Temperature-dependent stress-strain

Figure 11. Temperature-dependent stress—strain curves for [0] composite laminates. (Reproduced from reference 12.)...

The temperature-dependent stress-strain-behaviour of iPP is shown in figure 3. 

To describe the temperature-dependent stress-strain behaviour of semi-crystalline materials we established a model on the basis of the described structural elements. It describes the interaction of the temperature-dependent mobility of the amorphous phase, the initially relative stable crystalline phase, the step>-wise re-arrangement of the crystalline phase with respect to orientation and transformation via crystallite fragments and extended chains into fibrils. It will be soon published separately. 

Great importance is attached to the determination of required materials data, since simulations can only be as reliable as the underlying input data. Here all caloric materials data were taken from literature or databases. Only mechanical data, in particular temperature depending stress-strain curves, are rarely available. Therefore one-dimensional tensile tests were performed at different temperatures by using the Gleeble3500 equipment. 

Fig. 3.10 Temperature dependent stress-strain response of a typical brittle epoxy. (Data from Kiel, et al. (1983))...

Kawashima, K. Ito, T. Sakuragi, M. Strain rate and temperature dependent stress-strain curves of Sn-Pb eutectic solder. J. Mater. Sci. 1992, 27, 6387-6390. 

When an engineering plastic is used with the structural foam process, the material produced exhibits behavior that is easily predictable over a large range of temperatures. Its stress-strain curve shows a significantly linearly elastic region like other Hookean materials, up to its proportional limit. However, since thermoplastics are viscoelastic in nature, their properties are dependent on time, temperature, and the strain rate. The ratio of stress and strain is linear at low strain levels of 1 to 2%, and standard elastic design... 

Depending on the material and deformation conditions (strain rate, temperature) other stress-strain curve shapes can be observed (Fig. 2b and c). In Fig. 2b, the plastic flow occurs at the same stress level as that required for the yielding so the strain softening does not exist. In the case shown in Fig. 2c, the strain hardening happens very close to yielding, suppressing both strain softening and plastic flow behaviour. 

It is usual to assume that the shear yield stress has the same temperature dependence and strain rate dependence as the flow stress of the polymer in the active zone of the craze, i.e., n, = n, and in fact usually one go even further and sets How-... 

The safety of ship lock is related to the people s life and property in the downstream, so that the ship lock structure health monitoring is a critical issue to avoid its damages. The stress state of ship lock structure is dependent on its type and structural complexity. In addition, the temperature and construction methods have a great influence on the structural quality. Thus, strengthening the structural temperature and stress-strain monitoring during the construction plays a significant role to ensure the construction quality of the ship lock. 

Fig. 3.6 Typical temperature and rate dependent stress-strain response. Instrinsic yield points indicated by circles.

As a pipeline is heated, strains of such a magnitude are iaduced iato it as to accommodate the thermal expansion of the pipe caused by temperature. In the elastic range, these strains are proportional to the stresses. Above the yield stress, the internal strains stiU absorb the thermal expansions, but the stress, g computed from strain 2 by elastic theory, is a fictitious stress. The actual stress is and it depends on the shape of the stress-strain curve. Failure, however, does not occur until is reached which corresponds to a fictitious stress of many times the yield stress. 

The effect of temperature on PSF tensile stress—strain behavior is depicted in Figure 4. The resin continues to exhibit useful mechanical properties at temperatures up to 160°C under prolonged or repeated thermal exposure. PES and PPSF extend this temperature limit to about 180°C. The dependence of flexural moduli on temperature for polysulfones is shown in Figure 5 with comparison to other engineering thermoplastics. 

For a fiber immersed in water, the ratio of the slopes of the stress—strain curve in these three regions is about 100 1 10. Whereas the apparent modulus of the fiber in the preyield region is both time- and water-dependent, the equiUbrium modulus (1.4 GPa) is independent of water content and corresponds to the modulus of the crystalline phase (32). The time-, temperature-, and water-dependence can be attributed to the viscoelastic properties of the matrix phase. 

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 ... 

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.)... 

Strength and Stiffness. Thermoplastic materials are viscoelastic which means that their mechanical properties reflect the characteristics of both viscous liquids and elastic solids. Thus when a thermoplastic is stressed it responds by exhibiting viscous flow (which dissipates energy) and by elastic displacement (which stores energy). The properties of viscoelastic materials are time, temperature and strain rate dependent. Nevertheless the conventional stress-strain test is frequently used to describe the (short-term) mechanical properties of plastics. It must be remembered, however, that as described in detail in Chapter 2 the information obtained from such tests may only be used for an initial sorting of materials. It is not suitable, or intended, to provide design data which must usually be obtained from long term tests. 

In a fluid under stress, the ratio of the shear stress, r. to the rate of strain, y, is called the shear viscosity, rj, and is analogous to the modulus of a solid. In an ideal (Newtonian) fluid the viscosity is a material constant. However, for plastics the viscosity varies depending on the stress, strain rate, temperature etc. A typical relationship between shear stress and shear rate for a plastic is shown in Fig. 5.1. 

MFI of the composition to that of the matrix, as a function of the filler concentration. It can be seen that, as the concentration of a particular filler increases, the index increases too for one matrix but decreases for another, and varies by a curve with an extremum for a third one. Even for one and the same polymerfiller system and a fixed concentration of filler, the stress-strain characteristics, such as ultimate stress, may, depending on the testing conditions (temperature, rate of deformation, etc.) be either higher or lower than in the reference polymer sample [36],... 

As an example, for room-temperature applications most metals can be considered to be truly elastic. When stresses beyond the yield point are permitted in the design, permanent deformation is considered to be a function only of applied load and can be determined directly from the stress-strain diagram. The behavior of most plastics is much more dependent on the time of application of the load, the past history of loading, the current and past temperature cycles, and the environmental conditions. Ignorance of these conditions has resulted in the appearance on the market of plastic products that were improperly designed. Fortunately, product performance has been greatly improved as the amount of technical information on the mechanical properties of plastics has increased in the past half century. More importantly, designers have become more familiar with the behavior of plastics rather than... 

Avoiding structural failure can depend in part on the ability to predict performance of materials. When required designers have developed sophisticated computer methods for calculating stresses in complex structures using different materials. These computational methods have replaced the oversimplified models of materials behavior relied upon previously. The result is early comprehensive analysis of the effects of temperature, loading rate, environment, and material defects on structural reliability. This information is supported by stress-strain behavior data collected in actual materials evaluations. 

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