Tensile strength theoretical

Most solid surfaces are marred by small cracks, and it appears clear that it is often because of the presence of such surface imperfections that observed tensile strengths fall below the theoretical ones. For sodium chloride, the theoretical tensile strength is about 200 kg/mm [136], while that calculated from the work of cohesion would be 40 kg/mm [137], and actual breaking stresses are a hundreth or a thousandth of this, depending on the surface condition and crystal size. Coating the salt crystals with a saturated solution, causing surface deposition of small crystals to occur, resulted in a much lower tensile strength but not if the solution contained some urea. 

It is, however, possible to calculate the tensile strength of a liquid by extrapolation of an equation of state for the fluid into the metastable region of negative pressure. Burgess and Everett in their comprehensive test of the tensile strength hypothesis, plot the theoretical curves of T /T against zjp, calculated from the equations of state of van der Waals, Guggenheim, and Berthelot (Fig. 3.24) (7], and are the critical temperature and critical... 

A different approach is followed by Kadlec and Dubinin who calculate the theoretical tensile strength from a 6-12 relation for molecular forces (cf. Section 1.3) as... 

Theoretical Strength of Agglomerates. Based on statistical-geometrical considerations, Rumpf developed the following equation for the mean tensile strength of an agglomerate in which bonds ate localized at the points of particle contact (9) ... 

Type of Data In general, statistics deals with two types of data counts and measurements. Counts represent the number of discrete outcomes, such as the number of defective parts in a shipment, the number of lost-time accidents, and so forth. Measurement data are treated as a continuum. For example, the tensile strength of a synthetic yarn theoretically could be measured to any degree of precision. A subtle aspect associated with count and measurement data is that some types of count data can be dealt with through the application of techniques which have been developed for measurement data alone. This abihty is due to the fact that some simphfied measurement statistics sei ve as an excellent approximation for the more tedious count statistics. 

FIG. 20-65 Theoretical tensile strength of agglomerates. [Adapted from Rumpf Strength of Granules and Agglomerates, in Knepper (ed.). Agglomeration, Wiley, New York, 1962.]... 

Orowan (1949) suggested a method for estimating the theoretical tensile fracture strength based on a simple model for the intermolecular potential of a solid. These calculations indicate that the theoretical tensile strength of solids is an appreciable fraction of the elastic modulus of the material. Following these ideas, a theoretical spall strength of Bq/ti, where Bq is the bulk modulus of the material, is derived through an application of the Orowan approach based on a sinusoidal representation of the cohesive force (Lawn and Wilshaw, 1975). 

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. 

Since PAN-based carbon fibers tend to be fibrillar in texture, they are unable to develop any extended graphitic structure. Hence, the modulus of a PAN-based fiber is considerably less than the theoretical value (a limit which is nearly achieved by mesophase fibers), as shown in Fig. 9. On the other hand, most commercial PAN-based fibers exhibit higher tensile strengths than mesophase-based fibers. This can be attributed to the fact that the tensile strength of a brittle material is eontrolled by struetural flaws [58]. Their extended graphitic structure makes mesophase fibers more prone to this type of flaw. The impure nature of the pitch preciusor also contributes to their lower strengths. 

Fig. 12. Tensile strength a, vs. number of backbone bonds per monomer 1 /a, reported for a range of polymers by Vincent [75]. The solid line is the theoretical line for vector percolation analysis of strength discussed herein.

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. 

Table 10-3 Comparison of theoretically possible and actual experimental values for modulus of elasticity and tensile strength of various materials...

The diametral compressive strength has been used to estimate the tensile strength of certain AB cements (Smith, 1968). In this test, the load is applied diametrically across a cylinder of cement. Theoretical consideration of the test geometry shows that for a perfectly brittle material the failure that occurs is tensile in character. The difficulty in applying this test to AB cements is that they are not sufficiently brittle for this to hold true. In particular, the zinc polycarboxylate and glass-ionomer cements show sufficient plastic character to make the relationship between diametral compressive and tensile strength vary between AB cements of different types like the compressive strength test, this test is valid only as a means of comparison between similar materials (Darvell, 1990). 

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. 

Just as metals can be ductile or brittle, so can organic materials. The Brittle Fracture Index is a measure of the brittleness of a material. It is a measure of the ability of a compact of material to relieve stress by plastic deformation. The Brittle Fracture Index (BFI) is determined [29,31] by comparing the tensile strength of a compact, stress concentrator) in it, o-T0, using the tensile test we have described. A hole in the center of the compact generally weakens a tablet. If a material is very brittle, theoretical considerations show that the tensile strength of a tablet with a hole in it will be about one-third that of a solid tablet. If, however, the material can relieve stress by plastic deformation, then the strength of the compact with a hole in it will approach that of a compact with no hole. The Brittle Fracture... 

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]. 

---