Back to Basics

[ click here for the Back to Basics Archive ]

Integrating NDT with Computational Methods Such as Finite Element

by Ali Abdul-Aziz*

 

Computational methods are major tools utilized in many fields of science, engineering research, design and manufacturing. Many industrial fields, such as automotive, aerospace, pharmaceutical, electronics and communications, as well as newer and upcoming industries such as biotechnology, nanotechnology and information technology, depend on computational mechanics to model and numerically simulate complex systems for analysis, design, and manufacturing of high-technology products. These methods are also applied to verify experimental findings and improve the end products. Developments, improvements and modifications are ongoing phases to advance the robustness, applicability and efficiency of these computational techniques. Also, recent and rapid advancements in computer technology, software, hardware, and numerical and non-numerical methods are offering unprecedented contributions to the development of computational models and schemes to characterize materials and analyze the design of complex engineering systems.

Therefore, the need to integrate computational approaches with NDT is of high interest because it will offer the NDT community much needed support to confirm results obtained via certain testing methodologies and within various applications. Practical NDT methods are often applied to highly critical components and structures that have to be fully or individually tested. The results obtained from NDT can supplement the quality assurance task for components and structures during manufacturing and operating life as well. In order to conduct a broad evaluation, quantitative NDT techniques are desirable for determining sizes, shapes and locations of discontinuities and cracks. Computational mechanics is among the most practical tools for conducting such tasks. The recognized methods are the finite difference, finite element and boundary element methods. However, the finite element method (FEM) has been shown to be the primary and superior method due to its flexibility in modeling material properties and arbitrary domain shapes and in simulating boundary conditions. It offers researchers the means to go beyond simple image analysis and quantitative image assessment. It allows the use of accurate 3D visualization to generate an FEM model to calculate the localized stress and strain field around the observed internal discontinuities. The flexibility of FEM has won over an increasing number of NDT researchers (Abdul-Aziz et al., 2002; Abdul-Aziz et al., 2003; Abdul-Aziz et al., 2004; Abdul-Aziz et al., 2006; Cochran et al., 1995; Morgan et al., 1995).

The flexibility of FEM has won over an
increasing number of NDT researchers.

This paper presents a brief tutorial and summary of some available NDT techniques that are being incorporated with FEM to model hidden anomalies, discontinuities, cracks and other critical deformities in various structural and nonstructural components. Advantages and limitations of the NDT-FEM procedure and various applications are summarized. These procedures include the interaction of FEM with data from eddy current, X-ray computed tomography, infrared thermography and many other techniques to assess, predict and evaluate durability and material behavior. In addition, other NDT interactions with FEM and newer developments are discussed in the technical papers featured in this focus issue. The main purpose of this article is to illustrate the practicality of FEM with respect to NDT application and its applicability in providing a robust, simplified approach in analyzing, quantifying and translating NDT data into meaningful and informative analytical correlations. The sections below provide specific examples tied to integrating various NDT techniques with FEM.

Eddy Current Testing

Eddy current testing is one of several NDT techniques that uses the principle of electromagnetism as the basis for conducting examinations. Eddy currents are created through a process called electromagnetic induction. When alternating current is applied to a conductor, such as copper wire, a magnetic field develops in and around the conductor. This magnetic field expands as the alternating current rises to maximum, and collapses as the current is reduced to zero. If another electrical conductor is brought into close proximity to this changing magnetic field, current will be induced in this second conductor. Eddy currents are induced electrical currents that flow in a circular path. One of the major advantages of eddy current testing as an NDT tool is the variety of testing tasks and measurements that can be performed (Lord, 1980). Under proper circumstances, eddy currents can be used for crack detection, material thickness measurements, coating thickness measurements and other applications.

As an example of the integration of NDT applications with FEM, Allweins and von Kreutzbruck (2007) looked at imperfection issues in welds, such microcracks and porosities. Typically, these structural concerns have diameters as small as 100 mm. An eddy current testing system would be very suitable for detecting such small anomalies when using sensitive magnetometers such as magnetoresistive sensors (Lord and Hwang, 1975; Lord and Palanisamy, 1979). However, when looking at very small discontinuities, the field response caused by the texture of the weld significantly superimposed the imperfection's magnetic signature. A better understanding of the eddy current data required the exact determination of the weld's 3D texture. To analyze the influence of a weld's texture, FEM simulations using real surface data of laser welds was carried out. Surface data were obtained via scanning, and to obtain an estimation of the magnetic field's magnitude caused by the weld itself, the surface topology was transferred into an FEM model. Figure 1 shows the eddy current distortions when a homogeneous eddy current flow was induced in the sample (Allweins and von Krutzbruck, 2007).The current flow in the model enabled the calculation of the magnetic response of the weld. The FEM model also contains inclusions, with different sizes located within the weld at different depths.

