Numerical modeling of general cracks from the viewpoint of eddy current simulations

This study discusses numerical modeling of fatigue and stress corrosion cracking in eddy current simulations. Ten fatigue crack specimens and another 10 stress corrosion crack specimens are prepared for this purpose. The specimens are made of type 316 stainless steel and measure 10 mm in thickness for a general evaluation of the model. Eddy current inspections of the specimens are performed using a differential type plus point probe; the specimens then undergo destructive tests to confirm the true profiles of the cracks. Subsequent numerical simulations are conducted to evaluate the equivalent conductivity and width of the cracks. The simulations demonstrate that a fatigue crack can be modeled as a non-conductive region, and it is not necessary to know exactly how wide the opening of a fatigue crack is. They also revealed, in contrast, that stress corrosion cracking needs to be modeled as a conductive region with a certain width.     

Discussion on modeling of thermal fatigue cracks in numerical simulation based on eddy current signals

This study evaluates modeling of thermal fatigue cracks by the finite element method from the view point of eddy current testing. Five artificial thermal fatigue cracks introduced into type 304 stainless steel plates were prepared for the research. Eddy current signals were gathered by a differential type plus point probe and subsequent destructive tests were performed to confirm the true profiles of the cracks. Numerical simulation based on the results of eddy current testing and destructive tests were carried out to show how the thermal fatigue cracks should be modeled in numerical simulations. The results of the numerical simulations revealed that thermal fatigue cracks tend to be much less conductive than stress corrosion cracks if they are assumed to have uniform conductivity inside. The results also imply that taking consideration of magnetization induced by the thermal fatigue process enables eddy current signals to be analyzed more quantitatively.     

Eddy current analysis of mid-bore and corner cracks in bolt holes

Fatigue cracks are prone to develop around fasteners found in multi-layer aluminum structures on aging aircraft. Probability of Detection (POD) studies using eddy current techniques within the bolt holes contribute to risk assessments used in evaluating the serviceability of these aircraft. The signal response to corner and mid-bore cracks by eddy current testing using standard split-D differential probes has been examined. The data indicate that split-D probes are primarily sensitive to cracks at the corners of the Ds and that this gives rise to a double maximum for small mid-bore cracks as the corners pass over the crack. The double signal is not seen for corner cracks because the excitation coil, which is almost completely out of the hole, excites almost no eddy currents when the second corner of the D is over the crack. However, the eddy current response is more sensitive to corner cracks. The a_90/95 for corner cracks was measured to be 0.22 mm (length) compared to 0.34 mm (depth) and 0.62 mm (length) for mid-bore cracks. The enhanced detectability of corner cracks is attributed to the presence of the edge, which restricts passage of eddy currents around the crack.     

Four-terminal measurement of the distribution of electrical resistance across stress corrosion cracking

This study measures electrical resistance of a stress corrosion crack directly by the four-terminal method to discuss appropriate modeling from the viewpoint of electromagnetic nondestructive evaluation. Two type-316 stainless steel plate specimens containing artificial stress corrosion cracks were prepared, and columnar samples containing penetrating cracks were cut from the plates for the measurements. The results obtained agree with recent reports discussing appropriate numerical modeling of stress corrosion cracking on the basis of finite element simulations. In contrast, this study also reveals that it is not always valid to assume that a stress corrosion crack has uniform conductivity internally.     

Numerical evaluation of the ill-posedness of eddy current problems to size real cracks

This study evaluates whether or not eddy current testing is applicable to the sizing of cracks that appear in a general structure. Two 10 mm thick specimens with artificial stress corrosion cracking are prepared, eddy current testing is performed to gather eddy current signals that result from cracking, and numerical inversions are performed to evaluate the maximum depths of the cracking. The inversions estimate the depths of the cracks are 0.8 and 1.6 mm. Although the simulated signals agree well with the measured ones, destructive tests reveal that the true depths are 1.27 and 2.58 mm. Another numerical simulation is conducted to discuss the ill-posedness of the inverse problem of sizing crack depths from eddy current signals. The simulation simply models a crack as a rectangular region with a constant length and uniform conductivity inside and calculates the eddy current signals of 1024 cracks having variety of depths, widths, and conductivities. Analyzing the results of the simulation reveal that information contained in conventional single-frequency eddy current tests is not sufficient to size conductive cracks in a general sense.     

