Stress-Strains

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...

Considerable attention is given in the Institute to the application of the methods of acoustic emission and optical holography for engineering diagnostics of the service life and the stressed-strained state of welded metal structures. 

The Institute has many-year experience of investigations and developments in the field of NDT. These are, mainly, developments which allowed creation of a series of eddy current flaw detectors for various applications. The Institute has traditionally studied the physico-mechanical properties of materials, their stressed-strained state, fracture mechanics and developed on this basis the procedures and instruments which measure the properties and predict the behaviour of materials. Quite important are also developments of technologies and equipment for control of thickness and adhesion of thin protective coatings on various bases, corrosion control of underground pipelines by indirect method, acoustic emission control of hydrogen and corrosion cracking in structural materials, etc. 

Spreading velocities v are on the order of 15-30 cm/sec on water [39], and v for a homologous series tends to vary linearly with the equilibrium film pressure, it", although in the case of alcohols a minimum seemed to be required for v to be appreciable. Also, as illustrated in Fig. IV-3, substrate water is entrained to some depth (0.5 mm in the case of oleic acid), a compensating counterflow being present at greater depths [40]. Related to this is the observation that v tends to vary inversely with substrate viscosity [41-43]. An analysis of the stress-strain situation led to the equation... 

Figure C2.1.17. Stress-strain curve measured from plane-strain compression of bisphenol-A polycarbonate at 25 ° C. The sample was loaded to a maximum strain and then rapidly unloaded. After unloading, most of the defonnation remains.

By combining random flight statistics from Chap. 1 with the statistical definition of entropy from the last section, we shall be able to develop a molecular model for the stress-strain relationship in a cross-linked network. It turns out to be more convenient to work with the ratio of stretched to unstretched lengths L/Lq than with y itself. Note the relationship between these variables ... 

The electromagnetic spectrum measures the absorption of radiation energy as a function of the frequency of the radiation. The loss spectrum measures the absorption of mechanical energy as a function of the frequency of the stress-strain oscillation. 

Osadchuk V.A. (1985) Stress-strain state and limiting equilibrium of shells with cuts. Naukova Dumka, Kiev (in Russian). 

A schematic stress-strain curve of an uncrimped, ideal textile fiber is shown in Figure 4. It is from curves such as these that the basic factors that define fiber mechanical properties are obtained. 

Fig. 4. Idealized stress-strain curves of an uncrimped textile fiber point 1 is the proportional limit, point 2 is the yield point, and point 3 is the break or...

The elasticity of a fiber describes its abiUty to return to original dimensions upon release of a deforming stress, and is quantitatively described by the stress or tenacity at the yield point. The final fiber quaUty factor is its toughness, which describes its abiUty to absorb work. Toughness may be quantitatively designated by the work required to mpture the fiber, which may be evaluated from the area under the total stress-strain curve. The usual textile unit for this property is mass pet unit linear density. The toughness index, defined as one-half the product of the stress and strain at break also in units of mass pet unit linear density, is frequentiy used as an approximation of the work required to mpture a fiber. The stress-strain curves of some typical textile fibers ate shown in Figure 5. 

Fig. 5. Stress—strain curves of some textile fibers (17). To convert N/mm to psi, multiply by 145.

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. 

Fig. 6. The effect of rate of extension on the stress—strain curves of rayon fibers at 65% rh and 20°C. The numbers on the curves give the constant rates of...

The mechanical properties of acryUc and modacryUc fibers are retained very well under wet conditions. This makes these fibers well suited to the stresses of textile processing. Shape retention and maintenance of original bulk in home laundering cycles are also good. Typical stress—strain curves for acryhc and modacryUc fibers are compared with wool, cotton, and the other synthetic fibers in Figure 2. 

Fig. 2. Typical stress—strain properties of staple fibers at 65% rh and 21°C. Rate of elongation is 50%/min. To convert N/tex to gf/den, multiply by 11.3.

