Displacement discontinuity method applied to nondestructive testing related stress problems

A numerical stress analysis technique using the displacement discontinuity method (DDM) is used to evaluate surface breaking and near surface flaws. DDM is described briefly, with the main body of the work devoted to exploring the use of DDM in a nondestructive evaluation (NDE) program. DDM is a subset of boundary element method technique, and it requires that only the boundaries of the problem be described. Two smooth subsurface voids are investigated. Results for two-dimensional circular and elliptical holes are presented. Comparisons with experimental and theoretical work are shown. The method of uneven element spacing is explored. The results are examined in the context of providing information for NDE inspection requirements and the definition of acceptable flaws. DDM is very well suited for examining the stress field around a surface crack. Surface cracks can be very dangerous and good NDE inspection techniques are required. A method of obtaining the stress intensity factors is developed and illustrated on angular surface breaking cracks. The results are compared with limited experimental and numerical results and interpreted in terms of NDE inspection requirements.     

Benchmark problems for defect size and shape determination in eddy-current nondestructive evaluation

A set of four benchmark problems is presented for verification of theoretical calculations of defect size and shape in eddy-current nondestructive evaluation. The benchmark problems are based on careful measurements of the change in coil impedance as a function of frequency for a circular air-cored coil which is scanned along the axis of an electrodischarge machined slot in a thick aluminum alloy plate. Slots of (i) semi-elliptical, and (ii) double-peaked profiles are considered. Deviations from ideal coil behavior are identified and corrected so that the final impedance data and experimental parameters can be directly used to verify theoretical inversion algorithms.     

Integrated niobium DC SQUID gradiometers for non-destructive evaluation and biomagnetism

We describe the design and fabrication of thin-film Nb gradiometers with integrated DC SQUIDs for use in non-destructive evaluation (NDE) and biomagnetism. Issues of sensitivity, imbalance and field response are considered. Results are presented from eddy-current NDE in an unshielded environment of aluminium plates with sub-surface flaws, and from biomagnetic measurements of spinal and peripheral nerve evoked fields.     

A benchmark problem for computation of ΔZ in eddy-current nondestructive evaluation (NDE)

Experimental results are presented for the change in coil impedance Z when a circular air-cored coil carrying an alternating current of fixed frequency is scanned across a rectangular slot in an aluminium alloy plate. It is proposed that these measurements be used as a benchmark test to verify theoretical calculations of probe response in eddy-current NDE.     

Imaging the continuous conductivity profile within layered metal structures using inductance spectroscopy

This paper presents an inverse method for determining the conductivity distribution of a flat, layered conductor using a multifrequency electromagnetic sensor. Eddy-current sensors are used in a wide range of nondestructive testing applications. Single-frequency sensors are very common; however, the potential of an eddy-current sensor with spectroscopic techniques offers the ability to extract depth profiles and examine more fully the internal structure of the test piece. In this paper, the forward solution for a small right-cylindrical air-cored coil placed next to a layered conductor is based on the analytic solution provided by the transfer matrix approach. For an inverse solution, a modified Newton-Raphson method was used to adjust the conductivity profile to fit a set of multifrequency inductances in a least-squared sense. The approximate Jacobian matrix (sensitivity matrix) was obtained by the perturbation method. Numerical results of the forward solution are provided for cases of step, continuous conductivity profiles. Good estimates for the conductivity profile were obtained. Experimental eddy-current tests are performed by taking the difference in inductance of the coil when placed next to a reference conductor and next to a layered conductor over the range 100 kHz - 1 MHz. Inverse results based on experimental and simulated data verified this method.     

A computational investigation and smooth-shaped defect synthesis for eddy current testing problems using the subregion finite element method

Eddy Current Testing (ECT) plays a key role in detecting cracks and defects in conductors. The present study examines for the first time how the subregion method as an effective mathematical and computational technique can be admixed with Finite Element Method (FEM) to study multiple defects parameters for ECT issues. Separating a defect region from the entire domain in any computational technique will save both time and storage space. Examples of different types of defects are presented in this article . A tangible result of processing time reduction by 90% has been achieved which has led us to consider the subregion FEM method as an effective method in solving different Nondestructive Evaluation (NDE) problems. An agreement between our results and others using classical FEM has been achieved which could lead to using this technique in online and field testing problems. The presented subregion FEM algorithm was verified experimentally with good agreement by testing Aluminum (T6061-T6) samples with defects. A Tunneling Magnetoresistive (TMR) sensor was used to measure the component of the magnetic field from normal to the sample top surface. A major component of minimizing processing time was achieved, which could lead to using this technique in online and field testing problems.     

