Fibers stress-strain relationships

The stress—strain relationship is used in conjunction with the rules for determining the stress and strain components with respect to some angle 9 relative to the fiber direction to obtain the stress—strain relationship for a lamina loaded under plane strain conditions where the fibers are at an angle 9 to the loading axis. When the material axes and loading axes are not coincident, then coupling between shear and extension occurs and... 

The stress-strain behavior of plastics in flexure generally follows from the behavior observed in tension and compression for either unreinforced or reinforced plastics. The flexural modulus of elasticity is nominally the average between the tension and compression moduli. The flexural yield point is generally that which is observed in tension, but this is not easily discerned, because the strain gradient in the flexural RP sample essentially eliminates any abrupt change in the flexural stress-strain relationship when the extreme fibers start to yield. 

The decrease in the fiber diameter of fabric resulted in a decrease in porosity and pore size, but an increase in fiber density and mechanical strength. The microfiber fabric made of PCLA (1 1 mole ratio) was elastomeric with a low Young s modulus and an almost linear stress-strain relationship under the maximal stain (500%) in this measurement. 

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. 

As the UTS is approached, significant fiber failures occur, which further reduce the tangent modulus. The basic stress-strain relationship is,64... 

B. Physical Properties of Animal Fibers 1. Stress-Strain Relationships... 

Host outstanding properties of these products were high resilience and good resistance to stress decay. Resilience Is Illustrated In Figure 1 which shows the stress-strain relationship of a poly[(plvalolactone-b-lsoprene-b-plvalolactone)-g-plvalo-lactone] fiber as It was stretched 300% and then allowed to relax. The shaded area Is the work lost as the fiber was loaded and then unloaded. This area amounts to 13% of the total, which shows that work recovered was 87%. Such high resilience compares very favorably with that of chemically-cured natural rubber. 

Creep appears in the 7-t plane (iso stress), while the stress-strain relationship (at a fixed time) is described by the S-7 plane. Stress relaxation (at constant strain) is described by the S-t plane. Premium engineering polymers or reinforced thermosets illustrate a relatively low creep. Fiber reinforcement usually decreases the creep. 

Stress-strain relationships for triaxial compression test of carpet-fiber-soil confined at 34.5 kPa [87],... 

Fig. 6.1 Typical stress-strain relationship of the ACL and the definition of material properties (modulus, strength, and strain at failure) with schematic drawings of the microstructure of collagen fibers. Numerical data of the strength, modulus, and strain at failure are referred from the original work [5]...

The interest of this study is on uniaxial stress-strain relationships, which can be used in the framework of a fiber beam-column element and also can capture accurately the response of a linear element with minor bending stiffness such as a reinforcing bar. In particular, special attention is paid on the model proposed by Monti and Nuti (1992). 

Stress-strain relationships are determined by DMA and temperature scans reveal glass transitions, crystallization and melting information. Blends of polypropylene and rubber have been studied by where the intensity of one of the two crystallization exotherms was used as a measure of the polypropylene domains and compared to the size determined by TEM cryomicrotomy and osmium tetroxide staining methods [25]. Isothermal annealing of PET above the crystallization temperature was shown to influence the morphology and increase thermal stability by combined SAXS and DSC analysis [26]. An excellent text edited by Turi [21] described the instrumentation and theory of thermal analysis and its application to thermoplastics, copolymers, thermosets, elastomers, additives and fibers. 

Semiciystalline Polymers There are two cases to be considered in the stress-strain relationships of semicrystalline plastics. If the amorphous portion is rubbery, then the plastic will tend to have a lower modulus, and the extension to break will be very large see polyethylene. Table 11.1. If the amorphous portion is glassy, however, then the effect will be much more like that of the glassy amorphous polymers. Orientation of semicrystalline polymers is also much more important than for the amorphous polymers. A special case involves fibers, where tensile strength is a direct function of the orientation of the chains in the fiber direction. 

Studies on randomness of filler distribution in polymethylacrylate nanocomposite are interesting. In this experiment, siUca particles were formed both before and after matrix polymerization. The results indicated that the concentration of silica was a controlling factor in the stress-strain relationship rather than the uniformity of particle distribution. Also, there was no anisotropy of mechanical properties regardless of the sequence of filler formation. This outcome cannot be expected to be duplicated in all other systems. For example, when nickel coated fibers were used in an EMI shielding application." When compounded with polycarbonate resin, fibers had a much worse performance than when a diy blend was prepared first and then incorporated into the polymer (Figure 7.1). In this case, pre-blending protected the fiber from breakage. 

Any material, when stressed, stretches or is otherwise deformed. If the plastic and fiber are firmly bonded together, the deformation is the same. Since the fiber is more unyielding, a higher stress is developed in the glass than the plastic. If the stress-strain relationships of fiber and plastic are known, the stresses developed in each for a given strain can be computed and their combined action determined. Fig. 2.27 stress-strain (S-S) diagrams provide the basis for this analysis it provides related data such as strengths and modulus. 

Suhir E, Effect of the nonlinear stress-strain relationship on the maximum stress in silica fibers subjected to two-point bending , Appl. Optics, 1993,32(9), 1567-72. 

Compared to lumped plasticity, the main shortcoming of distributed plasticity elements is that they require more computing resources. Numerical instabilities may be encountered if criteria that introduce abrupt loss of capacity are adopted, e.g., when trying to predict collapse. On the other hand, distributed plasticity elements do not require any special calibration and can be easily adopted for sections that consist of different materials since they use stress-strain relationships suitable for each fiber material. A discussion on distributed plasticity elements can be found in Neuenhofer and Filippou (1997), while comparisons between the force... 

Typical patterns of stress—strain behavior and the relationship of molecular motion on stress—strain behavior have been discussed (10,18,19,21,49—51). At times, it becomes desirable to characterize stress—strain behavior numerically so that a large amount of information can be condensed and many fibers exhibiting different behaviors can be compared. Procedures for measurement of stress—strain parameters are described ia ASTMD3822 andD2101 (10). 

As expected, the residual extensibility of the fiber decreases at higher draw ratios. What is not so predictable is that the true stress at failure increases as the draw ratio increases fiber failure strength is improved by drawing the yarn. If a curve is drawn to connect the end points of the stress-strain curves, it is seen that there is an inverse relationship between tenacity and elongation to break (eb). The form of this relationship is as follows ... 

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