Hookean region

Hoogsteen hydrogen bonding, 17 609, 610 Hooke s law, 21 719 Hookean region of stress—strain curve, 11 183, 184... 

The extensive investigations by Astbury and Woods (1933) of the X-ray diffraction patterns of animal fibers before and after stretcihing, setting, or supercontraction (Section VI,5,2) have had a major influence on the models proposed to account for the load-extension properties. Astbury and Woods showed that when animal fibers are stretched, the characteristic a-pattern decreases in intensity with the simultaneous appearance of a d-pattern similar to that obtained from silk. The sharpness and intensity of the /3-pattern increases with sti ain, with temperature, and with time under strain. In the Hookean region the 5.1 A meridional spacing increases by up to 2 % (Astbury and Haggith, 1953). Astbury and Woods (1933) stated that virtually no /3-pattern appears until the fiber has been stret( hed by at least 20 %, and for 25 years this observation dominated the models proposed to explain the elastic properties of wool (Alexander and Hudson, 1954). 

Retractive forces in animal fibers stretched into the Hookean region of the stress-strain curve are generally attributed to the stretching of chemical bonds and hence to an increase in the internal energy of the fiber (Ast-bury and Haggith, 1953 Peters, 1956). 

Tensile properties that are related to fiber stiffness can be used to measure the T of almost all fibers. The elastic modulus, that is, the sl pe of the Hookean region of the fiber stress-strain curve, is a measure of the fiber stiffness and can be used for T determination since, by definition, a glass is stlffer than rubber (Figure 6). Since the transition from a glassy to a rubbery state Involves a reduction in stiffness, the temperature at which the modulus is abruptly lowered is taken as... 

Stretching a hair fiber in water and the curve at the top of the chart represents stretching at 65% RH. In the Hookean region of the load-elongation curves, the stress (load) is approximately linear to the strain (elongation), and the ratio of stress to strain in this region is the elastic modulus (Es), commonly called Young s modulus. The elastic modulus is usually expressed in dynes per square centimeter and may be calculated from this simple expression ... 

In this scheme, a fiber is attached to a beam with a known natural resonant frequency. Tension (within the Hookean region) is applied to the fiber. The beam is then deflected. From the change in the oscillation frequency of the... 

Initial niodidus. This term is intended as initial Young s modulus and is the ratio of specific stress (N tex) to fractional strain along the axis of the stress-strain curve in the Hookean region, with starting point being zero stress and zero strain. This is illustrated in... 

It is not always an easy matter however to determine the point of zero strain or indeed where the Hookean region in the stress-strain curve might be. 

The first prerequisite is obviously to establish if there is an obvious yield point, as this would clearly establish the upper extent of the Hookean region. The part of the stress-strain curve approaching the yield point and having the maximum gradient is taken to be the Hookean region, and the zero starting point of this gradient line, extended back to the... 

This is the underlying theory supporting the determination of initial modulus in ASTM D 3822, Appendi.x XI. where there arc two illustrations, one of a material with an obvious Hookean region and one of a material with no obvious Hookean region, as in Fig. 25. 

Second Hookean region Strain softening region... 

When a wool fiber is extended in water, the load-extension curve (Figure 5.12) shows the following features For a small extension, up to about 1%, the gradient of the curve increases as the crimp of the fiber is straightened. The gradient is then constant up to about 3% extension. Thus the extension of the fiber is approximately proportional to the load. Hooke s law is approximated this is the so-called Hookean region of the load-extension curve. 

When a wool fiber is extended in water to a definite extention—say, halfway along the Hookean region of the load-extension curve—and held at this extension, the stress in the fiber gradually decays and therefore the force necessary to hold the fiber at this extension gradually decreases. The slow decrease of stress with time is responsible for the fact that the Hookean region of the load-extension curve is not exactly straight [280], but concave with respect to the extension axis, since the extension of the fiber takes a finite time. 

In the Hookean region of the load-extension curve, up to about 3% extension, hydrogen bonds between the turns of the a-helices may be strained, but there may be no decrease in the total proportion of the total length of the protein chains in crystallites in the a conformation. 

Figure 12 Typical stress-strain curve of an a-keratin fiber showing the Hookean region (AB), the yield region (BC), and the postyield region (CDE). 

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