Crack circular

One of the simplest techniques to determine in a complex configuration is to use superposition to build up the solution from a set of simpler and known solutions. Clearly, the precision with which the superposed geometries replicate the final, more complex, structure will impact the accuracy of the final solution. Consider the situation shown in Fig. 8.24, in which cracks emanating from a circular hole is subjected to a biaxial stress. This solution can be broken down into two uniaxial stress solutions, and K. Thus, the total stress intensity factor is found by superposition, K=K, +K. A somewhat more complex configuration is shown in Fig. 8.25. The problem again involves a cracked circular hole but, in this case, it is being loaded along a semi-circular portion of the hole. The problem is asymmetric but, as shown, it can be found from the superposition of two symmetric solutions, i.e., K = K +K H. 

The calibration in UTDefect is perfomed by a side-drilled hole or a flat-bottomed hole. The flat-bottomed hole is approximated by an open circular crack with the probe s beam axis going normally through its centre. This approximation should be sufficiently accurate as long as the crack diameter is larger than about a wavelength. 

Becker et al. (11) have performed extensive experiments on surface-breaking cracks, tilting both the cracks or the back-side. The cracks are like a half ellipse, but could presumably be reasonably approximated by a strip-like crack. Figure 3 shows a comparison between the experiments and UTDefect for a 2.54 mm crack with varying tilt. The thickness of the plate with the crack is 15.24 ram. The probe is a circular 45 SV probe with frequency 2.25 MHz and diameter 12.7 mm. The experiments are calibrated with a notch but this is presently not... 

Using Equ. (3.1), we can now compute the optimum frequency for cracks in various depths (see Fig. 3.2). For comparison, the optimum excitation frequency for a planar wave or a sheet inducer (300 x 160 mm) is also displayed. One finds that for a planar excitation source, a much lower excitation frequency is required, which causes a reducfion in the response signal of the crack of up to an order of magnitude in case of a small circular coil. 

Figure 3.3 shows the increasing attenuation for cracks in a depth between 5 and 30 mm, using the optimised excitation frequency for each depth. The coils (circular, double-D) have a current density of lOWm. In case of circular and double-D coil, this corresponds to an... 

We have perfomied some simulations of the eddy current distribution in a test object for a spiral coil and a circular one (see Fig. 4.1). Both coils had 9 turns and the excitation current was 6 mA. Figs. 4.1 show the cross section of the sample at the location of the crack and the amplitude of the eddy current density. One observes a 1.5 higher current density at the sides of the crack for the case of the circular coil. 

Fracture mechanics analysis requires the determination of the mode I stress intensity factor for a surface crack having a circular section profile. Here the circular section flaw will be approximated by a semi-elliptical flaw. 

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. 15 Initiation of fibre fracture by a crack oriented parallel to the chain direction in a domain. It is proposed that a circular crack with a radius q releases the strain energy in a sphere around the crack with the same radius. Note that in this two-dimensional drawing only the circular crack is shown in perspective...

In fact at least this amount of strain energy is needed for the formation of the circular crack with radius q. The total free energy contribution due to the presence of the crack is... 

When some solid propint grains, particularly those with relatively long circular channels available for gas flow, are fired in rockets, there are frequently observed certain periodic pressure oscillations. These resonating pressures sometimes reach amplitudes high enough to cause the grain to crack and, in some cases, ultimately to rupture the rocket chamber. 

On normal skin NaOH erosions first develop at hair follicles and orifices of sweat gland ducts, usually after 4 to 5 min. They are small and circular in appearance. However, erosions on xerotic leg skin look different, they often develop along cracks in the SC, revealing the weak spots of xerotic skin. Erosion times are significantly reduced, on severely dry skin erosions develop within the first minute. 

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