An arrayed uniform eddy current probe design for crack monitoring and sizing of surface breaking cracks with the aid of a computational inversion technique

This study demonstrates that eddy current testing can be an effective method for monitoring the growth of surface breaking cracks with the aid of computational inversion techniques. A uniform eddy current probe with 23 arrayed detectors was designed, and pseudo monitoring tests were carried out to measure signals due to six mechanical fatigue cracks introduced into type 316L austenitic stainless steel plates. In the test the position of the probe was fixed to simulate monitoring. The depths of the cracks were evaluated using a computational inversion method developed on the basis of k-nearest neighbor algorithm. The depths of the mechanical fatigue cracks whose actual depths were 1.1, 2.1, 3.1, 5.5, 6.7, and 8.5 mm were evaluated to be 0.9, 1.9, 3.8, 4.3, 7.0, and 5.7 mm, respectively. Additional simulations were conducted to demonstrate the stability of the method.     

Atomistic simulation of martensitic phase transformation at the crack tip in B2 NiAl

Mechanisms of low-temperature deformation at the crack tip in B2 NiAl are studied by molecular dynamics simulations. The stress-induced martensitic transformation is found to occur at the crack tip when a sufficiently high stress concentration exists. For cracks with 〈1 0 0〉 crack fronts, the layered structures of martensites are formed at the crack tip, which is caused by the atoms’ relative displacement on a basal plane due to the shear stress at the crack tip. The mechanism of the martensitic transformation from the B2 to the L1₀ structures occurs along the Bain path. For cracks with 〈1 1 0〉 crack fronts, the martensitic transformation occurs without any layered structures existing. The phase transformation is caused by the atoms’ relative displacements at different atoms layers in the entire martensite formed region.     

In situ observation of short fatigue crack propagation in oxygenated water at elevated temperature and pressure

A new method is demonstrated for in situ measurement of short crack propagation rates during a corrosion fatigue test of an austenitic stainless steel within a windowed autoclave at 250 °C, 50 atmospheres, oxygenated water. Digital image correlation is used to monitor crack growth through measurement of the opening displacements of defects; either focused ion beam (FIB) milled notches from which fatigue cracks initiated, or stress corrosion cracks that subsequently propagated by fatigue.     

Large-scale parallel computation for the reconstruction of natural stress corrosion cracks from eddy current testing signals

An inversion algorithm for the reconstruction of cracks from eddy current signals is developed in this study and applied to the profile evaluation of natural stress corrosion cracks that were found in steam generator tubes of a nuclear power plant. A crack is modeled as an assembly of small regions having conductivities inside so that eddy currents that flow across the cracks are considered. The conductivity of each region, which is assumed to be a discrete value, is reconstructed by means of the algorithm. Since the algorithm is based upon a tabu search that usually requires a large number of evaluating solution candidates, simulations are carried out on a supercomputer with the use of parallel computation using up to 128 CPUs so as to reconstruct the crack profiles within a reasonable computational time. It is demonstrated that the algorithm can estimate the profiles of the natural cracks with sufficient accuracy. The simulations also show that the algorithm is highly compatible with parallel computation. Additional simulations using other models of natural cracks are performed. Reconstructed profiles of the natural cracks, as a notch with zero conductivity, are very different from the true profiles, even though the reconstructed signals agree well with the measured values. This reveals that it is necessary to take the internal conductivity into consideration when dealing with natural cracks.     

