Griffith length

First an expression of the Griffith length for the shear stresses is derived by taking into account the shear strain energy of the domain. An elongated crack is oriented parallel to the chains. Suppose the crack has a circular shape with a radius q as shown in Fig. 15. Due to the formation of the crack the strain... 

Fig. 16 Graph of the strain energy W2, the fracture energy Wl and their difference, resulting in the Griffith length L. Cracks with sizes larger than will propagate in the fibre...

This equation shows that for increasing angle the Griffith length, L, decreases. 

In a similar way the Griffith length, Lq, due to the strain energy caused by the stress transverse to the chain direction can be derived... 

In this expression ex is the modulus perpendicular to the chain axis and wj is the work of fracture for the transverse tensile stress. Equation 39 demonstrates that the Griffith length Lq increases rapidly with decreasing orientation of the chain angle 0. 

In conclusion, the initiation of fracture in a polymer fibre preferably occurs in the domains in the tail of the orientation distribution. The reasons are (1) in these domains the local shear stress will exceed the critical shear stress first, (2) the release of the strain energy is most effectively brought about by fracture of these domains and (3) the Griffith length in these domains adopts its lowest value. 

This section is concerned with the two-dimensional elasticity equations. Our aim is to find the derivative of the energy functional with respect to the crack length. The nonpenetration condition is assumed to hold at the crack faces. We derive the Griffith formula and prove the path independence of the Rice-Cherepanov integral. This section follows the publication (Khludnev, Sokolowski, 1998c). 

In this section we find the derivative of the energy functional in the three-dimensional linear elasticity model. The derivative characterizes the behaviour of the energy functional provided that the crack length is changed. The crack is modelled by a part of the two-dimensional plane removed from a three-dimensional domain. In particular, we derive the Griffith formula. 

To evaluate the influx solution experimentally for an A/B cantilever beam configuration as shown in Fig. 1, we apply Griffith s theory at the critical moment of fracture, such that the incremental change in stored elastic energy U. with change in crack length a, is Just sufficient to overcome the fracture surface energy S... 

An example of a theory is the Griffith theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittle fracture is based on the idea that the presence of cracks determines the brittle... 

Over a 30 m length of a 150 mm vacuum line carrying air at 295 K, the pressure falls from 0.4 kN/rrr to 0.13 kN/m2. If the relative roughness e/d is 0.003 what is the approximate flowrate It may be noted that flow of gases in vacuum systems is discussed fully by Griffiths 11. 

As a result of this additional work to create a surface over and above the thermodynamic surface energy assumed by Griffith, we need to rewrite his equation for the relationship between breaking stress and crack length. We modify equation (7.2) to ... 

These equations suggest that the rate of drying is independent of the geometrical shape of the surface. Work by Powell and Griffiths(9) has shown, however, that the ratio of the length to the width of the surface is of some importance, and that the evaporation rate is given more accurately as ... 

Figure 5.38 The Griffith model for micro-crack induced brittle failure. Cracks at the surface have a length of a, whereas internal cracks have a length of 2a.

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