Strain measurements

Plastic Stra.ln Ra.tlo. The plastic strain ratio is the ratio of strains measured in the width over the thickness directions in tensile tests. This ratio characterizes the abhity of materials to resist thinning during forming operations (13). In particular, it is a measure of the abhity of a sheet material to resist the thinning and failure at the base of a deep drawn cup. The plastic strain ratio is measured at 0°, 45°, and 90° relative to the rolling direction. These three plastic strain ratios Rq, R, and R q, are combined to obtain the average strain ratio, cahed the R or the R value, and its variation in strain ratio, cahed... 

Given limits to the time resolution with which wave profiles can be detected and the existence of rate-dependent phenomena, finite sample thicknesses are required. To maintain a state of uniaxial strain, measurements must be completed before unloading waves arrive from lateral surfaces. Accordingly, larger loading diameters permit the use of thicker samples, and smaller loading diameters require the use of measurement devices with short time resolution. 

The thermal strain measurements were made in a low-temperature, high-resolution, three-terminal, capacitance dllatometer identical to the design of White and Collins."... 

The thermal strain measurements described above have the common feature of anisotropic behaviour in a supposed isotropic state (cubic structure). These observations go well beyond the short-range, static strain fields associated with the lattice impurities responsible for Huang scattering. This then raises the question of the temperature at which the lattice symmetry changes and the implications of this for the central mode scattering. 

Strain is defined as the deformation of a material divided by a corresponding undeformed dimension. The units of strain are meter per meter (m/m) or inch per inch (in./in.). Since strain is often regarded as dimensionless, strain measurements are typically expressed either as a percentage deformation or in microstrain units. One microstrain is defined as 10-6 m/m or in./in. 

Because strain measurements are difficult if not impossible to measure, few values of yield strength can be determined by testing. It is interesting to note that tests of bolts and rivets have shown that their strength in double shear can at times be as much as 20% below that for single shear. The values for the shear yield point (kPa or psi) are generally not available however, the values that are listed are usually obtained by the torsional testing of round test specimens. 

Recovery is the strain response that occurs upon the removal of a stress or strain. The mechanics of the recovery process are illustrated in Fig. 2-34, using an idealized viscoelastic model. The extent of recovery is a function of the load s duration and time after load or strain release. In the example of recovery behavior shown in Fig. 2-34 for a polycarbonate at 23°C (73°F), samples were held under sustained stress for 1,000 hours, and then the stress was removed for the same amount of time. The creep and recovery strain measured for the duration of the test provided several significant points. 

There are different techniques to evaluate the quantitative stress level in prototype and production products. They can predict potential problems. Included is the use of electrical resistance strain gauges bonded on the surface of the product. This popular method identifies external and internal stresses. Their various configurations are made to identify stresses in different directions. This technique has been extensively used for over a half century on very small to very large products such as toys to airplanes. There is the optical strain measurement system that is based on the principles of optical interference. It uses Moire, laser, or holographic interferometry (2,3,20). 

Figure 10.6 gives a schemahc view of the test setup of the strain measurement. The boundary conditions in this stretched him method are modeled by hnite element analysis with nonlinear material properties. 

In particular it can be shown that the dynamic flocculation model of stress softening and hysteresis fulfils a plausibility criterion, important, e.g., for finite element (FE) apphcations. Accordingly, any deformation mode can be predicted based solely on uniaxial stress-strain measurements, which can be carried out relatively easily. From the simulations of stress-strain cycles at medium and large strain it can be concluded that the model of cluster breakdown and reaggregation for prestrained samples represents a fundamental micromechanical basis for the description of nonlinear viscoelasticity of filler-reinforced rubbers. Thereby, the mechanisms of energy storage and dissipation are traced back to the elastic response of tender but fragile filler clusters [24]. 