Figure 1 - Finite element method (FEM) model: fringes of the 3D texture corresponding with the eddy current distribution when inducing a homogeneous current flow (dark red represents higher current densities).

This concludes that knowledge of the weld's 3D texture, obtained by simultaneous optical measurements, can be used to run a specific calculation that includes subtracting the discontinuity configuration from a reference model (without discontinuities), and will yield a residual field distribution containing information that relates solely to the discontinuity and its perturbation fields. Figure 2 represents a different NDT-FEM application showing the eddy current density in the cross section of the superconducting cable. In this case, the superconducting cable carried known discontinuities that were incorporated halfway between the two ends of the cable. The combined NDT-FEM led to the conclusion that, due to the skin effect, the strength of the distortion currents were higher at those NbTi filaments lying in the outer hexagon, which are closer to the surface (Figure 2). As a result, it was determined that very sensitive NDT tools, such as giant magnetoresistive sensors, fluxgate or superconducting quantum interference devices, must be used to completely detect even small and deep-lying discontinuities to solve this NDT problem (Allweins and von Krutzbruck, 2007). This exercise demonstrates in practical detail the joining of NDT and FEM to investigate the results produced by eddy current testing, and the corresponding conclusion produced by the FEM to improve the quality of the test outcomes.

Figure 2 - FEM model of superconducting wire with eddy current distribution in the cross-section of the total wire. Induced current density is about 100 mA/mm², the excitation current density is 5 A/mm² and the working frequency is 20 kHz.

Ceramic Materials Structural Testing

The ceramic matrix composite material system has been a focus for high temperature applications, such as engine hot section components, because of its low density compared to metals, and because it offers a lighter component mass (Bhatt, 2002). Currently, the manufacturing of these ceramic matrix composites is still not perfect, giving rise to matrix voids (Dicarlo, 1985). Hence, a detailed characterization of these discontinuities is imperative to the material researcher's being able to understand their role on the material behavior of such a complex material system. A study was undertaken using dog-bone shaped specimens (Figure 3) extracted from a flat panel made out of a ceramic matrix composite material that was fatigue tested and scanned with computed tomography before and after cycling to portray the initial matrix porosity's locations and sizes using a series of 2D computed tomography slice images (Abdul-Aziz et al., 2006). Thus, with the current advances in computed tomography imaging, 3D rendering techniques and computational interlinking, destructive characterizations can be eliminated for discontinuity sizes as small as the accuracy of the microfocal X-ray source used.

The NDT-FEM interface in this computed tomography imaging based example is initiated by generating a number of finite element meshes based on the 3D segmented image data. This is accomplished by invoking certain key features in highly specialized software to boost the density of the meshes generated. Since mesh refinement and accuracy is closely connected to image resolution, and in order to explore convergence of results (field parameters of interest), the image is down-sampled to create two different sizes of volumes to generate high- and low-resolution models. An obvious observation can be made here about image based models versus CAD models. For instance, unlike CAD models, where the geometry of the model is assumed to be exact and mesh density is increased principally in order to obtain a better model of the field parameters of interest (say the stress field within a loaded structure), with image based models, both the response and the geometry of the system are approximated. By generating models based on increasing image resolutions, one not only improves the modeling of the response but also the representation of the geometry. Hence, one can essentially perform a dual or coupled convergence study. This type of study provides powerful arguments for the validity of the simulations as a convergence of results demonstrates not only that the mesh is of sufficient density to capture the field parameter of interest, but also, and just as importantly, that the image resolution on which the model is based is high enough to capture relevant features in the scanned object.

Figure 3 - Ceramic matrix composite's tensile specimen dimensions and a selected computed tomography slice.

Ten models were generated using 20 iterations applying a multipart anti-aliasing algorithm, followed by two iterations of Laplacian smoothing. This ensured high accuracy of reconstruction. Mesh optimization parameters ensured that the element quality index reached an optimum value, allowing off-surface nodes to be within a pixel distance. Figure 4 shows a model that represents a view of the mesh and the internal features, illustrating various anomalies within the ceramic materials (Abdul-Aziz et al., 2006).

Structural deformities such as surface roughness of the matrix and other internal critical anomalies were all represented in the 3D rendered model. Prior to invoking the 3D volume construction process, image processing and other related manipulations to improve and enhance the quality of the computed tomography scan slices were made (Figure 5).

