Elastic and Tensile Deformations

Cross-sectional shape, friction, density, and static charge are described as other important physical properties, and hair shine, combing ease, body, style retention, manageability, and hair conditioning are the primary important consumer assessments described in this chapter. A new section describing normal variation that exists in the cross-sectional shape of hair fibers and a few examples are given describing how these variations influence both the physical and the chemical behavior of the fibers. 

For every strain (deformation) of an elastic substance, there is a corresponding stress (the tendency to recover its normal condition).The units of stress are force per unit area FIA). 

Only stretching, bending, and torsional strains are considered in this chapter. 

Each type of stress and strain has a modulus (the ratio of stress to strain) that also has units of FIA. The elastic modulus for stretching is commonly called Young s modulus. The bending modulus has also been called Young s modulus of bending, and the torsional modulus is called the modulus of rigidity. 

Human hair has been referred to as a substrate with only one dimension, length, suggesting why its tensile properties have been studied more than its other elastic properties. 

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Designers of most structures specify material stresses and strains well within the pro-portional/elastic limit. Where required (with no or limited experience on a particular type product materialwise and/or process-wise) this practice builds in a margin of safety to accommodate the effects of improper material processing conditions and/or unforeseen loads and environmental factors. This practice also allows the designer to use design equations based on the assumptions of small deformation and purely elastic material behavior. Other properties derived from stress-strain data that are used include modulus of elasticity and tensile strength. 

Three important properties can be inferred from the tensile test i.e. elastic limit (i.e. the point of maximum elastic elongation), tensile strength and E-modulus. In many cases the transition point between the elastic and plastic deformation is not visible in the graph. For that reason it has been determined that this point is situated at an value of 0.002 and the accompanying tensile stress is determined as represented in figure 10.9. 

The universal hardness , is obtained from the same formula if h is inserted instead of Aplastic- The universal hardness includes both the elastic and plastic deformation. The hnear part of the unloading curve corresponds to the elastic recovery when the diamond pyramid is in a constant area contact with the material. Therefore it represents Hooke s law and allows one to calculate the corresponding elastic modulus E/ — i/) which is a complicated function of the bulk, shear, and tensile moduli is the Poisson ratio). The details of the apparatus, the measuring procedure and possible errors are given in the relevant papers to which we refer here [25-28]. If done correctly, the plastic hardness measured by the indentation agrees within about 10-15% reasonably well with that from the classical Vickers method at least in the range H < 1500kgmm [25]. 

J Mechanical testing parameters (a) A representative strain-stress curve in tensile testing. Yield stress (o-yg) and yield point strain (eyp) can be obtained by recording values at the point where the curve transitions from a linear relationship between stress and strain (elastic deformation) to a non-linear relationship (plastic deformation). Ultimate tensile strength (fr ,s) is the maximum stress in the curve, and the corresponding strain is called uniform strain (cp). The strain at fracture (eO can also be obtained from the curve, (b) When the transition point between elastic and plastic deformation is difficult to identify, a 0.2% strain offset line parallel to the elastic portion is drawn to obtain the <7ys or 0.2% offset o-ys. (c) Schematic of the deformation that occurs when shear force is applied to a viscoelastic polymer. 

An important issue is the influence of an electrochemical environment on the cyclic deformation behavior of metals [74,33-35]. As illustrated by the data in Fig. 1 for a carbon-manganese steel in high-temperature water, environment does not typically affect the relationship between stresses and strains derived from the maximum tensile (or compressive) points of steady-state (saturation) hysteresis loops [36]. Such loops should relate to elastic and plastic deformation prior to substantial CF microcracking. CF data of the sort shown in Fig, 1 are produced by either stress or total strain controlled uniaxial fatigue experiments, identical to the methods... 

Figure 15.23 shows both the tensile stretching curve and the recoveiy curve of a typical fiber. The stretching curve shows the typical stress-strain behavior, which includes both elastic and plastic deformations. The recovering curve shows only the elastic deformation (or strain) is recovered after the removal of the applied tensile stress. The elastic recoveiy, or strain recovery, ean then be defined as ... 

When a plastic material is subjected to an external force, a part of the work done is elastically stored and the rest is irreversibly (or viscously) dissipated hence a viscoelastic material exists. The relative magnitudes of such elastic and viscous responses depend, among other things, on how fast the body is being deformed. It can be seen via tensile stress-strain curves that the faster the material is deformed, the greater will be the stress developed since less of the work done can be dissipated in the shorter time. 

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