Stationary formulas for computing the response in eddy-current NDE

Stationary or variational formulations have been proven to be useful in a number of electromagnetic problems. This paper presents such a formulation for the response in the eddy-current NDE problem. It thus provides an approach to estimating the response due to arbitrary defects in cases where a reasonable first guess for the current distribution responsible for the scattered fields can be obtained.     

高阶流形方法及其应用

流形方法是一种可进行连续与非连续变形问题分析的灵活而有效的数值计算方法。本文详细地推导了二阶流形方法的具体计算列式,分别开发了一阶流形方法与二阶流形方法的计算程序．通过实例计算表明：提高覆盖函数的阶次可有效地提高流形方法的计算精度。     

Some effects of the shape of a small defect in eddy-current NDE

Available theoretical models for predicting defect responses in eddy-current NDE apply only to defects of spheroidal shape. In this paper, the boundary-element integral-equation approach is extended to allow for defects of more irregular shape. Sample results for cylindrical and conical voids are presented and discussed.     

Vector potential integral formulation for eddy-current proberesponse to cracks

A boundary integral vector potential formulation has been developed to evaluate eddy-current interactions with three-dimensional finite cracks in conductors. The approach is compared with an electric field integral equation method also used for solving crack problems in eddy-current nondestructive evaluation. An important advantage of the vector potential integral formulation is that the kernel has a weak singularity, but a drawback is that two unknown functions must be found on the crack surface. One of these functions, the current dipole density, represents the effect of the crack in terms of an induced source, and the other function is a solution of the two-dimensional Laplace equation. By contrast, the source density alone is needed for a complete solution of the electric field integral equation. In order to determine the surface Laplacian for finite cracks of arbitrary shape, a general numerical solution utilizing the boundary element technique is introduced. Numerical predictions of the eddy-current probe response to a crack give good agreement with experimental measurements, supporting the validity of the formulation     

Comparison of Dynamic Young’s Modulus of Thin Concrete Disks to Stress Wave–Based Nondestructive Evaluation Findings

Stress wave–based nondestructive evaluation (NDE) techniques are frequently used for in-situ evaluation of concrete. Stress wave velocity in a material is related to Young’s modulus of elasticity. Cores for in-situ compressive strength are subject to a minimum length-to-diameter ratio requirement that enforce large specimen sizes. Thin circular disks sawn from cylinders or cores are widely used in measurement of chloride or air permeability of concrete. While these methods provide useful information on concrete properties with depth, the capability of measuring changes in mechanical properties such as elastic Young’s modulus in small depth increments is of value to both researchers and consulting engineers conducting condition assessment or NDE, particularly when damage gradients exist. Changes in properties over relatively small depths may be undetected otherwise due to limitations of test method, equipment, or imposed specimen size. This study presents applications of Young’s modulus of thin concrete disks to structural assessment projects involving damage and damage gradients. In-situ nondestructive ultrasonic pulse velocity (UPV) testing was used in identification of affected areas. Young’s modulus of thin concrete disks was used in interpretation of the NDE results and provided an improved understanding of the extent of damage that was indicated using NDE. Two different case studies are discussed: exposure to fire and exposure to thermal shock and cryogenic temperatures. The use of thin disks enabled determination of mechanical properties of relatively thin layers of concrete and, therefore, provided a means to quantitatively assess the extent of damage gradients. Confirmation of NDE results using modulus data and analytical modeling using the relationship between Young’s modulus and pulse velocity provided improved understanding of NDE findings reducing uncertainty in engineering analysis and improving repair recommendations.     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.     

Ill-posed and well-posed problems in inverse elastodynamic scattering for nondestructive evaluation

The practical significance of ill-posedness in a data reduction problem is reviewed. Inverse elastodynamic scattering is shown to be ill-posed in general, although suitably restricted problems may be well-posed. These results underscore the need to analyze carefully the errors of data reduction problems in NDE, and to focus attention on final results of an NDE exercise, rather than on intermediate steps.     