The final segment of this study combined imaging data with FEM, and analyses were performed under various specified loading conditions. A wide range of analyses were carried out to explore the sensitivity of numerical predictions to a range of parameters, including mesh density and segmentation parameters. The work shows that new image based meshing techniques can provide a robust and turnkey approach to the understanding of the influence of microstructural characteristics on macrostructural (bulk) properties of complex composites. Increasing mesh density provides not only better representation of the field parameter of interest, but also better geometric representation of the problem. The predicted effective modulus was relatively insensitive to mesh density; however, the peak stresses observed within the matrix (at stress concentration points caused by holes) were, as can be expected, quite sensitive. Also, peak stress concentration, and hence areas of potential failure through crack initiation, were identified (Figure 6). This combination of experimental testing with NDT-FEM allows carrying out experimental studies in parallel with analytical ones on the actual sample scanned, and the ability to better explore stability and failure mechanisms. Commercially available software was used to conduct these analytical calculations.

Infrared Thermography

For many years, infrared thermography has been broadly used to evaluate the reliability of joints in a wide range of industrial and research fields (Maldague, 1993). It is a safe and noncontact detection system for subsurface discontinuities, and is often used as an alternative test option or a complement to more conventional testing technologies (Inagaki et al., 1999; Madruga et al., 2005). In infrared thermography, the material surface is heated and an infrared camera records the resultant surface temperature. Heat flow into the material is perturbed by the presence of subsurface discontinuities, causing a temperature contrast at the surface. This feature is utilized in many NDT applications to check the reliability and quality of structural features, particularly joints.

Figure 4 - Model of the mesh and internal features: (a) general view; (b) detail of holes; (c) point cloud view.

Figure 5 - Noise filtering with the curvature anisotropic diffusion filter: (a) before; (b) after.

Figure 6 - Stress distribution showing critical regions/high stress risers.

An example will illustrate the applicability of infrared thermography with FEM to test the strength of brazed joints between the cooling tube and heat sink of a limiter test replicate (Chaudhuri et al., 2006). The work explains thermal images in which discontinuities are shown as a distortion in the temperature distribution. These results are compared with FEM simulations on the sample surface. The temperature distribution can be interpreted by quantitative analysis for discontinuity detection and classification. Infrared imaging relies on thermal contrasts to generate images. The thermal imager was a camera system capable of generating a 2D thermograph representing the radiation temperature.

This pattern of NDT-FEM interlink combined experimental activity from the infrared thermography data and a 3D FEM simulation to reproduce the brazing discontinuities between the cooling tube and the heat sink (copper backplate) in an attempt to recognize the thermal behaviors involved and to analyze the effect of the detachment of the cooling tube from copper backplate. An FEM model of the test specimen, including various sections, such as the cooling tube, brazed elements and heat sink, is shown in Figure 7. The temperature distributions presented in Figure 8 identify the areas in the modules of the test structure where cooling is inefficient. This simulation enabled the estimation of the proper amount of brazed joints necessary to keep the material surface temperature below a certain limiting value. Additionally, this combined infrared thermography FEM exercise demonstrated the capacity at which supportive analytical modeling could offer a qualitative assurance of the results obtained by the NDT technique of choice.

Figure 7 - FEM model of the test section: (a) cooling tube; (b) brazed elements; (c) heat sink; (d) full model; (e) FEM discretization.

Figure 8 - Infrared imaging showing defrosting sequence of the test section from 0 to 30 s.

Conclusion

This article provides a descriptive summary of the interaction between NDT techniques and computational methods, emphasizing the most popular one: FEM. The applicability of FEM combined with selected NDT techniques such as eddy current, computed tomography and infrared thermography are presented and discussed. The general approach to combing NDT with FEM begins by extracting data derived from NDT and modifying it to accurately reflect test article/component-specific characteristics, and then inputting it into an FEM model. The FEM analysis predicts the performance of the component in the service environment. This allows the development of a predicted margin of safety, which is a quantitative measure of component acceptance.

Computational methods, and in particular FEM, may not often provide the ultimate response expected from an NDT technique. The best approach is always to use the technique that provides the most efficient results for a given application. A combination of two techniques, provided that is possible, often yields greater benefits. Each one of these techniques has advantages as well as limitations. The main advantage of FEM is its efficient discretization of awkward geometries and calculations, available anywhere within the solution domain. It can considerably reduce the experimental work, help with understanding the principles of various NDT methods, improve methodology and help find the optimal operating conditions for testing.

However, it must be noted that it remains premature to adopt modeling as a practical tool in NDT, as it has not been evaluated throughout the industry. Many issues related to the limitations of modeling still exist: modeling tools for unique NDT applications require excessive development cost and time, numerical simulations can be time consuming and require intensive computer power, and models often do not have consistent agreement with experimental results due to various factors such as approximations or unknown features. Further, training of NDT practitioners is necessary to acquire proficiency in using the necessary simulation software.

Acknowledgments

The author would like to acknowledge Simpleware, Ltd., who developed the highly specialized software used to generate high-density meshes. The software used to conduct the analytical calculations was MSC/Patran and Abaqus/Standard. Figures 1 and 2 are taken from Allweins and von Kreutzbruck (2007). Figures 3-6 are taken from Abdul-Aziz et al. (2006).