Mechanisms of martensitic phase transformations in body-centered cubic structural metals and alloys: Molecular dynamics simulations

Two different mechanisms of the stress-induced martensitic phase transformation at the crack tip in body-centered cubic (bcc) structural metals and alloys have been studied by molecular dynamics simulations. For cracks with 〈1 0 0〉 crack fronts, the bcc (B2) to face-centered cubic (fcc) (L1₀) phase transformation along the Bain stretch occurs. Whereas for cracks with 〈1 1 0〉 crack fronts, either the bcc (B2) to fcc (L1₀) or the bcc (B2) to hexagonal close-packed (hcp) transformation is the candidate. We have found that the combination of local stress and crystal orientation plays an important role in the mechanism of the martensitic transformation. Thus a simple way to determine the mechanism of the martensitic transformation is developed. The complicated deformation behaviors at the crack tip in bcc iron and B2 NiAl are discussed in terms of this method.     

The effects of microstructure on Vickers indentation damage in TiC-316L stainless steel cermets

Titanium carbide (TiC) based cermets are commonly used as wear resistance and corrosion resistance components. In the present work, the effects of microstructure of TiC-316L stainless steel cermets are assessed in terms of Vickers indentation damage, with both the steel binder content and TiC grain size varied. Binder contents from 5 to 30 vol.% were examined, with samples fabricated using a simple vacuum melt-infiltration procedure at temperatures between 1475 °C and 1550 °C (held for up to 240 minutes). Two primary Vickers indentation-cracking patterns arise in these materials, namely median or Palmqvist cracks, and this response relates to both the volume fraction of ductile metal binder present and the binder ligament dimension. Focused ion beam microscopy has been utilised for sub-surface evaluation of the cracks, to confirm the anticipated crack patterns.     

Crack-particle interactions during intergranular stress corrosion of AA5083 as observed by cross-section transmission electron microscopy

Studies of intergranular stress corrosion cracks growing in AA5083 aged to contain β-phase (Al₃Mg₂) particles at the grain boundary are reported. These studies have shown that for tests in a NaCl + K₂CrO₄ solution that β-phase particles are converted to Al₂O₃ particles and that the crack propagates through or around them.     

Frictional heating model for efficient use of vibrothermography

This paper investigates vibrothermography for the detection of fatigue cracks in steel compact tension specimens using combined experimental and numerical analyses. First, a numerical modal analysis is carried out to predict the optimal excitation parameters. A coupled thermo-mechanical model is then built to simulate the thermographic inspection. The model predicts the detection of cracks as short as 0.1 mm that is also confirmed experimentally using a commercial infrared camera with a maximum error of 2.13% on the temperature distribution. The model reveals that the specimens’ temperature increases at the crack vicinity according to the excitation frequency and is modulated due to the nonlinearity induced by the crack. The model also shows that the stress at the crack tip is lower than the material's yield stress, which makes the test truly non-destructive.     

Crack shape and rust distribution in corrosion-induced cracking concrete

This study investigated a reinforced concrete specimen that had deteriorated in an artificial environment for 2 years. The crack width and the rust distribution were observed by digital microscopy. The variation of the total circumferential crack width along the radial direction is presented using a linear function. Observation reveals that rust does not penetrate into the corrosion-induced cracks before concrete surface cracking. After concrete surface cracking, rust fills the cracks, lining the edges of the cracks due to the circulation of the outer solution. A schematic diagram is proposed to describe crack propagation and rust development.     

Electrochemical short crack effect in environmentally assisted cracking of a steam turbine blade steel

Measurement has been made of the corrosion fatigue short crack growth rate in a 12Cr steam turbine blade steel subjected to low frequency trapezoidal loading in aerated and deaerated 300 ppb¹ Cl⁻ and 300 ppb ${\text{SO}}_4^{2-}$, simulating early condensate chemistry. No difference in growth rate compared to that for long cracks was observed in deaerated solution but significantly enhanced growth rate was obtained in aerated solution for a short crack of length less than 250 μm. Complementary stress corrosion cracking tests were conducted but to ensure crack development at modest applied stresses the environment adopted was aerated 35 ppm Cl⁻, representing a severe system upset. In this case, the growth rate of the short crack was up to 20 times higher than that for a long crack (>6 mm), even though the crack length had reached 1.6 mm. An explanation for both sets of data based on the difference in potential drop between a short and long crack is expounded.     

