neilscn ct ai. (234), and Sabia and Eirich (243). These last workers also studied stress relaxation (244). In the case of crystalline polymers, plasticizers and Copolymerization reduce the melting point and the degree of Crystallinity. These factors tend to increase the creep and stress relaxation, especially at temperatures approaching the melting point. 

In a further development of the continuous chain model it has been shown that the viscoelastic and plastic behaviour, as manifested by the yielding phenomenon, creep and stress relaxation, can be satisfactorily described by the Eyring reduced time (ERT) model [10]. Creep in polymer fibres is brought about by the time-dependent shear deformation, resulting in a mutual displacement of adjacent chains [7-10]. As will be shown in Sect. 4, this process can be described by activated shear transitions with a distribution of activation energies. The ERT model will be used to derive the relationship that describes the strength of a polymer fibre as a function of the time and the temperature. 

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