REFERENCES

Abdul-Aziz, A., Y.G. Baaklini and R. T. Bhatt, "Nondestructive Evaluation of Ceramic Matrix Composites Coupled with Finite Element Analyses," Proceedings of SPIE, Volume 4704, 2002, pp. 32-39.

Abdul-Aziz, A., Louis J. Ghosn, George Y. Baaklini and Ramakrishna Bhatt, "Combined NDE/Finite Element Technique to Study the Effects of Matrix Porosity Influence in the Behavior of Ceramic Matrix Composites," Proceedings of SPIE, Volume 5046, 2003, pp. 144-151.

Abdul-Aziz, A., Louis J. Ghosn, George Y. Baaklini, Richard W. Rauser and John D. Zima, "A Combined NDE-Fatigue Testing and Three-Dimensional Image Processing Study of a SiC/SiC Composite System," Proceedings of SPIE, Volume 5393, 2004, pp. 103-110.

Abdul-Aziz, A., C. Saury, Bui Xuan and P.G. Young, "On the Material Characterization of a Composite Using Micro CT Image Based Finite Element Modeling," Proceedings of SPIE, Vol. 6176, 2006, pp. 05-1-0.5-8.

Allweins, K. and M. von Kreutzbruck, "Magnetic Modelling in Eddy Current Testing Using FEM," Institut für Angewandte Physik,
Justus-Liebig-Universität Gießen, available at wwwiap.physik.uni-giessen.de/sensorik/magnetosensorik/pdf/FEM%20in%20NDE.pdf, accessed 2007.

Bhatt, T.R., L.Y. Chen and N.G. Morsher, "Microstructure and Tensile Properties of BN/SiC Coated Hi-Nicalon, and Sylramic SiC Fiber Preforms," NASA Report Number TM-2001-210695, August 2002.

Chaudhuri, Paritosh, P. Santra, Sandeep Yoele, Arun Prakash, D. Chenna Reddy, L.T. Lachhvani, J. Govindarajan, Y.C. Saxena, "Non-destructive Evaluation of Brazed Joints between Cooling Tube and Heat Sink by IR Thermography and Its Verification Using FE Analysis," NDT and E International, Vol. 39, 2006, pp. 88-95.

Cochran, S., G.B. Donaldson, C. Carr, D.M. McKirdy, M.E. Walker, U. Klein, A. McNab and J. Kuznik, "Recent Progress in SQUIDs as Sensors for Electromagnetic NDE," Proceedings of the Second European Conference on Applied Superconductivity, Bristol, IOP Publishing, 1995, pp. 53-64.

Dicarlo, J.A., "Fibers for Structurally Reliable Metal and Ceramic Composites," Journal of Metals, Vol. 37, 1985, pp. 44-49.

Inagaki, Terumi, T. Ishii and T. Iwamoto, "On the NDT and E for the Diagnosis of Defects Using Infrared Thermography," NDT and E International, Vol. 32, 1999, pp. 247-257.

Lord, W., "A Survey of Electromagnetic Methods of Nondestructive Testing," Mechanics of Nondestructive Testing, W.W. Stinchcomb, ed., New York, Plenum Press, 1980, pp. 77-100.

Lord, W. and J.H. Hwang, "Finite Element Modeling of Magnetic Field/Defect Interactions," ASTM Journal of Testing and Evaluation, Vol. 3, 1975, pp. 21-25.

Lord, W. and R. Palanisamy, "Development of Theoretical Models for NDT Eddy Current Phenomena," Eddy Current Characterization of Materials and Structures, G.B. Birnbaum and G. Free, eds., Philadelphia, ASTM, 1979, pp. 5-21.

Madruga, Francisco J., Daniel A. González, Jesús M. Mirapeix and José M. López Higuera, "Application of Infrared Thermography to the Fabrication Process of Nuclear Fuel Containers," NDT and E International, Vol. 38, 2005, pp. 397-401.

Maldague, Xavier P., Nondestructive Evaluation of Materials by Infrared Thermography, London, Springer-Verlag, 1993.

Morgan, L.N.C., C. Carr, A. Cochran, D.M. McKirdy and G.B. Donaldson, "Electromagnetic Nondestructive Evaluation with Simple HTS SQUIDS - Measurements and Modeling," IEEE Transactions on Applied Superconductivity, Vol. 5, 1995, pp. 3127-3130.

 

* Optical Instrumentation and NDE Branch, NASA Glenn Research Center, MS 6-1, 21000 Brookpark Rd., Cleveland, OH 44135; (216) 433-6729; fax (216) 977-7150; e-mail ali.abdul-aziz-1@nasa.gov.

 

Copyright © 2008 by the American Society for Nondestructive Testing, Inc. All rights reserved.

[ Back to Materials Evaluation ]