Penetration depths

We can use the London equations to describe the behavior of a magnetic field inside a superconductor. Taking the curl of the Maxwell equation V x B = p,Q js in which the D term has been dropped since electric fields cannot exist in a superconductor. 

Assume B is along the x-direction, parallel to the surface of the superconductor and z is perpendicular to the surface directed inward. Since V B = 0, the Equation 26.31 can be written 

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The standard NF T 65-001 gives a classification for bitumen as a function of their hardness. This is measured using a needle penetrability test, which measures the penetration depth of a weighted needle into the bitumen. Five grades have been defined. 

The detection of residual austenite in fact requires average frequency, however for comparison reasons (reference) with a different recognized method, it is recommended to use high frequency, as with high frequency of eddy currents the penetration depth is comparable in the diffraction method and eddy current method. 

Three different specimens are considered here. Penetration depths range from 0.7 mm for aluminium to 0.15 mm for the steel block. For the experimental test frequencies used the electromagnetic skin depth is much smaller than the depth of the cracks for all the measurement considered. 

In this case the probe diameter and the slot length are of similar size. The material chosen has penetration depth of 0.7 ram at the given frequency of 16.9 kHz. The slot depth is 7 times larger than the penetration depth. 

In this paper we present simulations and measurements of several types of excitation coils, which match the special requirements for a SQUID based eddy current NDE system. We note however that all calculations presented here on penetration depths, current distributions and crack-detecting algorithms are also useful for conventional eddy current testing systems. 

Dependence of the penetration depth on materials properties and excitation coil geometry... 

For a rough estimation of the optimum excitation frequency for a given test object, one can use the well known expression for the skin penetration depth S ... 

In contrast to the planar wave solution, the penetration depth in case of a coil can be described —besides the dependence on co and a— as a function of the depth z and the coil diameter R ... 

Fig. 2.2 Correcting function e for a real penetration depth, calculated by 3D-FEMfor different coils and frequencies.

First, the eddy current density is damped while penetrating into the conductor (penetration effect). Here the frequency dependence of the penetration depth implies that for deep lying cracks low frequencies must be used for obtaining a sufficient current density in the vicinity of the crack. Secondly, due to the induction law the induced current density at the surface jco is diminished when using lower frequencies. Therefore, in total, there is a certain excitation frequency which results in a maximum response field from the crack. 

The simulation of the actual distortion of the eddy current flow caused by a crack turns out to be too time consuming with present means. We therefore have developed a simple model for calculating the optimum excitation frequencies for cracks in different depths of arbitrary test sarriples Using Equ. (2.5), we are able to calculate the decrease in eddy current density with increasing depth in the conductor for a given excitation method, taking into account the dependence of the penetration depth c on coil geometry and excitation frequency. 

Illuminating the sample at grazing angles. The penetration depth of photons depends on the cosine of the incidence angle and, therefore, can be reduced by this procedure. Although such an approach has limited use, it has been successfully employed in a few instances, such as for x-ray diffraction experiments. 

In each of these approaches, imaging is confined to the top of a single polymeric film by adjusting optical absorption. The penetration depth of the silylation agent and the attendant swelling of the polymer film must also be controlled to avoid distortion of the silylated image. Resists of this type are capable of very high resolution (Fig. 37). 

The penetration depth of this evanescent field, (defined to be the depth at which the evanescent field decays to 1/ of its original value,) is given... 

The shallow penetration of ion implantation would in itself make it appear useless as a technique for engineering appHcations however, there are several situations involving both physical and chemical properties in which the effect of the implanted ion persists to depths fat greater than the initial implantation range. The thickness of the modified zone can also be extended by combining ion implantation with a deposition technique or if deposition occurs spontaneously during the ion implantation process. In addition, ion implantation at elevated temperatures, but below temperatures at which degradation of mechanical properties could occur, has been shown to increase the penetration depths substantially (5). 

Penetration depth, Z9, at which fields are reduced by a factor of 1/, is given by the following formula ... 

