Strength Concepts

What has been accomplished in preceding sections on stiffness relationships serves as the basis for determination of the actual stress field what remains is the definition of the allowable stress field. The first step in such a definition is the establishment of allowable stresses or strengths in the principal material directions. Such information is basic to the study of strength of an orthotropic lamina. 

For a lamina stressed in its own plane, there are three fundamental strengths if the lamina has equal strengths in tension and compression  

The stiffness wouid also be high in the 1-direction and low in the 2-direction, as is easily imagined on the physical basis of the fiber orientation. Imagine that, in the 1-2 plane, the stresses are 

obviously the maximum principal stress is lower than the largest strength. However, 02 is greater than Y, so the lamina must fail under the imposed stresses (perhaps by cracking parallel to the fibers, but not necessarily). The key observation is that strength is a function of orientation of stresses relative to the principal material coordinates of an orthotropic lamina. In contrast, for an isotropic material, strength is independent of material orientation relative to the imposed stresses (the isotropic material has no orientation). 

If the material has different properties in tension and compression as do most composite materials, then the following strengths are required  

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Other researchers have substantially advanced the state of the art of fracture mechanics applied to composite materials. Tetelman [6-15] and Corten [6-16] discuss fracture mechanics from the point of view of micromechanics. Sih and Chen [6-17] treat the mixed-mode fracture problem for noncollinear crack propagation. Waddoups, Eisenmann, and Kaminski [6-18] and Konish, Swedlow, and Cruse [6-19] extend the concepts of fracture mechanics to laminates. Impact resistance of unidirectional composites is discussed by Chamis, Hanson, and Serafini [6-20]. They use strain energy and fracture strength concepts along with micromechanics to assess impact resistance in longitudinal, transverse, and shear modes. 

The behavior of the nonpolar bonded phases, as well as the column packings based on crossbnked organic polymers of low polarity, however, differs from that of polar column packings and the classical solvent strength concept should be reevaluated. This is especially important for the alkyl bonded phases (Section 16.8.1). In this case, surface and interface adsorption of polymer species (Section 16.3.5) plays a less important role and macromolecules are mainly retained by the enthalpic partition (absorption) (Section 16.3.6). In order to ensure this kind of retention of polymer species, the mobile phase must push them into the solvated bonded phase. Therefore the interactions of mobile phase with both the bonded phase and (especially) with the sample macromolecules—that is, the solvent quality—extensively controls retention of latter species within the alkyl bonded phases. 

An interesting estimate of the significance of the core parameter can be constructed by harking back to our discussion of the ideal strength concept. There, we noted that when shear stresses reach a value on the order of /r/27r, the forces... 

Compression and compaction parameters such as density, porosity, stress, and strain are introduced. Furthermore, other factors of importance in stress measurement of powder beds in different situations such as compression, tension, shearing, and impact are explained. The fluidity of food powders is a controversial topic in food powder characterization and of top relevance in the food industry. Concepts such as compressibility and other flowability indicators are important for understanding the effects of compression phenomena during storage, production, and handling. Food powder strength concepts such as hardness relate to other concepts like attrition, which are a common occurrence in compaction processes. 

Let us consider the behavior depicted in Fig. 7-5b in terms of the asperity-junction mechanism for the boundary-lubricated case. The asperities actively in contact are classified into two categories bare asperities, and asperities protected by a film of lubricant. The junction strength concept gives the expression below for the tangential tractive force required for sliding ... 

However, in view of the detailed knowledge about the constitution of adsorbed monomolecular films (their structure and the successful application of van der Waals dispersion forces to account for their properties), it seems reasonable to require that the pressure-dependent shear strength concept be treated with equivalent detail and precision. Otherwise the concept is essentially data-fitting and leaves the door open for another empirical explanation which is strongly supported by observation namely, that in actual experimentation there are enough defects in the adsorbed film to permit significant contributions to the overall observed friction from microscopic regions not protected by the film. 

This mostly electrostatic, semiquantitative ("or nearly equal to") rule has turned out to be one of the most powerful ones, and the so-called bond-valence (or bond-length-bond-strength) concept is built upon it. For reasons of brevity, we will stop here but cover the latter concept - a quantitative one, in fact - in more detail in Section 1.5. 

The ions under consideration are assumed to be freely moving and charges of opposite sign are assumed not to be separated. The concept is much used in connection with the electrophoresis of proteins. The solubility of proteins depends partly on the ionic conditions of the environment. In salt solutions these ionic conditions can be discussed satisfactorily with the ionic strength concept, but not in ampholyte solutions. In spite of the fact that the ionic strength is low, the carrier ampholytes at their isoelectric points contribute to the ionic cloud surrounding the dissolved protein molecules. Thus they also contribute to the solubility and stability conditions of the protein molecule. 

The Soil Mechanics II (SMII) course is focused mainly on the mechanical behaviour of soils (in particular its strength). Concepts, theories and methods generally used for the design of civil engineering structures are presented. Emphasis is placed on situations... 

There are several definitions of acids and bases. We are especially interested here in the Br0nsted-Lowry definition and its consequences. After reviewing definitions, we shall study the strength concept of acids and bases. It is important because it allows us to predict acid-base reactions. 

From these considerations, we see that the stronger an acid is, the weaker its conjugate base is. We also see that once the Ka value is known, so is the case of Kb. There is redundancy between the two strength concepts. 

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