Uniaxial stress systems

Figure 3.5 shows this effect for an ordinary carbon steel and illustrates that the ductility of a material is affected by the type of stress system and the rate of application of this stress system. Between T2 and for example, the carbon steel displays ductile behavior in a simple uniaxial stress system (tensile test) or displays brittle characteristics at high rates of loading (impact test). Increasing either the strain rate or the complexity of the stress system moves the curve in Fig. 3.5 to the right. This amounts to an increase in the brittle transition temperature. Similar ductile or brittle behavior is observed above T4 and below Tj. 

In postulating a statistieal model for a statie stress variable, it is important to distinguish between brittle and duetile materials (Bury, 1975). For simple stress systems, i.e. uniaxial or pure torsion, where only one type of stress aets on the eomponent, the following equations determine the failure eriterion for duetile and brittle types to prediet the reliability (Haugen, 1980) ... 

The stress gradient also means that the occurrence of thermal softening failures is delayed. At any particular frequency of stressing, thermal softening failures will not occur until higher stresses if the stress system is bending rather than uniaxial. 

During service the impact behaviour of a plastic article will be influenced by the combined effects of the applied stress system and the geometry of the article. Although the applied stress system may appear simple (for example, uniaxial) it may become triaxial in local areas due to a geometrical discontinuity. Fig. 2.78... 

The material properties used in the simulations pertain to a new X70/X80 steel with an acicular ferrite microstructure and a uniaxial stress-strain curve described by er, =tr0(l + / )", where ep is the plastic strain, tr0 = 595 MPa is the yield stress, e0=ff0l E the yield strain, and n = 0.059 the work hardening coefficient. The Poisson s ratio is 0.3 and Young s modulus 201.88 OPa. The system s temperature is 0 = 300 K. We assume the hydrogen lattice diffusion coefficient at this temperature to be D = 1.271x10 m2/s. The partial molar volume of hydrogen in solid solution is... 

The second term is the reversible work done at a given stress by the volume expansion (contraction) Vdujk if one adds dn,- to the system under stress. For uniaxial stress, this is (q = cross section area = crystal length)... 

Figures 20A and B show the PL spectra, recorded at 290 K, at 600 nm, and as a function of pressure, for Cs9(SmW10O36) and SmWi0O36-LDH, respectively (Park et al., 2002). For the sake of comparison, the line shapes are normalized and displaced along the vertical axis. In both cases, the peak position is red-shifted by 4—5 nm when the hydrostatic pressure increases from 1 bar to 61 kbar. It was shown that the red-shift from A to A lies solely in the deformation of the samarium complexes by the uniaxial stress exerted by the host layers, whereas the shift from B to B is also influenced by the change in the cation environment. Under the same conditions, B is not at the same position for the non-intercalated (HN (n -b u t y 1) 3) 9 (SmW10O3e) and Cs9(SmWi0O36) compounds (Park et al., 2002). Thus only peak A is available to measure the unixial stress. This observation can be used to determine the uniaxial stress, when the external pressure is zero. For the SmW10O36—LDH system, the uniaxial stress varies significantly from 75 at 28 K to 140 kbar at 290 K (Park et al., 2002).

Until we discovered the constancy of the surface potential from the uniaxial stress results, like most other people, I had been more interested in constant surface charge models. If you do not know how the valency of a macroion varies with the external conditions, it is reasonable to assume it to be constant unless given evidence to the contrary. Given the evidence that y/0 70 mV is roughly constant for the n-butylammonium vermiculite system, what other consequences follow from this In particular, what happens if we apply the coulombic attraction theory with the constant surface potential boundary condition ... 

Clay system studied rigorously as a function of uniaxial stress p over a wide range of well-defined salt concentrations between 0.001 and 0.1 M... 

Given the volume fraction of the polymer inside the gel, we are now able to propose a quantitative model of bridging flocculation. Because Crawford et al. [4] studied the contraction of the interlayer spacing as a function of uniaxial stress for the same system without any added polymer, we are able to convert the observed d-values to effective uniaxial pressures caused by the bridging polymers. If we assume that we have one polymer bridge when the end-to-end polymer distance l (calculated according to Equation 12.1) exactly matches the d-value with the... 

Most of the above-cited work neglects the effect of stress or strain as a tensor. They mostly apply uniaxial stress or strain criteria. Unfortunately, most of the applications where ESC has been reported apply biaxial or multiaxial stresses to the polymer. Therefore, a more general model of the phenomenon of ESC is expected to account for generalized polymer-surface active agent systems, but also to account for generalized stress states in the material. 

Note also that Eq. (16-10) is valid whether the stress system is uniaxial or biaxial, i.e., whether is the only stress or is part of a biaxial system. If a transverse stress exists at right angles to a, it will alter d-, and d by the same... 

Fig. 4.7. Schematic of a stress apparatus of the compressing-spring type devised by C. Naud to be inserted in a continuous-flow optical cryostat for measuring the absorption of a sample under uniaxial stress. Extra optical apertures are indicated. The height adjustment system to the top of the cryostat is not shown (after [6])...

A uniaxial stress is usually designated by the symbol o, and a shearing stress by X. For certain lipids that behave like solid food systems, the relationship between stress and strain is represented by a straight line through the origin, up to the so-called limit of elasticity. The proportionality factor E for uniaxial stress is called Young s modulus, or the modulus of elasticity. For a shear stress, the modulus is called Coulomb modulus, or the tensile modulus G. 

Figure 8.10 gives an ensemble-average uniaxial stress-strain curve for PC and the associated system pressure resulting from this monotonic deformation. The smoothed stress-strain curve shows many of the same special features as the two individual stress-strain curves of PP in Fig. 8.8, as well as the ensemble-average result of Fig. 8.8. 

Attempts have also been made (Baker and Currell 1976, Baker et aL 1977) to correlate measured spin-lattice relaxation rates with orbit-lattice parameters derived from EPR measurements on the systems MgOrEr and CaPjtDy under uniaxial stress. For these ions the ground states are Pg quartets, for which a range of... 

To locate AE sources, 5-channel system is at least necessary for three-dimensional (3-D) analysis. Since 6-channnel system is the minimum requirement, 6-channel system is required for SiGMA. In contrast, 4-channel system is available for the 2-D analysis. One application is given in Fig. 8.14 (Shigeishi and Ohtsu 1999). Uniaxial stress is applied vertical to the plate specimen made of concrete, which contains a through-thickness slit. 4-channel system was employed for the measurement. Results show the case that slit angle to the loading axis is equal to 45°. 

The converse electrostrictive effect—the stress dependence of the permittivity—is also used in stress sensors [19]. A himorph structure provides superior stress sensitivity and temperature stability. A measuring system with a himorph structure, which subtracts the static capacitances of two dielectric ceramic plates, has been proposed [ 19]. The capacitance changes of the top and bottom plates have opposite signs for uniaxial stress and the same sign for temperature deviation. The response speed is limited by the capacitance measuring frequency to about 1 kHz. Unlike piezoelectric sensors, electrostrictive sensors are effective in the low-frequency range, especially DC. 

For isotropic bodies Poisson s ratio is defined as the negative ratio of transverse and longitudinal strain produced by the same stress system as above, that is uniaxial stress T[. For crystals it becomes necessary to relate the corresponding quantity to two directions. If we consider x as the transverse direction, we find... 

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