Here we describe the strain history with the Finger strain tensor C 1(t t ) as proposed by Lodge [55] in his rubber-like liquid theory. This equation was found to describe the stress in deforming polymer melts as long as the strains are small (second strain invariant below about 3 [56] ). The permanent contribution GcC 1 (r t0) has to be added for a linear viscoelastic solid only. C 1(t t0) is the strain between the stress free state t0 and the instantaneous state t. Other strain measures or a combination of strain tensors, as discussed in detail by Larson [57], might also be appropriate and will be considered in future studies. A combination of Finger C 1(t t ) and Cauchy C(t /. ) strain tensors is known to express the finite second normal stress difference in shear, for instance. 

On poly(dimethylsiloxane) (PDMS) networks having comb-like crosslinks, torsional vibration experiments and static stress-strain measurements at small deformations were performed as a function of temperature, torsional vibrations also as a function of frequency. 

Plots of G at 0.5 Hz and the reduced stress ore(j obtained from stress-strain measurements at small strains against temperature, give almost identical straight lines (Figure 5). This similarity was expected because no frequency dependence of G had been observed. Hence G equals the equilibrium modulus G G moreover equals the reduced stress ore(j, if the latter is measured in the vicinity of X= 1. The measurements were always performed at X = 1.02 - 1.04, so that this requirement is fulfilled. 

Being a very sensitive quantity, however, the relative energy part of the modulus is different for some of the samples, if calculated from static or dynamic data, respectively. (For the calculation method, compare ref. 2J3, K ) Table III gives the values for the relative energy part. ore(j u/ored the ener9Y part calculated from stress-strain measurements Gy/G is the corresponding number obtained from dynamic data at 0.5 Hz. 

Relative energy part of the modulus at T = 298K, from stress-strain measurements with X = 1.02-1.04 (ored u red and from torsional vibration experiments (G y/G 5... 

In order to check this prediction, stress-strain measurements were made up to moderate strains at room temperature. The obtained data are plotted in the usual manner as a versus 1/X in Figure 8. Table V gives the Mooney-Rivlin constants 2C and 2C calculated from these plots and also the ratio C./Cj. 

Networks were prepared in all cases using the amount of endlinking agent necessary to give a minimum Mc. Values of Mc were calculated from the Mooney-Rivlin elasticity coefficient Cj, determined from tensile stress-strain measurements (10),... 

The results of stress-strain measurements can be summarized as follows (1) the reduced stress S (A- A ) (Ais the extension ratio) is practically independent of strain so that the Mooney-Rivlin constant C2 is practically zero for dry as well as swollen samples (C2/C1=0 0.05) (2) the values of G are practically the same whether obtained on dry or swollen samples (3) assuming that Gee=0, the data are compatible with the chemical contribution and A 1 (4) the difference between the phantom network dependence with the value of A given by Eq.(4) and the experimental moduli fits well the theoretical dependence of G e in Eq.(2) or (3). The proportionality constant in G for series of networks with s equal to 0, 0.2, 0.33, and 0. Ewas practically the same -(8.2, 6.3, 8.8, and 8.5)x10-4 mol/cm with the average value 7.95x10 mol/cm. Results (1) and (2) suggest that phantom network behavior has been reached, but the result(3) is contrary to that. Either the constraints do survive also in the swollen and stressed states, or we have to consider an extra contribution due to the incrossability of "phantom" chains. The latter explanation is somewhat supported by the constancy of in Eq.(2) for a series of samples of different composition. 

Residual radiation, from nuclear power facilities, 17 553-554 Residual stress/strain measurement diffractometers in, 26 428—430 Residual thermal stresses ceramics, 5 632-633... 

The effect of radiation on the thermal expansion of this toughened composite (T300/CE 339) is shown (191 in Figure 24. The thermal strains measured during the cool-down portion of the first thermal cycle (cooling from RT to -150°C) are shown for the baseline composite (no radiation exposure) and for samples exposed to total doses as high as 10 0 rads. Radiation levels, as low as 10 rads... 

Figure 11.13 Changes of PTT ( ) and PBT ( ) fibers c-axis lattice strains measured from X-ray diffraction spacings as a function of applied external strains the dotted line represents affine deformation between lattice and applied strains...

The creep modulus for a specified stress, time and temperature is the value of the stress divided by the strain measured after the selected time. 

This measures the likeness of two patterns, which is useful for pattern matching as we will see in the application of lattice parameter and strain measurements. 

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