Strength theoretical limits

The importance of inherent flaws as sites of weakness for the nucleation of internal fracture seems almost intuitive. There is no need to dwell on theories of the strength of solids to recognize that material tensile strengths are orders of magnitude below theoretical limits. The Griffith theory of fracture in brittle material (Griflfith, 1920) is now a well-accepted part of linear-elastic fracture mechanics, and these concepts are readily extended to other material response laws. 

The energy stored in a flywheel depends on the strength of the rotor material. Carbon fiber tensile strength remains well below theoretical limits. Expected increases in strength along with reduction in cost as the use of this material expands will translate into more energy dense, less expensive rotors. 

The tensile strength of a pure liquid is determined by the attractive intermolecular forces which maintain its liquid state the calculated tensile strength of water, for example, is in excess of -1000 atmospheres (7). In practice however, the measured threshold for initiation of cavitation is never more than a small fraction of that. Indeed, if the observed tensile strengths of liquids did approach their theoretical limits, the acoustic intensities required to initiate cavitation would be well beyond that generally available, and no sonochemistry would be observed in homogeneous media Cavitation is initiated at a nucleation site where the tensile strength is dramatically lowered, such as small gas bubbles and gas filled crevices in particulate matter, which are present in the liquid. 

Attempts to totally remove all particulate matter (i. e. ultrafiltration) have not been completely successful in that the theoretical limit for water s tensile strength ( 1500 atm) has not been achieved. One of the largest experimental threshold values 200 atm) is that found by Greenspan [11]. 

At higher ionic strength the limiting Debye-HOckel treatment no longer adequately describes the effect of the ionic atmosphere on the activity of an ion, and this deficiency has been the subject of much theoretical investigation. 

To this end we use the boundary models derived in Chapter 19. Since each model has its own characteristic dependence on substance-specific properties (primarily molecular diffusivity in air or water), the experimental data from different compounds help us recognize the strengths and limitations of the various theoretical concepts. 

It is well known that this theoretical strength is seldom, if ever, achieved by solids, although freshly drawn glass fibres and certain whisker crystals do appear to exhibit tensile strengths approaching the theoretical limit. 

The transferability of the mechanical properties of unidirectionally or multidirectionally incorporated reinforcing fibers to the entire composite material is determined by the interface between the fiber and the matrix. At sufficient bonding strengths, the mechanical properties are proportional to the volume fraction of the fibers. Filling levels of 30 to 60 % by volume and in extreme cases up to 80% can be attained, depending upon the location and mutual orientation of the fibers. The theoretical limit for unidirectional fibers is 90.7% by volume (by comparison... 

The theoretical limits of wood strength are impressive. The strength of a cellulose molecule dwarfs the values associated with high strength steel (Table 10.1). Individual fibres are incredibly strong in tension, but once assembled into solid wood, much of this potential is lost because of weakness across the grain. 

This chapter describes applications of attribute relationships in aquatic chemistry. The underlying theoretical basis for these methods is explored, along with heir strengths and limitations as analytical and predictive tools for contaminant fate in aquatic systems. 

In spite of its theoretical limitations, this hnear extrapolation of the thorium data was adopted by [1975RAN] and [1976FUG/OET], As pointed out by Wagman [1976WAG], a Debye-Htickel correction of the solution data, followed by an extrapolation against the ionic strength, yields an extrapolated value of (ThCLt,... 

The committee made two assumptions to formulate the interrelationships between application requirements and fiber properties. First, the combination of tensile strength, creep resistance, and rupture resistance exhibited by available SiC fibers is approaching theoretical limits. Second, enhancing the creep strength of oxide fibers by several hundred degrees centigrade may be possible although this has not been demonstrated. 

Highly oriented crystalline polymers ( molecular composites ) clearly also fall in this class (Lindenmeyer, 1975 Porter, 1975 Society of Plastic Engineers, 1975 Halpin, 1975 Kardos and Raisoni, 1975). This is an area of high current interest, for exceptional strengths and moduli can be obtained, often approaching theoretical limits. 

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