Stress, types shear

Fig. 2. Flow curves (shear stress vs shear rate) for different types of flow behavior.

The equations and methods for determining viscosity vary greatly with the type of instmment, but in many cases calculations may be greatly simplified by calibration of the viscometer with a standard fluid, the viscosity of which is known for the conditions involved. General procedures for calibration measurement are given in ASTM D2196. The constant thus obtained is used with stress and shear rate terms to determine viscosity by equation 25, where the stress term may be torque, load, or deflection, and the shear rate may be in rpm, revolutions per second (rps), or s F... 

The stress-intensity factors are quite different from stress concentration factors. For the same circular hole, the stress concentration factor is 3 under uniaxial tension, 2 under biaxiai tension, and 4 under pure shear. Thus, the stress concentration factor, which is a single scalar parameter, cannot characterize the stress state, a second-order tensor. However, the stress-intensity factor exists in all stress components, so is a useful concept in stress-type fracture processes. For example. 

Generic Material Type Shear Modulus, MPa Shear Stress, MPa At Poisson s Ratio... 

In this volume not all stress types are treated. Various aspects have been reviewed recently by various authors e.g. The effects of oxygen on recombinant protein expression by Konz et al. [2]. The Mechanisms by which bacterial cells respond to pH was considered in a Symposium in 1999 [3] and solvent effects were reviewed by de Bont in the article Solvent-tolerant bacteria in biocatalysis [4]. Therefore, these aspects are not considered in this volume. Influence of fluid dynamical stresses on micro-organism, animal and plant cells are in center of interest in this volume. In chapter 2, H.-J. Henzler discusses the quantitative evaluation of fluid dynamical stresses in various type of reactors with different methods based on investigations performed on laboratory an pilot plant scales. S. S. Yim and A. Shamlou give a general review on the effects of fluid dynamical and mechanical stresses on micro-organisms and bio-polymers in chapter 3. G. Ketzmer describes the effects of shear stress on adherent cells in chapter 4. Finally, in chapter 5, P. Kieran considers the influence of stress on plant cells. 

In addition to the measurement of the viscosity, this technique also allows the yield stress to be estimated. For a typical yield stress type material, there is a critical shear stress below which the material does not deform and above which it flows. In pipe flow, the shear stress is linear with the radius, being zero at the center and a maximum at the wall. Hence, the material would be expected to yield at some intermediate position, where the stress exceeds the yield stress. The difficulty with this method is in the determination of the point at which yielding occurs and, indeed, whether the material is appropriately modeled as having a yield stress or is... 

Fig. 4.3.2 (a) The relationships of shear stress and shear rate for several types of common materials, where the slope is the viscosity T). A non-Newtonian fluid is characterized by its... 

When the measured values of shear stress or viscosity are plotted versus shear rate, various types of behavior may be observed depending upon the fluid properties, as shown in Figs. 3-5 and 3-6. It should be noted that the shear stress and shear rate can both be either positive or negative, depending upon the direction of motion or the applied force, the reference frame, etc. (however, by our convention they are always the same sign). Because the viscosity must always be positive, the shear rate (or shear stress) argument in... 

In the simplest case, that of time-independent behaviour, the shear stress depends only on the shear rate but not in the proportional manner of a Newtonian fluid. Various types of time-independent behaviour are shown in Figure 1.19(a), in which the shear stress is plotted against the shear rate on linear axes. The absolute values of shear stress and shear rate are plotted so that irrespective of the sign convention used the curves always lie in the first quadrant. 

DIF values vary for different stress types in both concrete and steel for several reasons. Flexural response is ductile and DIF values are permitted which reflect actual strain rates. Shear stresses in concrete produce brittle failures and thus require a degree of conservatism to be applied to the selection of a DIF. Additionally, test data for dynamic shear response of concrete materials is not as well established as compressive strength. Strain rates for tension and compression in steel and concrete members are lower than for flexure and thus DIF values are necessarily lower. 

Further non-Newtonian types of behavior appear when time is introduced as a variable. Fluids whose viscosity decreases with time when sheared at a constant rate are called thixotropic, whereas fluids whose viscosity increases with time when sheared at a constant rate are termed rheopectic. Thixotropic behavior is represented schematically in Figure 4.6. Note that the two viscosities (slope of shear stress vs. shear rate) rip and r P2 are different, depending upon the time they were sheared at a given rate. 

Data from viscometers are often presented as a linear plot of shear stress versus shear rate, sometimes called a rheogram (Figure HI.1.2). This type of plot allows the viewer to see directly if there is Newtonian behavior because the plot will take the form of a straight line through the origin. A non-Newtonian response is, by definition, nonlinear and may or may not pass through the origin. If the sample has an apparent yield stress, then the line or curve will... 

