Constant stress

Tests using a constant stress (constant load) normally by direct tension have been described in ISO 6252 (262). This test takes the specimen to failure, or a minimum time without failure, and frequently has a flaw (drilled hole or notch) to act as a stress concentrator to target the area of failure. This type of testing, as well as the constant strain techniques, requires careful control of specimen preparation and test conditions to achieve consistent results (263,264). 

There are many types of deformation and forces that can be applied to material. One of the foundations of viscoelastic theory is the Boltzmann Superposition Principle. This principle is based on the assumption that the effects of a series of applied stresses acting on a sample results in a strain which is related to the sum of the stresses. The same argument applies to the application of a strain. For example we could apply an instantaneous stress to a body and maintain that stress constant. For a viscoelastic material the strain will increase with time. The ratio of the strain to the stress defines the compliance of the body ... 

The piezoelectric stress constant (e-constant) is defined as the polarization per unit volume induced by unit strain ... 

Fig. 5. Block diagram of the direct-reading apparatus for measuring the complex piezoelectric stress constant of polymer films with varying frequency...

The piezoelectricity of polymeric materials has in general a relax-ational nature and the piezoelectric stress constant e is a function of the frequency of the applied strain in a similar way to the elastic modulus and dielectric constant. The induced polarization has in-phase and out-of-phase components to the strain and the e-constant is expressed as a complex quantity, as in Eq. (32). 

Fig. 24. Piezoelectric stress constant of roll-drawn polyfvinylidene fluoride) films plotted against angle 0 between draw-axis and elongational strain (O) draw-ratio =2.1, ( ) draw-ratio = 1.6. Drawn after Nakamura and Wada [J. Polymer Sci. A-2,9,161 (1971)] by permission of John Wiley Sons, Inc.

Fig. 28. Piezoelectric stress constant obtained from inverse piezoelectric effect and electrostriction constant of drawn and polarized poly(vinylidene fluoride) film plotted against temperature. Draw ratio = 7. Polarized at 90° C under the field of 400 kV/ctn for 3 hours. Frequency of applied voltage = 37.5 Hz. (Oshiki and Fukada, 1971) Broken line represents dielectric constant at 21.5 Hz for roll-drawn poly (vinylidene fluoride) film (Peterlin and Eiweil, 1969)...

Date,M., Fukada,E. An apparatus for measuring piezoelectric strain and stress constants in polymers. Rep. Progr. Polymer Phys. Japan 13, 375 (1970). 

Material Symmetry Class Piezoelectric Stress Constants (coulomblm ) ... 

Line positions cannot be measured with sufficient precision on a chart recording made with a ratemeter. Instead, a scaler is used to determine the count rate at several positions on the line profile, and from these data the position of the line center is calculated. This procedure is particularly necessary when the lines are broad, as they are from hardened steel the line width at half-maximum intensity is then 5°-10° 29. If the line is 8° wide and the stress constant AT, is 86.3 ksi/ deg A20, as given above, a stress of 50 ksi will cause the line to shift by only 7 percent of its width when the specimen is turned through 45°. Measurement of such a small shift requires that the line center be accurately located at each angle ij/. 

For the measurement of stress by x-rays we have developed three working equations, namely, (16-14), (16-17), and (16-26). Each contains an appropriate stress constant K, by which diffraction line shift is converted to stress. Furthermore each was derived on the assumption that the material under stress was an isotropic body obeying the usual laws of elasticity. This assumption has to be examined rather carefully if a calculated value of K is to be used for stress measurement. 

The stress constant K contains the quantity /(l -I- v), and we have tacitly assumed that the values of and v measured in the ordinary way during a tensile test are to be used in calculating the value of K. But these mechanically measured values are not necessarily the correct ones to apply to a diffraction measurement. In the latter, strains are measured in particular crystallographic directions, namely, the directions normal to the hkl) reflecting planes, and we know that both and... 

These considerations are amply supported by experiment. By making x-ray measurements on materials subjected to known stresses, we can determine the stress constant K experimentally. The values of K so obtained can differ substantially from the values calculated from the mechanically measured elastic constants. Moreover, for the same material the measured values of K usually vary with the indices hkl) of the reflecting planes. 

The strain due to bending is measured by an electrical-resistance strain gauge mounted near the region examined by x-rays. The product of this strain and the mechanically measured elastic modulus E of the material is the surface longitudinal stress direct loading of the same kind as that used, in the x-ray calibration, e.g., by four-point bending.)... 

The x-ray technique used in calibration should match the technique to be used later for the measurement of unknown stresses. For example, the stress constant determined with the focusing technique of Fig. 16-7 is not expected to agree with the stress constant determined by the parallel-beam technique. 

The stress constant K appropriate to any technique can be usefully divided into two parts, as suggested by Norton [16.13] ... 

The A e part of any stress constant is the important part, because it is determined only by the properties of the material, and it is the quantity that should be reported as the result of a calibration experiment. Similarly, any report of x-ray stress measurements should include the value of Kg used in the calculations. 

Experimentally determined stress constants are given in Table 16-1 for a variety of industrial alloys, ferrous and nonferrous. All have been determined with the diffractometer. 

High accuracy requires that systematic errors be minimized. These errors are chiefly of two kinds, those of a geometrical nature and those involved in the elastic-constant portion of the stress constant. The systematic errors cause an error in the measured stress which is proportional to the magnitude of the stress. 

The circumferential (hoop) stress in a cylinder of 1045 steel, due to water quenching followed by glass bead peening, is measured with a diffractometer (Cr Ka radiation, 211 reflection). The line shift A20 when a stiess-free specimen is rotated from = 0 to ij/ = 45° is -0.10°. Take the stress constant A", as 90 ksi/deg. The time 1 given below is the time required to accumulate 20,000 counts at each angle. 

KEY WORDS gypsum, physical tests, physical propenies, gypsum board, constant stress, constant strain... 

The Bueche-Halpin theory accounts well for the principal features of the tensile strength of unfilled rubbers. Because of the direct connection between ab and a viscoelastic function, time-temperature superposition of the strength follows naturally. Halpin (216) also found experimentally that ab was apparently the same function of the reduced time to break, tb/aT, whether the rupture experiment was carried out at constant stress, constant extension or constant rate of extension. 

C0 yield stress constant, Robertson-Stiff model (s 1)... 

Secondly, horizontal normal boundary stress is increased incrementally while keeping the vertical normal stress constant to produce increased shear stress in the fractures in various orientations. Through this process, anisotropic permeability and the effect of dilation on the permeability change is observed. 

Stress variables mean stress, maximum stress, minimum stress, constant load/constant strain, strain rate, plane stress/plane strain, biaxial, cyclic frequency wave shape. 

Hk = iXa- (A and a being the longitudinal saturation magnetostriction and isotropic stress constant, respectively)... 

Nematic monodomains have been prepared using a variant of the method introduced by Kiipfer and Finkelmann [10, 18] instead of keeping the stress constant in the second crosslinking step the strain was held constant in the second crosslinking step [53]. As for the case studied by Kupfer and Finkelmann, it is found that the monodomain character is retained after heating the sample into the isotropic phase upon return into the nematic phase. Stress strain relation has been measured for two classes of poly-siloxane elastomers. 

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