Fracture criteria linear-elastic

A more practical approach for quantifyiag the conditions required for fracture uses a stress intensity criterion instead of an energy criterion. Using linear elastic theory, it has been shown that under an appHed stress, when the stress intensity K,... 

In graphic presentation of Kk results, the error bars given for the control are typical of all those data points which do not have their own error bars. In cases where error exceeded 10%, individual error bars are provided and labelled with the corresponding symbol. Such large deviations are thought to result from the violation of the homogeneity criterion of linear elastic fracture mechanics at 15% of certain oligomers. (See, for example, Fig. 7). 

The above refers primarily to linear elastic fracture mechanics (LEFM) studies related to the onset of brittle fracture as well as fatigue. The states of the sciences of ductile and dynamic fracture, which only became of serious concern in the early 1960s and 1970s, respectively, have not reached a similar level of maturity despite the immense research efforts expended on these topics in recent years. Yet to be resolved in the former is a viable ductile fracture criterion in view of the recently uncovered uncertainties regarding the /-integral as a crack tip parameter.5,6 As for the latter, a reliable dynamic crack propagation criterion is yet to be established, as will become apparent in subsequent sections of this chapter. 

A purely mechanical criterion for the existence of a critical nucleus is that Ki > Kiscc, where Ki is the Mode I loading stress intensity ratio and iscc is the (lower) critical stress intensity ratio for slow (environment-assisted) crack growth (Fig. 38). Because the stress intensity can be defined in terms of crack length (a) and stress a) as (assuming linear elastic fracture mechanics, LEFM)... 

FRACOD is a two dimensional BEM/DDM code for fracturing analysis in rocks, (see Part 11 in Rinne, 2003). The code is based on the principles of linear elastic fracture mechanics and has been developed to track both fracture initiation and propagation. The initiation of fracturing can be specified using any criterion, but once initiated fracture growth is controlled by the fracture toughness. 

Equation (10.5) is more generally applicable than Eq. (10.6) because it is not restricted to linearly elastic materials. It constitutes a criterion for tensile rupture of a highly elastic material having a cut in one edge of length, /, in terms are of the fracture energy, Gc- Two important examples of test pieces of this type are (1) the ASTM tear test piece for vulcanized rubber (ASTM D624-54) and (2) a typical tensile test piece that has accidental small nicks caused, for example, by imperfections in the surface of the mold or die used to prepare it. 

The linear elastic (X/c) fracture criterion with its inherent plane strain specimen size limitation cannot produce valid fracture toughness results on tough austenitic materials unless specimens of very large thickness are employed. These, in turn, are not representative of the cross-sectional thickness found in the majority of actual cryogenic structures. Furthermore, if a failure should occur, proper design would cause these structures or components to fail plastically (elastic plastic fracture), as opposed to catastrophically (linear elastic fracture). Therefore, all fracture toughness values were obtained via the elastic plastic (Jjc) fracture criterion and associated resistance curve test technique [ ]. 

Crack growth occurs when the energy release rate J is greater than or equal to the crack propagation resistance 7. The criterion 7 /r is similar to the condition Gi Giq in linear elastic fracture mechanics. 

As mentioned at the start of this section, the J-integral concept was originally applied to metals, in which the linear elasticity concept might include the plastic observations, i.e., plastic flow in the close vicinity of the tip. Reservations regarding the use of the J-integral in brittle materials, such as ceramics, are a consequence of the presence of microcracks or rather subcritical crack growth before fracture sets in, making it not strictly applicable. However, in ceramics, in which extensive inelastic processes are active in the crack-tip process zone, the use of J is not more restrictive than the use of the Kic criterion in linear elastic firacture mechanics. 

To suggest an alternative failure criterion, based on the assumption that all materials contain inherent flaws, linear elastic fracture mechanics applied to adhesive joints was introduced. Basic fracture mechanics approaches were discussed, as well as available test techniques and the influence of various test conditions. 

Thus quasi static and unsteady statement may be used for simulation of fracture propagation caused by viscous and inviscid fluid pumping. Rock deformation is described in scope of linear elasticity equation of homogeneous rmiform material. Classical (similar to one used in [1]) and dual bormdary element methods are used for this equations solution. Rock breaking caused by the fracture propagation is described by Irwin s criterion coupled with maximal circumferential stress criterion for calculation of propagation direction. Various approaches are used to obtain stress intensity factors that are necessary for both criteria. 

C = 0. For a perfectly brittle material, the fracture criterion of G = R has been met and the material will fail catastrophically, producing a load-displacement trace similar to the middle diagram in Figure 1, perfectly linear elastic to failure. 

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