Crack sizes

One of the most important appHcations of LEFM is to estimate the critical crack or defect size which causes fast fracture to occur. This occurs when the value of iCin a stmcture becomes equal to the plain strain fracture toughness, of the material the critical crack size, for a given stress and fracture toughness, is then given by equation 31. 

Substantial work on the appHcation of fracture mechanics techniques to plastics has occurred siace the 1970s (215—222). This is based on earlier work on inorganic glasses, which showed that failure stress is proportional to the square root of the energy required to create the new surfaces as a crack grows and iaversely with the square root of the crack size (223). For the use of linear elastic fracture mechanics ia plastics, certaia assumptioas must be met (224) (/) the material is linearly elastic (2) the flaws within the material are sharp and (J) plane strain conditions apply ia the crack froat regioa. 

Fig. 5c. Relation of T-curve to crack growth and strength (c) fracture strength as a function of crack size showing region of flaw size tolerance.

Figure 16.5 shows the loci of general yielding and fast fracture plotted against crack size. The yield locus is obviously independent of crack size, and is simply given by ct = (jy. The locus of fast fracture can be written as... 

But what is the proper way to use toughness values The most sensible thing to do is ask suppose the panel is loaded up to its yield load (above this load we knoiu it will begin to fail - by plastic flow - so it does not matter whether other failure mechanisms also appear) what is the maximum crack size that is still stable If this is large enough... 

In metals, inelastic deformation occurs at the crack tip, yielding a plastic zone. Smith [34] has argued that the elastic stress intensity factor is adequate to describe the crack tip field condition if the inelastic zone is limited in size compared with the near crack tip field, which is then assumed to dominate the crack tip inelastic response. He suggested that the inelastic zone be 1/5 of the size of the near crack tip elastic field (a/10). This restriction is in accordance with the generally accepted limitation on the maximum size of the plastic zone allowed in a valid fracture toughness test [35,36]. For the case of crack propagation, the minimum crack size for which continuum considerations hold should be at least 50 x (r ,J. 

Example 2.19 During tensile tests on 4 mm thick acrylic sheets of the type shown in Fig. 2.63(a), the force-displacement characteristics shown in Fig. 2.64(a) were recorded when the crack lengths were as indicated. If the sheet containing a 12 mm long crack fractured at a force of 330 N, determine the fracture toughness of the acrylic and calculate the applied force necessary to O acture the sheets containing the other crack sizes. 

This is an alternative form of equation (2.91) and expresses the fundamental material parameter Gc in terms the applied stress and crack size. From a knowledge of Gc it is therefore possible to specify the maximum permissible applied stress for a given crack size, or vice versa. It should be noted that, strictly speaking, equation (2.96) only applies for the situation of plane stress. For plane strain it may be shown that material toughness is related to the stress system by the following equation. 

Where rj is the plastic zone size along the plane of the crack and perpendicular to the applied stress. The above two equations are only a first approximation as the plastic zone contributes to the crack size. The true plastic zone is twice the initial approximation. 

Figure 3. Evolution of normalized NILS hydrogen concentration C, IC vs. normalized distance R lb ahead of the crack tip for crack size r/ = 1.9 mm (a) near crack tip solution, (b) solution over the entire uncracked ligament. The parameter b denotes the crack tip opening displacement which varies with time as the hydrogen pressure increases toward its final value of 15 MPa over 1 sec. The parameter C =2.659x10 H atoms/m ( = 3.142x10 H atoms per solvent atoms) denotes the hydrogen concentration on the inner wall-surface and crack faces in equilibrium with the hydrogen gas.

Person 2 The % increase in crack size required for this structural steel to undergo fast fracture at an applied load of 500 MPa. 

Form groups of three. Each person should select a material from the three categories under consideration for this application (steel, aluminum alloy, and titanium alloy) other than the three listed in Table 8.3 and should perform a similar analysis—that is, calculate or look up yield strength, fracture toughness, critical crack size, number of cycles to failure, and the constants A and m in the Paris equation. Combine your results and compare your answers. Do you obtain a result similar to that in Table 8.3 ... 

Figure 16-7. Relation between crack size and strain (diagrammatic). T is the threshold strain curve A, average crack length curve B, average crack length with coalescence of cracks ...

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