Creep stress-strain-time

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... 

Fig. 2-37 Tensile stress-strain-time correlation resulting from creep for PC.

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

The time-dependent elastic moduli of the concretes were obtained from the creep stress-strain curves and were fitted into Eq.(3) ... 

FIGURE 4.9 Creep curve strain-time under constant stress. 

The flexural creep stiffness, or the flexural creep compliance, describes the low-temperature stress-strain time response of bituminous binder at the test temperature within the range of linear viscoelastic response. 

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... 

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. 

Figure 3-45. The tensile stress—strain—time correlation resulting from creep for polycarbonates at 23 C (73 F). Courtesy, Mobay Chemical Corp.

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. 

The basic variables involved are stress, strain, time, temperature, and strain rate. Any two of these basic variables may be selected as plotting coordinates, with the remaining variables treated as parametric constants for a given curve. Three commonly used methods for extrapolating short-time creep data to long-term applications are the abridged method, the mechanical acceleration method, and the thermal acceleration method. 

Figure 11.1 The stress-strain time relation obtained from creep. (Reproduced from Turner, S. (1966) The strain response of plastics to complex stress histories. Polym. Eng. Sci., 6, 306. Copyright (1966) Society of Plastics Engineers.)...

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. 

ISOCHRONOUS STRESS - STRAIN CURVE CREEP MODULUS - TIME CURVE... 

Figure 9.10. Presentation of creep data sections through the creep curves at constant time and constant strain give curves of isochronous stress-strain, isometric stress-log (time) and creep modulus-log (time). (From ICI Technical Service Note PES 101, reproduced by permission of ICI...

Long-term deformation such as shown by creep curves and/or the derived isochronous stress-strain and isometric stress-time curves, and also by studies of recovery for deformation. 

The maximum temperature at which mild steel can be used is 550°C. Above this temperature the formation of iron oxides and rapid scaling makes the use of mild steels uneconomical. For equipment subjected to high loadings at elevated temperatures, it is not economical to use carbon steel in cases above 450°C because of its poor creep strength. (Creep strength is time-dependent, with strain occurring under stress.)... 

The most characteristic features of viscoelastic materials are that they exhibit a time dependent strain response to a constant stress (creep) and a time dependent stress response to a constant strain (relaxation). In addition when the... 

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