Static compressive stress/strain

From previous statistical studies on similar systems which Include the combination of errors Involved in sample preparation and measurement of static compressive stress-strain characteristics, the following reproducibility results were obtained (4,5, ) ... 

A considerable range of mechanical material property tests was conducted at the RWTUV facilities, including cold static compressive stress-strain (SCSS) of brick-only and composite samples, cold crushing strength (Sc) of brick-only, creep in compression (CIC) of brick-only and composites, thermal expansion (TE) of brick-only, and modulus of rupture (MOR) of brick-only. 

The testing at the Didier facilities at Weisbaden, Germany, was hot static compressive stress-strain (SCSS) of brick-only and composites and hot crushing strength of brick-only and composites. 

The above example is used to define the two load types in refractory fining systems. Since refractory finings are primarily exposed to thermal expansion loads, it is important to have accurate static compressive stress/strain (SCSS) data in order to determine the MOE data. It will be shown in later discussions on the SCSS data that most refractory materials become softer (lower MOE) at higher temperatures and also become more plastic at higher temperatures. SCSS data curves obtained from laboratory testing are used to define the MOE property as well as the plastic behavior of the refractory material in question. 

Figure 1 Static compressive stress-strain data for a fired 70% alumina brick.

Let us assume there are two candidate refractory materials. Refractory A and Refractory B, chosen for the lining project. We will also assume that both materials have the same thermal material properties, meaning that both refractories have the same temperature profiles. For the mechanical material properties, we assume that both materials have the same coefficient of thermal expansion and Poisson s ratio. The only difference is in the static compressive stress-strain (SCSS) data. Figure 4 shows the hypothetical SCSS data curves for the two materials at an operating temperature Tq. Since both materials have the same temperature and the same coefficient of thermal expansion, both materials have the same thermal strain, The ultimate crushing stress for Refractory A is /ca... 

Static compressive stress-strain (SCSS) data should be obtained on all candidate refractories. These data provide valuable information on which refractory has the greatest strain range, an important property for the thermal expansion strains. 

The compressive stress-strain measurements are performed in an Instron Universal Test Machine. Pad specimens (Figure 1) are loaded to the bottomed deflection (Figure 2) at 1.1 in. and unloaded without pause. A cross-head rate of 2.0 in./min which is sufficiently slow as to give essentially a static loading condition is employed. Compressive stress data are reported for deflections of 0.2, 0.4 and 0.6 in. 

Figure 13.13. Compressive stress-strain curves of native silica (SiOx and X-SiOx) and polyurea-crosslinked vanadia (VO and X-VOx) aerogels. Bulk densities SiOx - 0.213 gcm X-SiOx- 0.548 gcm VOx-0.121 gcm and X-VOx 0.430 gcm . A. Quasi-static compression of SiOx at a strain rate of 9 x 10 " s at 23°C X-SiOx at 5 x 10 s at 23°C and X-SiOx at 5 x 10 s at —196°C inset same curves plotted using a different scale. B. Quasi-static compression of yO iat a strain rate of 9 x 10 s at 23°C X-VOx nt 5 x 10 s at 23°C and X-VOx at 5 x 10 s at — 196°C inset up to 10% compressive strain.

A strength value associated with a Hugoniot elastic limit can be compared to quasi-static strengths or dynamic strengths observed values at various loading strain rates by the relation of the longitudinal stress component under the shock compression uniaxial strain tensor to the one-dimensional stress tensor. As shown in Sec. 2.3, the longitudinal components of a stress measured in the uniaxial strain condition of shock compression can be expressed in terms of a combination of an isotropic (hydrostatic) component of pressure and its deviatoric or shear stress component. 

Stress-strain relationships for soil are difficult to model due to their complexity. In normal practice, response of soil consists of analyzing compression and shear stresses produced by the structure, applied as static loads. Change in soil strength with deformation is usually disregarded. Clay soils will exhibit some elastic response and are capable of absorbing blast-energy however, there may be insufficient test data to define this response quantitatively. Soil has a very low tensile capacity thus the stress-strain relationship is radically different in the tension region than in compression. 

Najafbadi and Yip (18) have investigated the stress-strain relationship in iron under uniaxial loading by means of a MC simulation in the isostress isothermal ensemble. At finite temperatures, a reversible b.c.c. to f.c.c. transformation occurs with hysteresis. They found that the transformation takes place by the Bain mechanism and is accompanied by sudden and uniform changes in local strain. The critical values of stress required to transform from the b.c.c. to the f.c.c. structure or vice versa are lower than those obtained from static calculations. Parrinello and Rahman (14) investigated the behavior of a single crystal of Ni under uniform uniaxial compressive and tensile loads and found that for uniaxial tensile loads less than a critical value, the f.c.c. Ni crystal expanded along the axis of stress reversibly. 

Deformability and Wet Mass Rheology The static yield stress of wet compacts has previously been reported in Fig. 21-113. However, the dependence of interparticle forces on shear rate clearly impacts wet mass rheology and therefore deformabihty. Figure 21-117 illustrates the dynamic stress-strain response of compacts, demonstrating that the peak flow or yield stress increases proportionally with compression velocity [Iveson et al., Powder Technol., 127, 149 (2002)]. Peak flow stress of wet unsaturated compacts (initially pendular state) can be seen to also increase with Ca as follows (Fig. 21-118) ... 

Deformation such as drawing, compression, annealing, strain, creep and stress relaxation of polymers including fibers may produce quite different orientational behavior, the results of which can be examined with solid-state NMR from both the static and dynamic viewpoints. The accurate model produced on the basis of atomic resolution of the local structure and the local dynamics can be built up in order to interpret the mechanical properties of polymers and the deformation mechanisms. 

As in true strain, the expression above takes into account cross-sectional area changes in a certain cohesive structure (or cake) of powdered material. If the material is isotropic, another possible expression that includes the Poisson s ratio p (the ratio of transverse strain and axial strain resulting from uniformly distributed axial radial stress during static compression of the material in absolute value). The Poisson s ratio, or bulk modulus, permits prediction of the transverse contraction or expansion that occurs when a stress is applied longitudinally. 

Static mechanical measurements to evaluate the stress-strain relationship in cholesteric sidechain LCEs have been described [71, 72]. In [72] it has been found, for example, thatfor0.94nominal stress Cn is nearly zero as the poly domain structure must be converted first into a monodomain structure. For deformations A < 0.94, the nominal stress increases steeply. Similar results have also been reported elsewhere [71]. The nominal mechanical stress as a function of temperature for fixed compression has also been studied for cholesteric sidechain elastomers [71]. It turns out that the thermoelastic behavior is rather similar as that of the corresponding nematic LCE [2, 5]. 

Tangent modulus n. The slope of the curve at any point on a static stress-strain graph (dcr/ds) expressed in pascals per imit of strain. This slope is the tangent modulus in whatever mode of stress the curve has arisen from — tension compression, or shear. [Since strain is dimensionless, the unit given for modulus is normally just stress (Pa)]. Sepe MP (1998) Dynamic mechanical analysis. Plastics Design Library, Norwich, New York. 

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