Creep physical model

In the railroad industry, structures usually are designed by applying static load assumptions. In reality, however, cyclic loading, creep, temperature, and environmental influences occur which should be considered in adhesive joint design. Generic physical models taking into account all the possible effects are not applicable for a practical design concept. 

The ability of the physical model to correctly and quantitatively represent the macroscopic creep behavior is shown in Figures 16.9 and 16.10. 

Significant scatter is often evident in time to failure data obtained from stress rupture tests conducted on either neat materials or on bonded joints. This scatter may obscure trends and frustrate the user. Results are typically plotted as load level versus the time to failure, a form that is analogous to S-N plots used in fatigue tests (see Durability Fatigue). In keeping with the principles of polymer physics, the time to failure axis should be plotted on a log scale, as illustrated in Fig. 1. Many creep-rupture models for homogeneous materials are based on forms like... 

Figure 85 shows the CR spectrum (micro-plasticity) of brittle porcelain at low temperatures compared with its fracture stress Of vs temperature dependence. One can see that the increased micro-plasticity (creep rates) arising at ca. 200 K in porcelain corresponds to a bend in the Of(T) plot towards the higher strength values. Such an effect is in accordance with a physical model for brittle fracture [278,338,339] that takes the role of micro-plasticity (local shear strains in the loaded brittle solid) into account. The latter results in some relaxation of dangerous local overstresses and, therefore, increasing the strength. 

The determination of the initial conditions is best accomplished by inspection of the physical model. Since the input stress is constant for the creep test, the stress rate is zero, 6 = 0 and the differential equation for the three-parameter solid, Eq. 5.8, becomes. 

Service lifetime prediction of polymers and/or polymer based materials may be undertaken from different types of tests, such as creep behavior tests (linear and non-linear creep, physical aging, time-dependent plasticity), fatigue behavior tests (stress transfer and normalized life prediction models, empirical fatigue theories, fracture mechanics theory and strength degradation) and standard accelerated aging tests (chemical resistance, thermal stability, liquid absorption) [32]. 

Based on the above consideration, simphfied models are deemed preferable for the determination of the gravity load distribution, since they are easy to calibrate and their reliability is not necessarily inferior to that of more refined models. Such a simplified physical model is shown in Fig. 11a. The model consists of springs and dash-pots to represent the instantaneous axial stiffness and the viscoelastic (creep) properties of the RC columns and the masonry infill. The gap Uq, shown in Fig. 11a, corresponds to the short-term deformation of the coluirms due to the gravity loads that are applied before the constmction of the infill walls. The spring-and-dashpot assemblages representing the concrete columns and masonry walls can be calibrated with data from... 

Time-temperature superposition is frequently applied to the creep of thermoplastics. As mentioned above, a simple power law equation has proved to be useful in the modelling of the creep of thermoplastics. However, for many polymers the early stages of creep are associated with a physical relaxation process in which the compliance (D t)) changes progressively from a lower limit (Du) to an upper limit (DR). The rate of change in compliance is related to a characteristic relaxation time (x) by the equation ... 

Kinetic models of physical aging are available in the literature (Kovacs et al., 1979). During this process, volume changes are very low, typically less than 1 m3 kg but they affect a component of free volume that plays a crucial role in creep, relaxation, yielding and fracture (see Chapter 12). 

However, in the transition from model to full-scale, a complete similarity cannot be achieved. This is because in using the same material system ReH = p v L/H = idem, v /L = idem cannot be ensured at the same time. It is recommended to use the same material system, but to change the model scale. An exception to this is represented by pure hydrodynamic processes in the creeping flow region (p irrelevant) at steady-state and isothermal conditions. Here mechanical similarity can be obtained in spite of constant physical properties see Example 26 Single-screw machines. 

