Fracture Griffith concept

To give the Griffith concept of fracture a concrete structure, which can... 

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. 

Although Griffith put forward the original concept of linear elastic fracture mechanics (LEFM), it was Irwin who developed the technique for engineering materials. He examined the equations that had been developed for the stresses in the vicinity of an elliptical crack in a large plate as illustrated in Fig. 2.66. The equations for the elastic stress distribution at the crack tip are as follows. 

The principle behind the phenomenon of fracture of materials can be described by having recourse to Griffith s theory. Alternatively, this can be done by introducing the concept of fracture toughness. 

Brittle fracture mechanisms of the type first proposed by Griffiths [122] are based on the concept of cpmpetition between a decrease of... 

The energy balance considerations in Griffith s original concept were later refined by Orowan and Irwin to include the effects of plasticity and elasticity for applicability to metals (Orowan, 1952 Irwin, 1957). Metals fail by ductile fracture, where the crack growth occurs in the direction of the primary slip system. When the slip plane is inclined to the crack, atoms across the slip plane slide past one another, relieving the stress, which results in a zigzag crack path. This is illustrated in Figure 10.14. 

In fact, the first quantitative attempt to incorporate the dynamics of the crack into the Griffith energy balance concept was given by Mott (1948). He suggested that unlike the Griffith case of fracture initiation or nucleation... 

Irwin proposed the concept of quasi-elastic fracture, which allows us to extend the limits of applicability of Griffith s theory [11], Irwin s criterion is valid not only for brittle materials, but also for elastic-plastic materials with significant plastic deformation developing until the moment of actual destruction of a material. 

The concept of quasi-brittle fracture implies that some materials that exhibit the characteristics of plastic materials at standard test, collapse in tests of the sample with a crack due to the quasi-brittle mechanism, that is, plastic deformation is concentrated in a narrow layer near the tip of a crack. For such materials, Griffith s criterion is relevant instead of the value of the surface energy to introduce the work of plastic deformation at the crack tip. 

Thus, these two concepts are equivalent. In the classical failure context, fracture depends on some critical combination of stress at the crack tip and the tip radius, neither of which are precisely defined (or definable) or accessible to measurement. For experimental accuracy and practical apphcation, it is more appropriate to use the accessible quantities o and a to determine the fracture toughness of the material. It is to be recognized that the quantities involving a a and a represent the crackdriving force, and 2y, in the Griffith sense, represents the material s resistance to crack growth, or its fracture toughness. 

To see how the fracture energy may be used in the initiation of chemical reactions, the concepts of fracture mechanics are introduced, including the strain rate and temperature dependence of the ductile-brittle behavior. The starting point is the Griffith theory which in its simplest form applies to perfectly brittle materials and states that for a crack to form, the elastic strain energy available must be at least sufficient to provide the energy of the new surfaces formed [74]. 

We may thus conclude that the fracture process is determined by crack formation and crack propagation. Griffith crack theory is essentially a static conception of critical crack formation. Crack growth, however, also depends on dissipative processes. Below the critical load, crack propagation may advance very slowly. In such a case there is a dissipation of energy due to creep processes. Therefore, fracture is a time-dependent process. This aspect is neglected in the Griffith-Irwin theory of fracture. 

The fracture mechanics approach to evaluating joint durability basically relates to the early work of Griffith(i 72) in 1920 with brittle materials like glass. IrwinO S) in i960 used the concept to measure a materials resistance to fast crack extension in the presence of a flaw. 

In many particular cases, there is a direct correspondence between the Irwin and Griffith criteria, as was noted above an connection with the result in (4.27). However, the latter criterion has the distinct advantage that the energy release rate can often be determined, or at least estimated, without the need for a complete solution of the boundary value problem for the stress field in the body. For this reason, it is selected as the basis for the present discussion. Many of its special features and numerous extensions of the basic concept will become evident in the sections that follow, in the course of discussing various issues concerned with delamination and fracture in thin film configurations. 

On the other hand, the criterion of Griffith [61] is widely accepted for the theory of fracture. It is based on the concept that the fracture takes place when there is an increase in the energy of the surface formed by the growth of the crack and it predominates over the elastic energy due to the deformation in the vicinity of the crack. 

The studies carried out earlier have shown that polymer film samples strength to a considerable extent is defined by growth parameters of stable crack in local deformation zone (ZD) at a notch tip [1-3], As it has been shown in Refs. [4, 5], the fiactal concept can be used successfully for the similar processes analysis. This concept is used particularly successfully for the relationships between fracture processes on different levels and subjecting fracture material microstructure derivation [5]. This problem is of the interest in one more respect. As it has been shown earlier, both amorphous polymers structure [7] and Griffith crack [4] are fractals. Therefore, the possibility to establish these objects fractal characteristics intercommunication appears. The authors of Refs. [8, 9] consider stable cracks in polyarylatesul-fone (PASF) film samples treatment as fractals and obtain intercommunication of this polymer structure characteristics with samples with sharp notch fracture parameters. 

Pressure on resources had materials science improving its products in leaps and bounds - not just metals but also the earlier polymers and natural fibres. The concept of fracture mechanics had been introduced during the First World War by the aeronautical engineer Alan Arnold Griffith (1893-1963) to explain brittle failures. The microscopic behaviour of materials, the way cracks propagated from surface flaws, led to the development of a particular palette of structural materials suited to severe conditions - elastic and ductile, with reserves of energy absorption when approaching failure point. 

Brittle Fracture Methods for estimating the risk of brittle fracture originate in concepts proposed by Griffith. To this end, let us assume that the material is in the... 

It is evident that the theory of failure of adhesion joints should be based on the general principles of solid destruction. However, the transfer of the classical concept of Griffith s theory to two-phase systems is very complex. The difficulties are related to determination of two main parameters in the equation for critical stress of fracture ... 

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. 

The work 7" of fracture was identified hy Dupr and Griffith with the surface energy of solids. In reality work is spent on the deformation leading to rupture rather than on the Break itself. In simple instances it is equal to the work needed to extend a column of material (of unit cross-section) in front of the growing crack until the column snaps. This extension may he purely elastic. The new concept contraiy to the old (a) indicates the analogy Between the Breaks of a liquid and a solid (B) accounts for the absolute value of y/ (c) agrees with the effect of cross-linking on (h) is compatible with the rate dependence of... 

One of the purposes of this paper is to differentiate between surface free energy and fracture surface energy. Thus, several basic principles of fracture mechanics are discussed with reference to the Griffith s energy-b J nce concept and the Irwin-Orowan s plastic-zone concept. We also define several frequently misused terms, e.g., effective fracture surface energy, fracture energy and fracture toughness. Actual values of related parameters are presented to illustrate the applicability of fracture mechanics to the selection of polymers for structural materials. 

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