Composition dependence of indentation deformation and indentation cracking in glass

Crack initiation and deformation behaviors of oxide glasses belonging to different chemical systems were studied using the Vickers indentation test. The crack initiation resistance is chiefly governed by the extents to which densification and isochoric shear flow develop in a process zone beneath and within the contact area. Densification is favored in glasses with relatively small Poisson’s ratio (ν), whereas shear is favored at large ν. Glasses were ranged according to their resistance to the formation of corner cracks as follows: Resilient, for 0.15 ? ν ? 0.20; Semi-Resilient, for 0.20 ? ν ? 0.25; and Easily-Damaged for 0.25 < ν < 0.30. Radial-median cracks occur at low load (?50 mN) in Easily-Damaged glasses, while cone cracks predominate in Resilient glasses under higher loads. A critical value for ν (～0.22 depending on the Young’s modulus/hardness ratio) was identified, at which the intensity of the indentation stress field tends to vanish, preventing crack formation on loading, while the driving force on unloading remains very small.     

The role of deformation twins in brittle crack propagation in iron–silicon steel

Crack initiation and propagation in polycrystalline metals and alloys can be characterized by the crack driving force and the resistance to fracture. Interfaces such as grain, sub-grain and interphase boundaries are microstructural features that can resist crack propagation. For iron–silicon polycrystalline steels, brittle fracture occurs predominately by transgranular cleavage but intergranular fracture is enhanced by embrittling heat-treatments. In this paper, we consider the role of deformation twin boundaries on the brittle crack propagation and fracture resistance of poly and single crystals of Fe–3 wt.% Si steel. Three-point bend, impact and miniaturized disc tests have been undertaken at temperatures in the range of 77–273 K. The fractographic features have been characterized with attention being given to (i) the role of the {1 1 2} deformation twins on the propagation of the {0 0 1} cleavage cracks and (ii) the process-zone of the propagating cleavage cracks. The results are discussed with reference to three-dimensional model predictions.     

An eddy current probe suitable to gain information about the depth of near-side flaws much deeper than the depth of penetration

This study proposes an approach to gain information about the depth of near-side flaws using eddy currents. The approach utilizes only two coils, one of which works as an exciter and the other as a detector, like conventional eddy current testing using a transmitter–receiver probe. The uniqueness of this approach is that signals obtained by this approach change significantly with the depth of a flaw even though the flaw is much deeper than the depth of penetration. After the physical background of the approach is explained, its validity is confirmed in experiments. The experiments utilize a 25 mm thick austenitic stainless steel plate with five artificial rectangular slits of 40 mm length, 0.5 mm width, and 1, 5, 10, 15, and 20 mm depth. The experiments confirm clear differences between signals generated by the five slits even although the exciter is driven at 50 kHz at which the depth of penetration is approximately 2.0 mm. Subsequent finite element simulations are carried out to confirm the validity of the experimental results and to support discussion about the physical background of the approach.     

Numerical modeling of vibrothermography based on plastic deformation

This paper investigates vibrothermography for the detection of fatigue cracks in aluminum beams using combined experimental and finite element (FE) analyses. First, a FE modal analysis is carried out to predict the optimal excitation parameters to be employed in experimental investigations performed with an infrared camera. A coupled thermo-mechanical model involving plastic deformation heating is then built and used to simulate the thermographic inspection process. The model shows that the stress at the crack faces exceeds the material’s yield stress confirming that the heat generated during plastic deformation leads to crack detection. The model also predicts the detection of cracks as short as 1 mm that is confirmed experimentally with a maximum error of 0.46% on the temperature evolution. The Fourier transform applied on the numerical thermal response shows that the specimen’s temperature at the crack vicinity changes according to the excitation frequency and presents harmonics due to the nonlinearity induced by the crack.