Analysis of eddy-current loss for design of small active magnetic bearings with solid core and rotor

As the size of rotors levitated by active magnetic bearings (AMBs) gets smaller, it becomes increasingly difficult to make laminated cores and rotors that have low eddy-current loss, and solid cores and rotors have to be substituted. Thus, accurate modeling of eddy-current loss is important for small-size AMB systems with solid cores and rotor. In this paper, we propose a new eddy-current loss model for AMB systems, based on the eddy-current brake concept. We show that the eddy-current loss in AMBs strongly depends on the arrangement and size of poles. We compare test results for hetero- and homopolar AMBs having nonlaminated cores and rotor to analytical findings based on the eddy-current loss model. The experimental results confirm that the eddy-current loss in small homopolar AMBs with nonlaminated cores and rotor can be greatly reduced by optimizing the arrangement and size of poles.     

Development of high-order manifold method

The Manifold Method of Material Analysis (MM) with high-order displacement functions has been derived based on triangular meshes for the requirement of high accurate calculations from practical applications. The matrices of equilibrium equations for the second-order MM have been given in detail for program coding. The derivation of the method is made by means of approximation theory and very few new mathematical concepts are used in this paper. So, it may be understood by most engineering researchers. By close comparison with widely used Finite Element Method, the advantages of MM can be seen very clearly in the following aspects: (1) the capability of processing large deformation and handing discontinuities like block oriented Discontinuous Deformation Analysis method; (2) making element meshes easily and (3) using high-order displacement functions easily. The C program codes for the second-order MM has been developed, and it has been applied to the example of a beam bending under a central point loading. The calculated results are quite good in agreement with theoretical solutions. By contrast, the results calculated for the same model by use of the original first-order MM are far from the theoretical solutions. Therefore, it is important and necessary to develop high-order Manifold Method for the complicated deformation problems. © 1998 John Wiley & Sons, Ltd.     

Effect of magnetic hysteresis on rotational losses in heteropolar magnetic bearings

This paper extends a method for predicting rotational losses for laminated rotors of heteropolar magnetic bearings by using an eddy-current model to include the effect of magnetic hysteresis in the rotor material. It compares the modeling results to the experimental data that were used earlier to assess the loss model neglecting hysteresis. The correction to the total electromagnetic loss in the rotor due to the hysteresis is significant at rotational speeds below 6000 revolutions per minute (RPM), where the model including hysteresis effects provides much better agreement with existing experimental data.     

跑道型差动式涡流探头设计及其性能研究

针对传统差动式涡流探头几何尺寸大、缺陷检测灵敏度低的问题,在传统差动式涡流探头的基础上,设计了一种跑道型差动式涡流探头。它由激励线圈包裹2个尺寸相同、反向连接的感应线圈而构成。首先,利用COMSOL Multiphysics仿真软件建立了跑道型差动式涡流探头模型,比较了跑道型差动式涡流探头与传统差动式涡流探头涡流场分布的差异,并研究了在不同缺陷深度、不同扫查角度下2种差动式涡流探头的检测灵敏度。接着,制作了跑道型差动式涡流探头实物和碳钢板缺陷试件,利用试验测试的方法比较了跑道型和传统差动式涡流探头的检测灵敏度。试验结果表明,与传统差动式涡流探头相比,跑道型差动式涡流探头具有更紧凑的结构、更高的缺陷检测灵敏度。研究结果可为小尺寸、高精度差动式涡流探头的优化设计提供参考。     

Ultrasonic Transducer Sensitivity and Model-Based Transducer Characterization

Abstract

It is shown that the role that an ultrasonic piezoelectric transducer plays in both generating and receiving ultrasound in an ultrasonic nondestructive evaluation (NDE) measurement system can be completely described in terms of the transducer's electrical impedance and open-circuit, blocked force receiving sensitivity. Furthermore, it is shown that both of these quantities can be obtained experimentally via a model-based approach and purely electrical measurements. The measurement of sensitivity uses a method originally developed for lower-frequency acoustic transducers. However, it is shown that at the higher frequencies found in ultrasonic NDE applications electrical cabling effects play an important role and must be compensated for in determining the transducer sensitivity. Examples of experimental measurement results using these new approaches are given.