Theories of Brittle Fracture

In principle, the force necessary to cause a brittle break F = E/L can be calculated from the energy E required to separate chemical and physical bonds by an interbond-partner distance L. To break extended-chain poly(ethylene) crystals perpendicular to the chain direction (i.e., breaking covalent bonds), a force of about 20,000 N/mm is necessary, whereas to cause a break parallel to the chain direction (i.e., working only against dispersion forces), only 200 N/mm is required. Experimentally, however, a maximum tensile strength of 20 N/mm is observed (the so-called crystal paradox). Consequently, the break must occur at inhomogeneities, since these lead to an inhomogeneous distribution of the tensile stress onto disruption points and thus lead to stress concentrations. 

The break behavior of energy-elastic and entropy-elastic bodies is different. According to the break theory of Ingles for energy-elastic bodies, there is a relationship between the critical break stress (o, .j)crit, the stress operating at the top of a crack Oa, the geometry of the crack, and the modulus of elasticity. In the simplest case of a crack of length L with a 

The break behavior of any desired elastic body is described by the Griffith theory. According to Griffith, a crack in an elastic body only propagates further when the elastically stored energy just exceeds the energy required to break chemical bonds. Combination of this with the Ingles concept leads to 

Crazes occur perpendicular to the Stress direction shortly before a destructive break. They may be up to 100 fitn long and up to 10 /im wide. Crazes are not hairline cracks, that is, they ate not totally void between the break surfaces. The spaces between the break surfaces in crazes mostly contain molecular bundles or lamellar material stretched in the stress direction. Consequently, in contrast to genuine breaks, crazes possess a structural and mechanical continuity. Because certain materials whiten on crazing, crazes arc often called white breaks. 

According to electron spin resonance data, free radicals are produced at chain ends even before a macroscopic break occurs. The free radical concentration depends only on the extension, and not on the tensile stress. Concentrations of 10 -10 free radicals/cm are generally observed. Since free radical concentrations of only about 10 free radicals/cra occur 

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Weibull developed his statistical theory of brittle fracture on the basis of the weakest link hypothesis, i.e. the specimen fails if its weakest element fails [6, 7], In its simplest form and for an uniaxial homogenous and tensile stress state, ct, and for specimens of the volume, F, the so called Weibull distribution of the probability of failure, F, is given by ... 

The Griffith theory of brittle fracture postulates that the fracture is due to ... 

Polymers tend to have rather lower fracture strengths than materials such as metals or ceramics, but not concrete The theory of brittle fracture applies for polymers as for metals, but with greater emphasis on the development of a plastic zone around the tip of the growing crack (Fig. 4.5). The brittle mechanism is favoured in unmodified epoxies, and as a result of reducing the temperature, increasing the strain-rate or specimen thickness, and having sharp notches. Traditionally, susceptibility to brittle fracture has been assessed by some form of impact testing. 

Cottrell AH (1958) Theory of brittle fracture in steel and similar metals. Trans Metall Soc AIME 212 192... 

Batdorf Theory. A theory of brittle fracture which assumes random flaw orientation and a consistent crack geometry, proposing that reliability predictions should be based on linear... 

Sih, G.C., Liebowitz, H. (1968) Mathematical Theories of Brittle Fracture , in Fracture An Advanced Treaties Vol. II, ed. by H. Liebowitz (Academic, New York) pp. 67-190 Sneddon, I.N. (1951) Fourier Transforms (McGraw-Hill, New York)... 

Methods for mechanical testing of materials are briefly introduced along with various strengthening mechanisms. The number and siu-face area of the slip systems in metals and in ceramics are shown to be responsible for the ductility (or the lack of it) and for ductile-to-brittle transitions. Griffith s theory of brittle fracture is used to introduce fracture mechanics and to develop the concept of fracture toughness. The viscoelastic behavior of polymers is briefly discussed. 

One of the most useful approaches that can be used to explain the fracture of brittle polymers is the theory of brittle fracture developed by Griffith to... 

The theory of brittle fracture arising from crack formation and... 

The Weibull s chain model of strength of materials, as today s foiandation of statistical theory of brittle fracture, been widely e plied and advanced due to its siitplicity in nathematical calculation has in the last decades. However, it has an obvious insufficiency. It does not take into account the interaction between various elements of calculation and in many cases, especially in the case of nonuniform stress field, it is the main cause which leads to ejnrors. The present paper, based on a large amount of ejq erimental data, attempts to put forward a hypothesis dealing with the mutual actions of the adjacent elements along coe direction and to correct the aforesaid insufficiency. The formulas obtained seem somevhat more ccmplicated than Weibull s, but they are more accurate vten verified by the ejqjerimental data. 

The mutual action between elements of a body must be considered on the statistical theory of brittle fracture. 

Sih, 6.C. and Liebowitz, H., Mathematical theories of brittle fracture in Fracture. vol.Il. Academic Press. 

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