Stress-strain-time in creep

Figure 1.2 Highlighting load-time/viscoelasticity of plastics (1) stress-strain-time in creep and (2) strain-stress-time in stress relaxation.

The theory relating stress, strain, time and temperature of viscoelastic materials is complex. For many practical purposes it is often better to use an ad hoc system known as the pseudo-elastic design approach. This approach uses classical elastic analysis but employs time- and temperature-dependent data obtained from creep curves and their derivatives. In outline the procedure consists of the following steps ... 

Stress-strain-time data are usually presented as creep curves of strain versus log time. Sets of such curves, seen in Fig. 2-27, can be produced by smoothing and interpolating data on a computer. These data may also be presented in other ways, to facilitate the selection of information to meet specific design requirements. Sections may be taken t... 

In addition to those standardized tests, two other test methods, monotonic creep and microhardness, have been developed by Hough and Wright [48]. In the monotonic creep test, the strain response to a constant stress rate is monitored. The deviation of the stress-strain characteristics in air and in the fluid of interest is taken to be the initiation of ESC. This method is shown to differentiate to a high resolution between polymers, and in the short term, the ESCR of polymer/fluid pairs that exhibit mild/weak interactions can be distinguished. The microhardness method, in which a pyramidal diamond indentor is pressed into the surface of the polymer component at a known load and for a known time, has the potential for mass screening of plastic/fluid compatibility, including extraction as well as absorption, and should be of interest to polymer suppliers. 

In studying time dependence, Le. creep behaviour, it is necessary to carry out tests at several stress levels in each direction of interest in the oriented material. I his can involve a prohibitive amount of experimental work and, in practice, little is generally lost by reducing the tests to, say, one creep curve and one isochronous stress-strain curve in each direction. The problem then becomes one of selection of the absolute value of stress for each of the creep curves and is most severe when non-linearity and its anisotropy are well developed. The choice of stress levels is arbitrary but interesting special cases are (a) equal stress levels at all angles and (b) equal strain ranges at all angles. 

Figure 4.156 illustrates the detailed technical drawing of a dynamic mechanical analyzer by TA Instraments. The sample is enclosed in a variable, constant-temperature environment, not shown, so that the recorded parameters are stress, strain, time, frequency, and temperature. This instrument can be used for resonant and defined-frequency operation. Even creep and stress relaxation measurements can be performed. In creep experiments, a constant stress is applied at time zero and the... 

Viscoelastic phenomena may be described through three aspects, namely stress relaxation, creep and recovery. Stress relaxation is the decline in stress with time in response to a constant applied strain, at a constant temperature. Creep is the increase in strain with time in response to a constant applied stress, at a constant temperature. Recovery is the tendency of the material to return partially to its previous state upon removal of an applied load. The material is said to have memory as if it remembers where it came from. Because of the memory effect, in transient flows the behavior of viscoelastic fluids wUl be dramatically different from that of Newtonian fluids. Viseoelastie fluids are fiiU of instabilities. Some examples inelude instabilities in Taylor-Couette flow, in eone-and-plate and plate-and-plate flows (Larson 1992). The extrudate distortion, commonly called melt fraeture, is a notorious example of viscoelastic instability in polymer processing. The viseoelastie instability in injection molding can result in specific surface defects such as tiger stripes (Bogaerds et al. 2004). 

The computer can also be used to provide a singular solution to the required cross section. The time-stress-strain data to generate a set of creep curves for a specific material would be provided. The computer is then programmed with the problem of the stress-time profile for the part. Using the inverse curve as the strain relaxation curve, the computer can do an iterative solution to determine the minimum cross section. That would restrict the creep to the set amount in the desired design time. The WLF transformation can be done on the basic stress-strain time data to provide the solution for different operating temperatures. 

The alternative step-function experiment is stress-relaxation. A constant shear strain, say y, is applied at r = 0 and the stress time dependence of the stress is shown in Fig. 4.5(b). At low strains (as in creep) it is observed that the isochronals are linear. 

Viscoelastic creep When a plastic material is subjected to a constant stress, it undergoes a time-dependent increase in strain. This behavior is called creep. It is a plastic for which at long times of applied stress, such as in creep, a steady flow is eventually achieved. Thus in a generalized Maxwell model, all the dashpot viscosities must have finite values and in generalized models must have zero stiffness. 

The stress-strain-time data can be plotted as creep curves of strain vs. log time (Fig. 3.10 top view). Different methods are also used to meet specific design requirements. Examples of methods include creep curves at constant times to yield isochronous stress versus strain curves or at a constant strain, giving isometric stress versus log-time curves, as shown in the bottom views in Fig. 3.10. 

Characterization of the viscoelastic properties of polymers are classified into two categories static and dynamic measurements. The static mechanical tests involve creep, stress relaxation, and stress-strain measurements. In a creep test, a constant stress is applied to the specimen, and its deformation is measured as a function of time. In a stress relaxation test, the specimen is deformed a fixed amount, and the change in the stress is measured as a function of time. The stress-strain measurement is carried out by stretching the sample at constant tensile speed and then recording the load and deformation simultaneously. 

The deformation mechanisms associated with relaxation and creep are related to the long chain molecular structure of the polymer. Continuous loading gradually induces strain accumulation in creep as the polymer molecules rotate and unwind to accommodate the load. Similarly, in relaxation at a constant strain, the initial sudden strain occurs more rapidly than can be accommodated by the molecular structure. However, with time the molecules will again rotate and unwind so that less stress is needed to maintain the same strain level. It is also clear from these tests that polymers have some characteristics of a solid and some characteristics of a fluid. In a relaxation test, the ratio of the initial stress and strain is. 

The viscoelasticity of polymers is probed via several types of experiment. In stress relaxation measurements, the strain is held constant and the decay of stress is monitored as a function of time. In creep experiments, the stress is held constant and the increase in strain is monitored. It increases rapidly at first and then the rate of increase becomes smaller. Dynamic mechanical testing is probably the most important tool. It has the advantage that the deformation is applied under steady state conditions. Here an oscillatory shear deformation is applied to the sample and the dynamic elastic moduli are determined (Section 1.9.3). 

Stress-strain tests are considered short-term tests, which means that the mechanical loading is applied within a relatively short period of time. This limits the usefulness of stress-strain tests in the actual design of a plastic part. Stress-strain tests fail to take into account the dependence of rigidity and strength of plastics on time. This serious limitation can be overcome with the use of creep and stress relaxation data while designing a part. 

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