The ratio of stress to strain in the initial linear portion of the stress—strain curve indicates the abiUty of a material to resist deformation and return to its original form. This modulus of elasticity, or Young s modulus, is related to many of the mechanical performance characteristics of textile products. The modulus of elasticity can be affected by drawing, ie, elongating the fiber environment, ie, wet or dry, temperature or other procedures. Values for commercial acetate and triacetate fibers are generally in the 2.2—4.0 N/tex (25—45 gf/den) range. 

The abihty of a fiber to absorb energy during straining is measured by the area under the stress—strain curve. Within the proportional limit, ie, the linear region, this property is defined as toughness or work of mpture. For acetate and triacetate the work of mpture is essentially the same at 0.022 N/tex (0.25 gf/den). This is higher than for cotton (0.010 N/tex = 0.113 gf/den), similar to rayon and wool, but less than for nylon (0.076 N/tex = 0.86 gf/den) and silk (0.072 N/tex = 0.81 gf/den) (3). 

A fiber that is strained and allowed to recover releases a portion of the work absorbed during straining. The ratio of the work recovered to the total work absorbed, measured by the respective areas under the stress—strain and stress—recovery curves, is designated as resiUence. 

Fig. 1. Stress—strain curves A, hard fiber, eg, nylon B, biconstituent nylon—spandex fiber C, mechanical stretch nylon D, spandex fiber E, extruded latex...

Most extmded latex fibers are double covered with hard yams in order to overcome deficiencies of the bare threads such as abrasiveness, color, low power, and lack of dyeabiUty. During covering, the elastic thread is wrapped under stretch which prevents its return to original length when the stretch force is removed thus the fiber operates farther on the stress—strain curve to take advantage of its higher elastic power. Covered mbber fibers are commonly found in narrow fabrics, braids, surgical hosiery, and strip lace. 

Eig. 1. Typical stress—strain curves for cotton and PET fibers. A, industrial B, high tenacity, staple C, regular tenacity, filament D, regular tenacity, staple ... 

Terephthahc acid (TA) or dimethyl terephthalate [120-61 -6] (DMT) reacts with ethyleae glycol (2G) to form bis(2-hydroxyethyl) terephthalate [959-26-2] (BHET) which is coadeasatioa polymerized to PET with the elimination of 2G. Moltea polymer is extmded through a die (spinneret) forming filaments that are solidified by air cooling. Combinations of stress, strain, and thermal treatments are appHed to the filaments to orient and crystallize the molecular chains. These steps develop the fiber properties required for specific uses. The two general physical forms of PET fibers are continuous filament and cut staple. 

Fig. 4. Representative stress—strain curves of spun and drawn PET A, low speed spun-mechanically drawn yam B, 6405 m /min C, 5490 m /min D, 4575...

The apparent viscosity, defined as du/dj) drops with increased rate of strain. Dilatant fluids foUow a constitutive relation similar to that for pseudoplastics except that the viscosities increase with increased rate of strain, ie, n > 1 in equation 22. Dilatancy is observed in highly concentrated suspensions of very small particles such as titanium oxide in a sucrose solution. Bingham fluids display a linear stress—strain curve similar to Newtonian fluids, but have a nonzero intercept termed the yield stress (eq. 23) ... 

Modified ETEE is less dense, tougher, and stiffer and exhibits a higher tensile strength and creep resistance than PTEE, PEA, or EEP resins. It is ductile, and displays in various compositions the characteristic of a nonlinear stress—strain relationship. Typical physical properties of Tef2el products are shown in Table 1 (24,25). Properties such as elongation and flex life depend on crystallinity, which is affected by the rate of crysta11i2ation values depend on fabrication conditions and melt cooling rates. 

The mechanical piopeities of stmctuial foams and thek variation with polymer composition and density has been reviewed (103). The variation of stmctural foam mechanical properties with density as a function of polymer properties is extracted from stress—strain curves and, owkig to possible anisotropy of the foam, must be considered apparent data. These relations can provide valuable guidance toward arriving at an optimum stmctural foam, however. 

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