Erequencies from 1 kHz to 50 MHz are used for various appHcations (3). Ferromagnetic materials have a skin-effect response to eddy currents which restricts the penetration depth. Nonferromagnetic materials on the other hand can be inspected to greater depth. In 6061-T6 aluminum, for example, a cod having a 1-kHz frequency effectively penetrates the surface to a depth of 3.2 mm (1). The same probe in steel penetrates to a depth of 0.5... 

Thickness of the laminar layer is deterrnined both by the need to reproduce fine detail in the object and by the penetration depth of the actinic laser light into the monomer bath (21,76). There is thus a trade-off between precision of detail in the model and time required for stereohthography, ie, the number of layers that have to be written, and an optimum Light-absorbing initiator concentration in the monomer bath corresponding to the chosen layer thickness. Titanocene-based initiators, eg, bis-perfluorophenyltitanocene has been recommended for this apphcation (77). Mechanistic aspects of the photochemistry of titanocenes and mechanisms of photoinitiation have been reviewed (76). 

Penetration—Indentation. Penetration and indentation tests have long been used to characterize viscoelastic materials such as asphalt, mbber, plastics, and coatings. The basic test consists of pressing an indentor of prescribed geometry against the test surface. Most instmments have an indenting tip, eg, cone, needle, or hemisphere, attached to a short rod that is held vertically. The load is controlled at some constant value, and the time of indentation is specified the size or depth of the indentation is measured. Instmments have been built which allow loads as low as 10 N with penetration depths less than mm. The entire experiment is carried out in the vacuum chamber of a scanning electron microscope with which the penetration is monitored (248). 

Eor t7-limonene diffusion in a 50-pm thick vinyUdene chloride copolymer film, steady-state permeation is expected after 2000 days. Eor a 50- pm thick LDPE film, steady-state permeation is expected in less than one hour. If steady-state permeation is not achieved, the effective penetration depth E for simple diffusion, after time /has elapsed, can be estimated with equation 8. 

The effectiveness of a porous electrode over a plane surface electrode is given by the product of the active surface area S in cm /mL and the penetration depth Tp of the reaction process into the porous electrode. 

Hardness is determined by measuring the penetration (depth or area) when a harder material, such as diamond, is pushed into the surface of the material of interest under a specified load. Tme hardness is defined as the force divided by the projected area. Vickers hardness tests, which employ a pyramid-shaped indentor, are frequently used to characterize ceramics however, Vickers hardness calculations normally employ total surface area rather than projected area (43). Measurements are made on the diamond impression shown in Figure 6. Vickers hardness is calculated using... 

The lower the value of the more likely it is that S is positive indicating a thermodynamic tendency for the process to occur. Longitudinal wave theory has been appHed to the defoamer spreading process as in equation 5 where P is the penetration depth of a spreading droplet of initial radius R, viscosity Tj, and density p. 

D is the final layer thickness and A( the change in surface tension during the passage of the wave. Spread insoluble films give low A(, ie, high penetration depth and maximum dismption. P can be of the order of ten times the droplet size. 

The grounding or penetration depth of the electrical resistance in conductors is, according to Eq. (3-42), dependent on the specific resistance and the frequency. The penetration depth, t, is the distance at which the field strength has fallen by 1/e,- is the relative permeability [35] ... 

On about 25(X) km of pipeline laid since 1970, overline surveys showed 84 places totalling 5 km in length where the protection criterion had not been reached. In 21 exploratory excavations, 7 cases of pitting corrosion with penetration depths > 1 mm were found. At three places the pipe had to be replaced or repaired with split sleeves. Seven hundred sixty-five places with a total length of 95 km in 25(X) km of pipeline laid between 1928 and 1970 were found to have failed to reach the protection criterion. Thirty-two examples of pitting corrosion with > 1 mm were... 

Referring to Fig. 23-6, through 3)3 are hereby the average distances of the conductor from the ground x, through X3 are the average distances of the conductor from the pylon axis a is the distance of the affected conductor from the pylon axis, and d is the penetration depth in the soil from ... 

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