Bulk modulus, yield stresses

The use of a rotating vane has become very popular as a simple to use technique that allows slip to be overcome (33,34). Alderman et al (35) used the vane method to determine the yield stress, yield strain and shear modulus of bentonite gels. In the latter work it is interesting to note that a typical toique/time plot exhibits a maximum torque (related to yield stress of the sample) after which the torque is observed to decrease with time. The fall in torque beyond the maximum point was described loosely as being a transition from a gel-like to a fluid-like behavior. However, it may also be caused by the development of a slip surface within the bulk material. Indeed, by the use of the marker line technique, Plucinski et al (15) found that in parallel plate fixtures and in slow steady shear motion, the onset of slip in mayonnaises coincided with the onset of decrease in torque (Fig. 8). These authors found slip to be present for... 

Recalling the dilational Equationfi (28) and (29) and the distortional Equations (30) and (31). These equations can be adjusted for stress relaxation boundary conditions shown in Equations (73) and (74). Thus, using the tensor Equations (73) and (74) and Equations (28) and (29) to compute the dilational and distortional stresses and strains. Once the dilational and distortional stresses and strains are computed, the shear and bulk modulus Equations (63) and (64) can be used to relate stress to strain yielding ... 

The rheological parameters of primary scientific and practical concern are the static and dynamic shear modulus, the yield stress, and the shear rate-dependent viscosity. The aim is to understand and predict how these depend on the system parameters. In order to accomplish this with any hope of success, there are two areas that need to be emphasized. First, the systems studied must be characterized as accurately as possible in terms of the volume fraction of the dispersed phase, the mean drop size and drop size distribution, the interfacial tension, and the two bulk-phase viscosities. Second, the rheological evaluation must be carried out as reliably as possible. 

On the other hand materials deform plastically only when subjected to shear stress. According to Frenkel analysis, strength (yield stress) of an ideal crystalline solid is proportional to its elastic shear modulus [28,29]. The strength of a real crystal is controlled by lattice defects, such as dislocations or point defects, and is significantly smaller then that of an ideal crystal. Nevertheless, the shear stress needed for dislocation motion (Peierls stress) or multiplication (Frank-Read source) and thus for plastic deformation is also proportional to the elastic shear modulus of a deformed material. Recently Teter argued that in many hardness tests one measures plastic deformation which is closely linked to deformation of a shear character [17]. He compared Vickers hardness data to the bulk and shear... 

Scanning electron microscope studies were performed on polystyrene spheres sitting on polished silicon surfaces by Rimai, Demejo and Bowen. The bulk polymer had a Young s modulus of 2.55 GPa and a yield stress of 10.8 MPa when measured on a testing machine. With such a low yield point it was estimated that the particles should be plastically deformed under the adhesion forces. Therefore they applied the plastic deformation theory of Maugis and Pollock to fit the results, as shown in Fig. 9.28. This gave the expression for contact diameter d in terms of sphere diameter D... 

A clearly visible application for the grafted from materials is also in ballistic protection. With a relatively low modulus (e.g., 148 MPa for polystyrene-crosslinked samples -Table 13.2) and bulk density (0.46 gcm ), it is calculated that the speed of sound (equal to [modulus/bulk density] ) is 635 m s This value is very low for a solid material and highly desirable because it will extend the duration of an impact reducing the effective force on the material. The relatively low yield stress (7.2 MPa) will allow early activation of the energy absorption mechanism, while the long stress plateau will allow for large energy absorption. 

This theory is more complicated than it may seem for three reasons. In order to predict failure of the joint it becomes necessary to know the fundamental properties of the adhesives in bulk form. Measuring properties such as tensile strength and modulus, yield strength, and shear strength is difficult due to specimen fabrication limitations. As mentioned, typical test methods measure properties of the bonded joint rather than just the adhesive s properties. Another complexity arises in the determination of local stresses in the adhesive joint. Stresses typically occur from the application of loads on a system however, deformation of the adherends with respect to the adhesive and stress concentrations in the joint can also produce large local stresses. The last reason for complications is that each joint geometry or design can produce different types of stresses and in different locations. 

Rheological measurements are used to investigate the bulk properties of suspension concentrates (see Chapter 7 for details). Three types of measurements can be applied (1) Steady-state shear stress-shear rate measurements that allow one to obtain the viscosity of the suspensions and its yield value. (2) Constant stress or creep measurements, which allow one to determine the residual or zero shear viscosity (which can predict sedimentation) and the critical stress above which the structure starts to break-down (the true yield stress). (3) Dynamic or oscillatory measurements that allow one to obtain the complex modulus, the storage modulus (the elastic component) and the loss modulus (the viscous component) as a function of applied strain amplitude and frequency. From a knowledge of the storage modulus and the critical strain above which the structure starts to break-down , one can obtain the cohesive energy density of the structure. 

The in-use performance and handling of agglomerated or tabletted products is often closely related to structure (e.g., porosity) and mechanical properties (hardness, yield stress, modulus, toughness, etc.). The compaction diagram is a useful method to measure the properties of granular materials as well as the characterization of bulk structures (e.g., tablets) formed by compaction. 

The mechanical properties of materials involve various concepts such as hardness, stiffness, and piezoelectric constants, Young s and bulk modulus, and yield strength. The solids are deformed under the effect of external forces and the deformation is described by the physical quantity strain. The internal mechanical force system that resists the deformation and tends to return the solid to its undeformed initial state is described by the physical quantity stress. Within the elastic limit, where a complete recoverability from strain is achieved with removal of stress, stress g is proportional to strain e. The generalized Hooke s law gives each of the stress tensor components as linear functions of the strain tensor components as... 

Abstract This paper describes a method of measuring the tensile properties of a bulk adhesive — including modulus of elasticity, yield stress and strain, and tensile strength and strairL The authors developed the method unaware of ASTM Test Method for Tensile Properties of Thin Plastic Sheeting (D 882). Not surprisingly, requirements founded on common sense are the same in the ASTM Standard as in the present study. 

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