A second important event was the development by Hosemann (1950) of a theory by which the X-ray patterns are explained in a completely different way, namely, in terms of statistical disorder. In this concept, the paracrystallinity model (Fig. 2.11), the so-called amorphous regions appear to be the same as small defect sites. A randomised amorphous phase is not required to explain polymer behaviour. Several phenomena, such as creep, recrystallisation and fracture, are better explained by motions of dislocations (as in solid state physics) than by the traditional fringed micelle model. 

The main consequence of this reduced mobility is an extension of the glass transition region towards the high temperature side it will show a lower and an upper value, viz. Tg(L) and Tg(U), the values of the undisturbed amorphous region and that of regions with reduced mobility. By means of this model, Struik could interpret his measurements on volume relaxation (physical ageing) and creep in semicrystalline materials. 

A wide variety of tests is performed in TMA, which are adapted from physical tests that were used before the instrument became commonly available. These tests may also be modeled or mimicked in TMA, such as heat distortion (Fig. 9) and softening points. Methods to obtain the modulus, compressive viscosity, and penetrative viscosity have been developed. Many of these methods, such as ASTM D648 for example, will specify the stress the sample needs to be exposed to during the run. In D684, a sample is tested at 66 and 264 psi. Most TMAs on the market today have software available that allows them to generate stress—strain curves and to run creep—recovery experiments. Some are also capable of limited types of stress relaxation studies (for example a constant gauge length test " ). 

First, volatiles exert an important control on the physical properties of the mantle. For example, the presence of water reduces the strength of olivine aggregates and seriously alters the viscosity of the mantle. Experimental studies show that at 300 MPa, in the presence of water, the viscosity of olivine aggregates deformed in the dislocation creep regime is reduced by up to a factor of 140. Thus a wet mantle is a low viscosity mantle. Conversely a mantle that is dried out by partial melting will be stiffer and more refractory, as is the case for the lithospheric "lid" to modern oceanic mantle. Thus, if it is possible to estimate the volatile content of the mantle both now and in the Archaean, it will be possible to set some physical constraints on models of mantle evolution over time. 

This equation indicates that the deformation does not appear instantaneously on application of stress, hut it increases gradually, attaining asymptotically its maximum value e=Voigt model is thus said to exhibit retarded elastic deformation in creep experiments. The quantity 7]IE=X is called a retardation time. It is the time (t=A) at which the deformation is retarded hy 1/e of its maximum value. (The physical meaning of tj/E for Maxwell and Voigt models should not he confused.)... 

After the creep simulation is stable, the stress neutral surface occurs in the anticline axis and the nearby area of the physical computing model, the horizontal stress of the nodes tends to zero on the surface. This is mainly because in the course of geological formations the coal here is prone to be damaged by the tectonic stress, the coal was damaged the most seriously, then the coal almost lost the ability to carry the stress load and the coal stress here tends to zero. 

Struik [3] originally proposed a method to model physical aging through the use of a momentary creep master curve obtained from a series of short term creep tests performed at various aging times. The momentary creep master curve was then used in conjunction with the effective time theory to predict long term creep in a polymer in the presence of physical aging. 

A comprehensive analytical model for predicting long term durability of resins and of fibre reinforced plastics (FRP) taking into account viscoelastic/viscoplastic creep, hygrothermal effects and the effects of physical and chemical aging on polymer response has been presented. An analytical tool consisting of a specialized test-bed finite element code, NOVA-3D, was used for the solution of complex stress analysis problems, including interactions between non-linear material constitutive behavior and environmental effects. 

Hadjicrnistantinou and Simek [35] investigated the case for fuUy developed flow with uniform wall temperature. They found that Eqs. 7 and 17 with both F = 1 and = 1 were adequate in determining the physics in this slip-flow problem. They compared their results with the direct simulation Monte Carlo method. They concluded that slip-flow models neglecting viscous dissipation, expansion cooling, and thermal creep were adequate in describing the heat transfer. However, when considering viscous dissipation, the Nu expression becomes [34]... 

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