Yield strain calculation

The yield strain obtained from the point of intersection of the two linear regions of the stress-strain curve is compared in Table III with the yield strain calculated from the yield stress and the modulus. There are slight differences between measured and calculated values the calculated values are considered... 

Indeed, it has been observed that the onset of yielding of isotropic polymers is approximately constant, 0.02< [<0.025, which implies that 0.04shear yield strain, the plastic shear deformation of the domain satisfies a plastic shear law. For temperatures below the glass transition temperature, the continuous chain model enables the calculation of the tensile curve of a polymer fibre up to about 10% strain [6]. Figure 7 shows the observed stress-strain curves of PpPTA fibres with different moduli compared to the calculated curves. 

Equation 133 is similar to the formula for the strain and temperature dependence of the yield point calculated with the thermally activated viscosity proposed by Eyring and Bauwens [37,59]. 

Replicate tests were conducted at 3, 25 and 75% RH and good repeatability was observed. The elastic modulus as function of RH calculated from these stress-strain curves is also shown. The shape of the stress-strain curve can be approximated by two linear segments. It is clear that RH affects the elastic modulus and the yield stress of these MEAs with Nation-type membrane. Note that the elastic modulus more than doubled when the MEA was dried from 75 to 3% RH. However, the yield strain and the slope of the second linear segment are affected to a lesser degree it is notable that the 3% RH condition exhibited the lowest strain-to-failure. Despite some variations, the MEAs tested at all four RH levels were found to be fairly ductile, with strain-to-failure exceeding 100%. The yield stress varies from approximately 12 MPa to 17.5 MPa and the strain-to-failure varies from 86.4 to 152.7%. This is indicative of the initial non-uniformity of the MEA and the presence of initial random defects in the as-fabricated membrane or MEAs. 

The stress-strain curve for a material can be represented by means of the function cr, = 12 where represents the true tension stress in MPa and 8 is strain. Calculate the value of the strain at the necking point and the value of the yield stress, [Pg.642]

The table shows the force needed to fracture single-edge bars of several polymers at room temperature in a three-point bending test. Bar dimensions are IT = 10 mm, B = 6 mm, a = 5 mm the test span S is 80 mm. The second column in the table gives the corresponding yield stress. Calculate Kic for each polymer, and indicate in which cases valid plane strain conditions exist. 

Measured Calculated Yielding Compatibilizer Yield Stress, Modulusa Yield Strain, Yield Strain, Angle,... 

All but four of the fifty specimens have yield strengths and offset strains calculated with the SED method that are equal to or lower than the values from the 0.2 % offset method. In the three environments (dry/cold, moderate, and humid/hot) the average yield strengths are ... 

Figures 9-11 show the effect of environment on the stress-strain curves at lO /s, IC /s, and lO /s strain rates, respectively. The arrows point to the yield strength calculated with the SED method.

Table 6 shows the tensile properties of six adhesives in the diy/cold and humid/hot environments. All adhesives were tested at a 10" /s strain rate. On average, the time to rupture was 6 min in the diy/cold environment and 9 min in the humid/hot environment. The tensile properties of adhesive FM 300K are averages for replicate specimens (Table 5). For the other adhesives, only one specimen was tested per environment. Nine of the twelve specimens have yield strengths and offset strains calculated with the SED method that are equal to or lower than the values from the 0.2 % offset method.

The configuration analyzed by Eager et al is a cylindrical disc-shaped joint whereas our joints are rectangular in cross-section (2.54 cm x 1.25 cm). For calculation purpose, we take an effective joint radius to be the minimum distance to the edge of our samples (0.625 cm). The calculations are made in terms of the dimensionless parameters H and defined in ref where Hi is the ratio of the thermal residual strain at the interface to the yield strain of the braze interlayer, and specifies the relative difference in CTE s between the ceramic (C), braze interlayer (1), and metal substrate (M). 

Based on the stress-strain diagram the values tensile stress at yield cXy and tensile strength at maximum (7m as well as the associated normative yield strain and nominal strain 8tM or normative strain 8m at tensile strength as well as strain at break 8b can be calculated (Eqs. 4.6. 11). For completely recorded diagrams the nominal strain at break 8tB can be determined additionally (Eq. 4.12). Because of the dependence on software and test equipment, especially sampling rate, the tensile stress at break (Tb should not be used (Eq. 4.13). Due to the viscoelastic behaviour of the plastics modulus of elasticity in tension is determined as secant modulus between the strain limits of 0.05 % and 0.25 % (Eq. 4.14). If the transverse strain is recorded simultaneously using strain gauges Poisson ratio jl can be calculated (Eq. 4.15). 

Calculate an equivalent strain rate corresponding to each yield stress by dividing yield strain time to yield. 

Fig. 4. Left Elasto-plastic (un-)loading including a non-imiqueness regime. Right Illustration of the ID-stress-strain-curve interpolation, the yield stress calculation and Drucker s postulate.

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. 

The thermally induced intramolecular 2 + 2-cycloaddition of A(-(buta-2,3-dienyl)-2-cyclopropylidenemethyl)anilines (12) yielded functionalized bicyclo[4.2.0]nitrogen heterocycles (13) in high yield. DFT calculations indicate that the mechanism involves a concerted process in which a strained small ring is essential (Scheme 4). ... 

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