This section describes common steps designed to measure the viscosity of non-Newtonian materials using rotational rheometers. The rheometer fixture that holds the sample is referred to as a geometry. The geometries of shear are the cone and plate, parallel plate, or concentric cylinders (Figure HI. 1.1). The viscosity may be measured as a function of shear stress or shear rate depending upon the type of rheometer used. 

Stability of an enzyme is usually understood to mean temperature stability, although inhibitors, oxygen, an unsuitable pH value, or other factors such as mechanical stress or shear can decisively influence stability (Chapter 17). The thermal stability of a protein, often employed in protein biochemistry, is characterized by the melting temperature Tm, the temperature at which a protein in equilibrium between native (N) and unfolded (U) species, N U, is half unfolded (Chapter 17, Section 17.2). The melting temperature of a protein is influenced on one hand by its amino acid sequence and the number of disulfide bridges and salt pairs, and on the other hand by solvent, added salt type, and added salt concentration. Protein structural stability was found to correlate also with the Hofmeister series (Chapter 3, Section 3.4 Hofmeister, 1888 von Hippel, 1964 Kaushik, 1999) [Eq. (2.18)]. 

The chemical cleaning methods used for aluminum will have slightly different effectiveness with different aluminum alloys. The permanence of these bonds will also depend on the type of alloys used because of their different corrosion rates under extreme environmental conditions. The yield strength of the alloy also has an influence on bond strength when stressed in shear. The peel test is usually considered a more meaningful... 

The maximum strain rate (e < Is1) for either extensional rheometer is often very slow compared with those of fabrication. Fortunately, time-temperature superposition approaches work well for SAN copolymers, and permit the elevation of the reduced strain rates kaj to those comparable to fabrication. Typical extensional rheology data for a SAN copolymer (h>an = 0.264, Mw = 7 kg/mol,Mw/Mn = 2.8) are illustrated in Figure 13.5 after time-temperature superposition to a reference temperature of 170°C [63]. The tensile stress growth coefficient rj (k, t) was measured at discrete times t during the startup of uniaxial extensional flow. Data points are marked with individual symbols (o) and terminate at the tensile break point at longest time t. Isothermal data points are connected by solid curves. Data were collected at selected k between 0.0167 and 0.0840 s-1 and at temperatures between 130 and 180 °C. Also illustrated in Figure 13.5 (dashed line) is a shear flow curve from a dynamic experiment displayed in a special format (3 versus or1) as suggested by Trouton [64]. The superposition of the low-strain rate data from two types (shear and extensional flow) of rheometers is an important validation of the reliability of both data sets. 

The third type of material behaves as a Mohr s body where the value of the yield stress in shear is a function of the normal stress on the plane of shear. A theoretical... 

Before recognition of the importance of inherent flaws in a material, the analyst relied upon one of several stress or strain criteria to predict conditions for failure. These criteria are still useful as failure predictors when flaws are less than the critical size. Typical criteria of this type include maximum principal stress, maximum shear stress, maximum octahedral shear stress, and others depending generally on experimental evidence and experience (, These criteria hypothesize, respectively, that... 

Illustrated in Fig. 9.1.1, relative to a Newtonian fluid, are the behaviors of the shear stress versus shear rate in a Couette flow for three principal types of non-Newtonian fluids that can be characterized by the form of the apparent viscosity function in Eq. (9.1.3). A number of empirical functions have been widely employed to characterize the apparent viscosities for these classes of fluids. One termed a Bingham plastic behaves like a solid until a yield stress Tq is exceeded subsequent to which it behaves like a Newtonian fluid with a plastic viscosity lip. The apparent viscosity for this fluid may be written... 

Two types of stress can be present simultaneously in one plane, provided that one of the stresses is shear stress. Under certain conditions, different basic stress type combinations may be simultaneously present in the material. An example would be a reactor vessel during operation. The wall has tensile stress at various locations due to the temperature and pressure of the fluid acting on the wall. Compressive stress is applied from the outside at other locations on the wall due to outside pressure, temperature, and constriction of the supports associated with the vessel. In this situation, the tensile and compressive stresses are considered principal stresses. If present, shear stress will act at a 90° angle to the principal stress. 

Since stress may act on a plane in different ways, this constant is defined in different ways depending on the applied force and the resultant strain. Two of the most important types of stress are shear stress, which acts in a plane, and tensile stress, which acts normally or perpendicular to the plane. Normal stresses may be tensile or compressive. 

Finally, it should be recognized that, when a stress is applied to a pressure-sensitive adhesive, it is either a tensile stress, a shear stress, or a combination of both. In the specific end use of a given pressure-sensitive adhesive system, a clear understanding should exist as to what type of stresses can be encountered, to ensure that the test methods applied bear a relationship to use. The various standard test methods can now be considered. 

With regard to pressure gradients, extrusion compounds tested to date all proved to answer one of two type descriptions. Figure 2 depicts the pressure as a function of cylinder length. Type-1 compounds have a linear pressure gradient resulting in constant shear stress. Type-2 compounds fol-... 

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