Shear diagram

Figure 8-5 Shearing Stress-Rate of Shear Diagrams. (A) Newtonian liquid, viscous flow, (B) dilatant flow, (C) pseudoplastic flow, (D) plastic flow.

Thixotropy can be defined as an isothermal, reversible, sol-gel transformation and is a behavior common to many foods. Thixotropy is an effect brought about by mechanical action, and it results in a lowered apparent viscosity. When the body is allowed sufficient time, the apparent viscosity will return to its original value. Such behavior would result in a shear stress-rate-of-shear diagram, as given in Figure 8-19. Increasing shear rate results in increased shear stress up to a maximum after the maximum is reached, decreasing shear rates will result in substantially lower shear stress. 

Figure 8-19 Shear Stress-Rate-of-Shear Diagram of a Thixotropic Body. Source From J.M. deMan amd F.W. Wood, Hardness of Butter. II. Influence of Setting, J. Dairy Sci. Vol. 42, pp. 56-61, 1959.

The major types of fluid flow behavior can be described by means of basic shear diagram of shear rate versus shear stress, such as Figures 1-2 and 1-3. In Figure 1-2, the shear stresses are plotted against the shear rates (independent variable) which is the conventional method. However, some authors plot shear rates against the shear stresses (independent variable) as shown in Figure 1-3. With the introduction of controlled-stress rheometers, the use of shear stress as the independent variable is often desirable. 

Figure 1-2 Basic Shear Diagram of Shear Rate versus Shear Stress for Classification of Time-Independent Fiow Behavior of Fiuid Foods Newtonian, Shear-Thinning, and Shear-Thickening. Also, some foods have yield stress that must be exceeded for flow to occur Bingham and Herschel-Bulkley (H-B).

F re 1-3 Basic Shear Diagram Similar to Figure 1-2, Except that Shear Stress is Plotted as the Independent Variable Newtonian, Shear-Thickening, Bingham, and Herschel-Bulldey. 

A flow model may be considered to be a mathematical equation that can describe rheological data, such as shear rate versus shear stress, in a basic shear diagram, and that provides a convenient and concise manner of describing the data. Occasionally, such as for the viscosity versus temperature data during starch gelatinization, more than one equation may be necessary to describe the rheological data. In addition to mathematical convenience, it is important to quantify how magnitudes of model parameters are affected by state variables, such as temperature, and the effect of structure/composition (e.g., concentration of solids) of foods and establish widely applicable relationships that may be called functional models. 

Time-Independent Non-Newtonian Fluids. Time-independent non-Newtonian fluids are characterized by having the fluid viscosity as a function of the shear rate (or shear stress). However, the fluid viscosity is independent of the shear history of the fluid. Such fluids are also referred to as non-Newtonian viscous fluids". Figure 1 shows a typical shear diagram for the various time-independent non-Newtonian fluids. 

Figure 1. Shear diagram for the various type of fluids.

The pile moment and shear diagram can be developed per above load/reaction diagram. Then, the pile section moment and shear strength should be checked. Finally, the strength of timber logging element shall be checked. 

Shear diagram when saddle is near head... 

Olmsted PD (1999b) Two-state shear diagrams for complex fluids in shear flow. Europhys Lett 48(3) 339-345... 

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