Theoretical brittle strength

The theoretical value for the brittle strength of a material is of the order of... 

The observed brittle strength is generally very variable, but is always 10-100 times smaller than the theoretical value. Only some very fine fibres (e.g. silica) have been... 

FE Estimate the theoretical fracture strength (in O MPa) of a brittle material if it is known that fracture occurs by the propagation of an elliptically shaped surface crack of length 0.25 mm that has a tip radius of curvature of 0.004 mm when a stress of 1060 MPa is applied. 

A crack will propagate when dU/ck < 0, where dc is the increase in the crack length. Using this theory, one can derive the Griffith equation, which gives the theoretical fracture strength for brittle, linearly elastic materials ... 

Brittle fracture is probably the most insidious type of pressure-vessel failure. Without brittle fracture, a pressure vessel could be pressurized approximately to its ultimate strength before failure. With brittle behavior some vessels have failed well below their design pressures (which are about 25 percent of the theoretical bursting pressures). In order to reduce the possibility of brittle behavior. Division 2 and Sec. Ill require impac t tests. 

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. 

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). 

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... 

Therefore, choosing a suitable load range for brittle crystals we can induce a plastic deformation in the crystal, seen as a starlike rosette around the indentation site, immediately after measurement or after etching the surface. Detailed tests and theoretical studies relating to fall in strength in brittle surfaces by the action of sharp and blunt indenters were conducted by Lawn et al. (1975, 1976). 

The brittle cracking and subsequent debonding of films deposited on flexible substrates subjected to uniaxial strain is described theoretically and illustrated with Ni films evaporated on ion-etched polyethylene terephthalate (PET). It is shown that, if the materials deform elastically, the shear strength of the interface, x, may be evaluated from the length,... 

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