By Montgomery T. Shaw
Chapter 1 creation (pages 1–14):
Chapter 2 rigidity (pages 15–44):
Chapter three speed, pace Gradient and expense of Deformation (pages 45–58):
Chapter four courting among pressure and fee of Deformation: The Newtonian Fluid (pages 59–70):
Chapter five Generalized Newtonian Fluids—A Small yet vital Step towards an outline of actual habit for Polymers (pages 71–96):
Chapter 6 common Stresses—Ordinary habit for Polymeric Fluids (pages 97–123):
Chapter 7 Experimental equipment (pages 125–196):
Chapter eight pressure, Small and massive (pages 197–238):
Chapter nine Molecular Origins of Rheological habit (pages 239–259):
Chapter 10 effortless Polymer Processing innovations (pages 261–290):
Chapter eleven Quality?Control Rheology (pages 291–309):
Chapter 12 stream of changed Polymers and Polymers with Supermolecular constitution (pages 311–336):
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Extra info for Introduction to Polymer Rheology
The stress is simply the force per unit area. If we want to stretch the sample in the x direction, we apply the pair of normal stresses in opposite directions, as shown. , σχχ = FXIAX, where σχχ is the stress, Fx is the force in the x direction, and Ax is the area pointed, via its normal, in the x direction. By convention, the first subscript in σ„ refers to the direction of the area normal, while the second refers to force direction. X 4 Figure 2-2. Association of the subscripts with the outward-pointing normal and the force direction, both pointed in the positive x direction.
A point attached to the material. In talking about material points, it is important to understand that these points are not subject to Brownian motion and thus diffusion through the material. For this reason, a tiny particle may be a better representation of the continuum than, say, a macromolecule with a molecular tag. Note the choices of nomenclature illustrated in Figure 3-1. As with stress, we can stick with the conventional abbreviations for the coordinate system—in this case, rectangular—or use the numbers as shown in Table 2-1.
To introduce matrix notation, we need to display an elementary matrix from high school algebra: X= \X2\ X (2-4) 22J Here X (bold type) stands for the entire matrix, and the xy are the elements of this 2x2 matrix. In the case of three-dimensional stress the relevant matrix will be σ12 σ13 σ21 σ22 2 3 <*n σ ν σ 31 σ 32 CT (2-5) 33y where σ is called the total stress tensor. Why the word "tensor" instead of "matrix"? The answer to this question is a bit more complicated than "convention," as tensors enjoy some properties that not all matrices share.