Shear stress yield point

We normally ascribe elastic and plastic behavior to be typical of the solid state, and the viscous behavior to that of the hquid state. It should, however, be understood that the real distinctions between a sohd state and a liquid state are truly subtle. A liquid has nearabsence of a shear stress yield point and a real-time-measurable shear stress relaxation rate. The drift of continents over millennia is one such thought-provoking example. Should the continents be classified as sohds or as hquids ... 

Stress, or force per unit area (SI units Pa or N/m2), has been defined as the intensity of the internal components of forces in a certain point through a given plane of a body. Compressive stress (or pressure) refers to the perpendicular components toward a normal plane on which compressive forces act. Different denominations can be used for stresses that characterize compression of a certain volume of powder mass natural and engineering stress, compressive, tensile, or shear stress, yield stress, unconfined yield stress, and principal stresses. 

Under compression or shear most polymers show qualitatively similar behaviour. However, under the application of tensile stress, two different defonnation processes after the yield point are known. Ductile polymers elongate in an irreversible process similar to flow, while brittle systems whiten due the fonnation of microvoids. These voids rapidly grow and lead to sample failure [50, 51]- The reason for these conspicuously different defonnation mechanisms are thought to be related to the local dynamics of the polymer chains and to the entanglement network density. 

Powder Mechanics Measurements As opposed to fluids, powders may withstand applied shear stress similar to a bulk solid due to interparticle friction. As the applied shear stress is increased, the powder will reach a maximum sustainable shear stress T, at which point it yields or flows. This limit of shear stress T increases with increasing applied normal load O, with the functional relationship being referred to as a yield locus. A well-known example is the Mohr-Coulomb yield locus, or... 

For a monolayer film, the stress-strain curve from Eqs. (103) and (106) is plotted in Fig. 15. For small shear strains (or stress) the stress-strain curve is linear (Hookean limit). At larger strains the stress-strain curve is increasingly nonlinear, eventually reaching a maximum stress at the yield point defined by = dT Id oLx x) = 0 or equivalently by c (q x4) = 0- The stress = where is the (experimentally accessible) static friction force [138]. By plotting T /Tlx versus o-x/o x shear-stress curves for various loads T x can be mapped onto a universal master curve irrespective of the number of strata [148]. Thus, for stresses (or strains) lower than those at the yield point the substrate sticks to the confined film while it can slip across the surface of the film otherwise so that the yield point separates the sticking from the slipping regime. By comparison with Eq. (106) it is also clear that at the yield point oo. 

Some materials have the characteristics of both solids and liquids. For instance, tooth paste behaves as a solid in the tube, but when the tube is squeezed the paste flows as a plug. The essentia] characteristic of such a material is that it will not flow until a certain critical shear stress, known as the yield stress is exceeded. Thus, it behaves as a solid at low shear stresses and as a fluid at high shear stress. It is a further example of a shear-thinning fluid, with an infinite apparent viscosity at stress values below the yield value, and a falling finite value as the stress is progressively increased beyond this point. 

Figure 3 gives an example of a typical force profile. The force is increased continuously and reaches the point - at the end of the first part of the force profile - where the pectin preparations start to flow. The so-called yield point is reached. The further increase leads to the continuous destruction of the internal structure and the proceeding shear thinning. The applied stress in part 3 of the stress profile destroys the structure of the fruit preparations completely. Now the stress is reduced linearly, see part 4 and 5, down to zero stress. The resulting flow curves 2, 3 and 4 and the enclosed calculated area from the hysteresis loop give important evidence about the time-dependent decrease of viscosity and a relative measure of its thixotropy. 

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... 

A plot of Tvs. G yields a rheogram or a flow curve. Flow curves are usually plotted on a log-log scale to include the many decades of shear rate and the measured shear stress or viscosity. The higher the viscosity of a liquid, the greater the shearing stress required to produce a certain rate of shear. Dividing the shear stress by the shear rate at each point results in a viscosity curve (or a viscosity profile), which describes the relationship between the viscosity and shear rate. The... 

The continuous chain model includes a description of the yielding phenomenon that occurs in the tensile curve of polymer fibres between a strain of 0.005 and 0.025 [ 1 ]. Up to the yield point the fibre extension is practically elastic. For larger strains, the extension is composed of an elastic, viscoelastic and plastic contribution. The yield of the tensile curve is explained by a simple yield mechanism based on Schmid s law for shear deformation of the domains. This law states that, for an anisotropic material, plastic deformation starts at a critical value of the resolved shear stress, ry =/g, along a slip plane. It has been... 

Concentrated particle suspensions may also show a yield point which must be exceeded before flow will occur. This may result from interaction between irregularly shaped particles, or the presence of water bridges at the interface between particles which effectively bind them together. Physical and chemical attractive forces between suspended particles can also promote flocculation and development of particle network structures, which can be broken down by an applied shear stress [2]. 

Khan and Armstrong [52] showed that the critical strain, and therefore the yield stress, was dependent on the initial orientation of the cells, for shearing and elongational deformations indeed, for one particular orientation under exten-sional deformation, a yield stress was not observed. Beyond the yield point,... 

Below the yield point, however, stress/strain behaviour was found to be independent of initial cell orientation, due to the threefold symmetry of the hexagonal cellular array [54], This allows a correlation between shearing and extensional deformations to be made [55], namely that shear can be considered as elongation followed by rotation. Thus, information on one type of deformation can be obtained by solving expressions for the other. 

It was found that increasing Ca caused the yield stress and yield strain to increase, along with cell deformation at the yield point. At sufficiently high values of Ca, cell distortion is so severe that film thinning and rupture can occur, resulting in mechanical failure of the foam (Fig. 6). This implies the presence of a shear strength for foams and HIPEs. The initial orientation of the cells was also found to affect the stress/strain behaviour of the system in the presence of viscous forces [63]. For some particular orientations, periodic flow was not observed for any value of Ca. 

Fluids with shear stresses that at any point depend on the shear rates only and are independent of time. These include (a) what are known as Bingham plastics, materials that require a minimum amount of stress known as yield stress before deformation, (b) pseudoplastic (or shear-thinning) fluids, namely, those in which the shear stress decreases with the shear rate (these are usually described by power-law expressions for the shear stress i.e., the rate of strain on the right-hand-side of Equation (1) is raised to a suitable power), and (c) dilatant (or shear-thickening) fluids, in which the stress increases with the shear rate (see Fig. 4.2). 

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... 

---