Stress and strain at yield

Stress and strain at yield are the values of the stress and strain corresponding to the yield point. 

Fig. 28 Evolution of stress and strain at yield point of the crosslinked EVA before and after...

Modulus, stress and strain at yield are reported in Figs. 18-20 as a function of the stabilizer content for two different processing temperatures. Modulus, stress and strain at yield increase with the content of stabilizer but, for all these properties, the improvement is evident but not very large. 

Each sample was tested at two crosshead speeds 1 and 5 mm/min for filled materials, and 1 and 50 mm/min for unfilled materials. The 1 mm/min speed was used to obtain the Young s modulus, while the 5 or 50 mm/min speed was used to obtain other tensile properties such as tensile strength, stresses and strains at yield and break. The tensile strain was measured fi om the narrow section of each specimen using a clip-on extensometer (Instron 2630-115) with a ge length of 50.8 mm. In some cases the crosshead position was also recorded and used to calculate the parent strain and modulus, as discussed later. 

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. 

Physical characterization of polymers is a common activity that research and development technologists at the Dow Chemical Company perform. A material property evaluation that is critical for most polymer systems is a tensile test. Many instruments such as an Instron test frame can perform a tensile test and, by using specialized software, can acquire and process data. Use of an extensometer eliminates calibration errors and allows the console to display strain and deformation in engineering units. Some common results from a tensile test are modulus, percent elongation, stress at break, and strain at yield. These data are then used to better understand the capabilities of the polymer system and in what end-use applications it may be used. 

Compressive measurements provide a means to determine specimen stiffness, Young s modulus of elasticity, strength at failure, stress at yield, and strain at yield. These measurements can be performed on samples such as soy milk gels (Kampf and Nussi-novitch, 1997) and apples (Lurie and Nussi-novitch, 1996). In the case of convex bodies, where Poisson s ratio is known, the Hertz model should be applied to the data in order to determine Young s modulus of elasticity (Mohsenin, 1970). It should also be noted that for biological materials, Young s modulus or the apparent elastic modulus is dependent on the rate at which a specimen is deformed. 

Tensile Tests. Tensile tests were done on an Instron tensile tester un er ambient coi dition at strain rates, , ranging from 1.0 X 10 to 5.5 x 10 sec. Experiments were done in triplicate at each strain rate. Stress, a, and strain, , at yield (not shown) were determined using tSe 0.2% offset method (5). Stress,, and strain, , at break and the work to break, W, (the area under the stress-strain curve) were also calculated. The latter was evaluated via a computer program using a Simpson s Rule method. 

Copolymer B/PPO blends. Curve 1, Copolymer B 2, 20% PPO 3, 40% PPO 4, 60% PPO 5, 80% PPO 6, 100% PPO. Error bars indicate 95% confidence intervals for both stress and strain at break (or yield) for sample populations. Curves 2-6 have been sequentially shifted 0.5% in strain along the abscissa for purpose of comparison. 

The effect of the degree of nanoclay dispersion and pol5uner-filler interaction on the mechanical properties was also studied by Bilotti et al. [11-16]. Figure 12.25 shows the Young s modulus, yield stress, and strain at break of PP/sepiolite nanocomposites compati-bilized by different functionalized polymers (Section 12.4.1). The results are also compared with a PP nanocomposite reinforced by an alkyl silane-coated sepiolite (Sep-sil), without any compatibilizers. 

The displacement of the point of initial load measurement along the strain axis, observed for curves 5-8 in Fig. 9b, indicates irreversible extension (or slack) resulting from previous displacement. As this was not observed for curves 2-4, this confirms that the material elongates irreversibly in extension where stress and strain levels exceed a critical value. Moreover, this demonstrates that the initial linear stress-strain region corresponds to Hookean or elastic behavior and the onset of irreversible extension is marked by the initial point of deviation from this linearity. It is therefore appropriate to calculate tensile modulus based on the slope of the initial linear stress-strain region. Additionally, yield stress and yield strain can be equated to the respective levels of stress and strain at the observed point of deviation from linearity. 

Hard, tough polymers having high moduli of elasticity and yield points and also high stress and strain at break. 

Tensile test according to ISO 527 [159] to measure tensile strength, yield stress and strain at break,... 

Stress and strain at failure are readily calculated from the sample geometry in both cases. If failure has not occurred with 5 percent deflection strain, this is usually reported as the flexural yield strength. In practice, results depend on the heat history of the sample, extent of fusion, uniformity of dispersion, and freedom from surface cracks. Generally, molded specimens yield higher values than those die-cut from pressed sheets or actual articles of commerce. 

The strength of the material as expressed by the stress and strain at break increases significantly witli the addition of LNR for both systems, NR-PP and NR-HDPE. For the NR-PP, the optimum value of LNR is about 15% whereas in the NR-HDPE, 27% LNR yields the maximum physical properties. A single glass transition temperature, Tg, strongly indicates a high homogeneity of the blend in both thermoplastics NR. 

Mun] Mechanical tests Hardness, yield stress, fracture stress and strain at fracture... 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Table 2 Average Values of the Modulus, Yield Stress, Yield Strain, and Strain at Break for Three Samples of PTEB Stretched at Different Temperatures and Deformation Rates...

In the region where the relationship between stress and strain is nonlinear, the material is said to be plastic. Elastic deformation is recoverable upon removal of the load, whereas plastic deformation is permanent. The stress at which the transition occurs, o, is called the yield strength or yield point of the material, and the maximum... 

When we begin to stretch a semicrystalline polymer it deforms affinely, that is, each element of the sample within the gauge region experiences identical stress and strain. As we continue to stretch the sample, we reach a point at which affine deformation ceases and the sample yields. At this point, it typically develops a local region of reduced cross-sectional area, known... 

Values of stress and strain obtained from Figure 1 and from similar plots of data obtained on the other elastomers yield the plots of Xo vs. (X — 1) in Figure 2, where Xo is the true stress, i.e., the force per unit cross-sectional area of the deformed specimen. The data at strains up to 1.0 (100% elongation) give straight lines whose slopes equal the equilibrium tensile moduli, E values of 1 /3 are given in Table I. 

Structural dements resist blast loads by developing an internal resistance based on material stress and section properties. To design or analyze the response of an element it is necessary to determine the relationship between resistance and deflection. In flexural response, stress rises in direct proportion to strain in the member. Because resistance is also a function of material stress, it also rises in proportion to strain. After the stress in the outer fibers reaches the yield limit, (lie relationship between stress and strain, and thus resistance, becomes nonlinear. As the outer fibers of the member continue to yield, stress in the interior of the section also begins to yield and a plastic hinge is formed at the locations of maximum moment in the member. If premature buckling is prevented, deformation continues as llic member absorbs load until rupture strains arc achieved. 

When a linear relationship between the stress and strain is no longer present, the proportional limit is reached. On the diagram this is the highest point on the linear portion of the graph or where the curve no longer is a straight line. The material at this point is still elastic. The proportional limit is sometimes called the yield point. 

At high stresses and strains, non-linearity is observed. Strain hardening (an increasing modulus with increasing strain up to fracture) is normally observed with polymeric networks. Strain softening is observed with some metals and colloids until yield is observed. 

The mechanical properties are good with medium to low elongations at break and more limited strains at yield. Moduli and hardnesses are in a high range but notched impact strengths are in a medium range. Polyetherimide displays notch sensitivity and stress concentrators must be avoided when designing. 

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