Fracture mechanics examples

In order to apply the crack nucleation approach, the mechanical state of the material must be quantified at each point by a suitable parameter. Traditional parameters have included, for example, the maximum principal stress or strain, or the strain energy density. Maximum principal strain and stress reflect that cracks in rubber often initiate on a plane normal to the loading direction. Strain energy density has sometimes been applied as a parameter for crack nucleation due to its connection to fracture mechanics for the case of edge-cracked strips under simple tension loading. ... 

Knott, J., and P. Withey, Fracture Mechanics Worked Examples, Institute of Materials, London, 1993. 

There are several important things to note. The first is that elastic deformation is a reversible process, but plastic deformation and brittle fracture are not. More importantly, plastic deformation and viscoelastic behavior are kinetic phenomena time is important, and they can be affected by press speed. In reality, most materials exhibit both plastic and brittle behavior, but specific materials can be classified as primarily plastic or primarily brittle. For example, microcrystalUne cellulose defonns primarily by a plastic deformation mechanism calcium phosphate de-fonns primarily by a brittle fracture mechanism lactose is in the middle [8]. 

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). 

Examples of accounts of applying the fracture mechanics approach to the fatigue behaviour of rubbers are given in references 15-19. In a review of testing methodology for reinforced rubber composites20 it is concluded that... 

Crack growth models in monolithic solids have been well document-ed. 1-3,36-45 These have been derived from the crack tip fields by the application of suitable fracture criteria within a creep process zone in advance of the crack tip. Generally, it is assumed that secondary failure in the crack tip process zone is initiated by a creep plastic deformation mechanism and that advance of the primary crack is controlled by such secondary fracture initiation inside the creep plastic zone. An example of such a fracture mechanism is the well-known creep-induced grain boundary void initiation, growth and coalescence inside the creep zone observed both in metals1-3 and ceramics.4-10 Such creep plastic-zone-induced failure can be described by a criterion involving both a critical plastic strain as well as a critical microstructure-dependent distance. The criterion states that advance of the primary creep crack can occur when a critical strain, ec, is exceeded over a critical distance, lc in front of the crack tip. In other words... 

The processes at the crack tip of a notched specimen in a stress cracking liquid under mechanical stresses and possibly elevated temperatures can be regarded as local aging phenomena. Fracture mechanics, on the one hand, is a very sensitive method of detecting a polymer s behavior with regard to these influences. On the other hand, as demonstrated in the previous examples, FCP measurements can distinguish between small material differences. As depicted in Fig. 21, PE-HD shows the different behavior in static fracture mechanics tests with respect to water at a temperature of 80 °C for two different stabilizers. Stabilizer 2 leads to higher K values at comparable da/dt values and is therefore more appropriate for hot-water applications when oxidation processes also have to be taken into account [88]. 

Fracture Mechanics describes the behavior of sharp cracks in loaded materials and thus enables to characterize the strength of materials and components. Since Griffith s early considerations and Irwin s basic work, fracture mechanics has been systematically developed and has now reached a high level of sophistication. Correspondingly, there is extensive literature on the subject and the interested reader should consult, for example. Ref. for general aspects of the subject or Refs. for specific considerations of polymer fracture. The present... 

Another aspect to be considered is the difficulty in producing curved structures with the same fibre content as flat laboratory panels. This effect is shown in Figure 16, at the comer the laminate thickness is larger than at the flat section and fibre content is rather lower. This will affect the bending stiffness of the arm and the predicted failure load. This figure also shows the fillet, which is critical to initiation in the specimens without implanted defects. It is well known that fillets can significantly alter the load path in lap shear joints and increase the failure loads (see [1] and Figure 3 for example). If a fracture mechanics approach is to be applied this effect must be considered. Some recent studies on stress intensity factors for such cases may allow this to be addressed [22]. 

Because the fracture toughness depends both on cure time and temperature, the arbitrary selection of time and temperature for accelerated tests may not be appropriate for reliable prediction of longterm service life of joints (J7). In order to reduce test variability and improve the durability prediction of adhesive joints, it would be necessary first to control the cure temperature and time required to produce a level of fracture toughness that does not change further (14). The study is thus an excellent example of a multidisciplinary approach combining chemistry, fracture mechanics, and wood science in the investigation of the adhesive bonding of wood. 

Applications of fracture mechanics to ice. There are many natural examples, such such as the fracture in lake ice and in ice shelves (ice sheets that extend over water), crevasse formation in glaciers, and fracture in sea ice and these may be used as natural examples in terrestrial ice. ... 

The subject of fracture has already arisen in several different contexts throughout the book. In chap. 2 we described the rudiments of the theory of linear elastic fracture mechanics. In addition, in the previous chapter we described the interplay of cracks and dislocations. The current discussion is aimed at elucidating yet another feature of fracture, namely, the fact that the study of fracture serves as a paradigmatic example of some of the ideas on bridging scales introduced earlier in the chapter. 

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