Diagrams stress-strain

As discussed in Section 2.0 (Exploration), the earth s crust is part of a dynamic system and movements within the crust are accommodated partly by rock deformation. Like any other material, rocks may react to stress with an elastic, ductile or brittle response, as described in the stress-strain diagram in Figure 5.5. 

Figure 5.5 The stress - strain diagram for a reservoir rock...

Little error is introduced using the idealized stress—strain diagram (Eig. 4a) to estimate the stresses and strains in partiady plastic cylinders since many steels used in the constmction of pressure vessels have a flat top to their stress—strain curve in the region where the plastic strain is relatively smad. However, this is not tme for large deformations, particularly if the material work hardens, when the pressure can usuady be increased above that corresponding to the codapse pressure before the cylinder bursts. 

Fig. 2. Schematic stress—strain diagram, where UTS = ultimate tensile stress and (-------------) represents the demarcation between elastic and plastic behavior.

Both % El and % RA are frequendy used as a measure of workabifity. Workabifity information also is obtained from parameters such as strain hardening, yield strength, ultimate tensile strength, area under the stress—strain diagram, and strain-rate sensitivity. 

Fig. 3. Effect of temperature and strain rate on stress—strain diagram of Ti—5% Al—2.5% Sn where A—E correspond to the strain rates 1.6x10, ...

Mechanical Behavior of Materials. Different kinds of materials respond differently when they undergo basic mechanical tests. This is illustrated in Eigure 15, which shows stress—strain diagrams for purely viscous and purely elastic materials. With the former, the stress is reheved by viscous flow and is independent of strain. With the latter, there is a direct dependence of stress on strain and the ratio of the two is the modulus E (or G). 

Fig. 15. Stress—strain diagrams, (a) Viscous material of viscosity Tj the stress is independent of strain, but dependent on the speed of testing, (b) Elastic material of modulus E the slope is the modulus which is independent of the speed of testing.

A typical stress—strain curve generated by a tensile tester is shown in Eigure 41. Creep and stress—relaxation results are essentially the same as those described above. Regarding stress—strain diagrams and from the standpoint of measuring viscoelastic properties, the early part of the curve, ie, the region... 

It is important to differentiate between brittie and plastic deformations within materials. With brittie materials, the behavior is predominantiy elastic until the yield point is reached, at which breakage occurs. When fracture occurs as a result of a time-dependent strain, the material behaves in an inelastic manner. Most materials tend to be inelastic. Figure 1 shows a typical stress—strain diagram. The section A—B is the elastic region where the material obeys Hooke s law, and the slope of the line is Young s modulus. C is the yield point, where plastic deformation begins. The difference in strain between the yield point C and the ultimate yield point D gives a measure of the brittieness of the material, ie, the less difference in strain, the more brittie the material. 

There is Httle difference between the wet and the dry stress—strain diagrams of hydrophobic fibers, eg, nylon, acryHc, and polyester. Hydrophilic protein fibers and regenerated cellulose exhibit lower tensile moduH on wetting out, that is, the elongations increase and the strengths diminish. Hydrophilic natural ceUulosic fibers, ie, cotton, linen, and ramie, are stronger when wet than when dry. 

In other words, tensile stress/strain diagrams of the filler and the matrix. 

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... 

Fig. 2-7 (a) Generalized tensile stress-strain curve for plastics and (b) example of a commodity plastic s stress-strain diagram. 

The secant modulus measurement is used during the designing of a product in place of a modulus of elasticity for materials where the stress-strain diagram does not demonstrate a linear proportionality of stress to strain or E is difficult to locate. 

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. 

Creep modeling A stress-strain diagram is a significant source of data for a material. In metals, for example, most of the needed data for mechanical property considerations are obtained from a stress-strain diagram. In plastic, however, the viscoelasticity causes an initial deformation at a specific load and temperature and is followed by a continuous increase in strain under identical test conditions until the product is either dimensionally out of tolerance or fails in rupture as a result of excessive deformation. This type of an occurrence can be explained with the aid of the Maxwell model shown in Fig. 2-24. 

In conclusion regarding creep testing, it can be stated that creep data and a stress-strain diagram indicate whether plain plastic properties can lead to practical product dimensions or whether a RP has to be substituted to keep the design within the desired proportions. For long-term product use under continuous load, plastic materials have to consider creep with much greater care than would be the case with metals. 

These stress-strain diagrams may be applied, for example, to the investigation of a rod of which has its total volume is glass fiber and half plastic. If the glass fibers are laid parallel to the axis of the rod, at any cross-section, half the total cross-sectional area is glass and half plastic. If the rod is stretched 0.5%, reference to the stress-strain diagrams... 

Figure 1.3 Elastic stress-strain diagram (A) linear (B) nonlinear.

Stress-strain diagram, 27 721 Stress-strain instrument, 27 744 Stress-strain properties, of styrene plastics, 23 359-362... 

Response of a material under static or dynamic load is governed by the stress-strain relationship. A typical stress-strain diagram for concrete is shown in Figure 5.3. As the fibers of a material are deformed, stress in the material is changed in accordance with its stress-strain diagram. In the elastic region, stress increases linearly with increasing strain for most steels. This relation is quantified by the modulus of elasticity of the material. 

Concret does not have well defined elastic and plastic regions due to its brittle nature. A maximum compressive stress value is reached at relatively low strains and is maintained for small deformations until crushing occurs. The stress-strain relationship for concrete is a nonlinear curve. Thus, the elastic modulus varies continuously with strain. The secant modulus at service load is normally used to define a single value for the modulus of elasticity. This procedure is given in most concrete texts. Masonry lias a stress-strain diagram similar to concrete but is typically of lower compressive strength and modulus of elasticity. 

FIGURE 15.34 A representative stress-strain diagram for a ductile material. 

On the stress-strain diagram, what does the elastic range indicate The plastic range ... 

Figure 15.4 Stress-strain diagrams for typical polymers. (Source Wittcoff and Reuben, Industrial Organic Chemicals, John Wiley Sons, 1996. Reprinted by permission of John Wiley Sons, Inc.)...

Figure 15.4 gives the stress-strain diagrams for a typical fiber, plastic, and elastomer and the average properties for each. The approximate relative area under the curve is fiber, 1 elastomers, 15 thermoplastics, 150. Coatings and adhesives, the two other types of end-uses for polymers, will vary considerably in their tensile properties, but many have moduli generally between elastomers and plastics. They must have some elongation and are usually of low crystallinity. 

Fig.2.21. Stress-strain diagram for various types of polymers (for explanation, see text) Og = yield strength Og = tensile strength at break...

Finally, the modulus of elasticity E (Young s modulus), which is a measure of the stiffness of the polymer, can be calculated from the stress-strain diagram. According to Hooke s law there is a linear relation between the stress o and the strain e ... 

Determine strength and modulus from a stress-strain diagram. 

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