Gert Persson

Model Based Capability Assessment of an Automated Eddy Current Inspection Procedure on Flat Surfaces

The probability of detection (POD) of a well-controlled, automated eddy current (EC) procedure is evaluated in a numerical model and compared with experiments. The procedure is applied in laboratory environment with a single absolute probe which is positioned for raster scan over flat surfaces containing fatigue cracks. The variability of the signal amplitude, due to small fatigue cracks in the Titanium alloy Ti-6Al-4 V, is expected to mainly originate from crack characteristics and the index distance of the raster scan. The POD model is based on the signal versus crack size ( versus a) result. The presented procedure provides a well-defined basis for a comparison between a simulated and an experimentally based POD assessment. Finite element analysis is used to model the EC method. A simplified fatigue crack model is first introduced and evaluated experimentally. Numerical computations are then used to build the corresponding model-based POD curve which shows good agreement with the experimental result. The model-based POD curve is generated both by means of a parametric and a nonparametric approach. Differences between model-based and experimental POD are discussed as well as the delta POD approach using transfer functions.

2-D elastodynamic scattering from a semi-infinite cracklike flaw with interfacial forces

Abstract The canonical problems of 2-D elastodynamic scattering of longitudinal (L), ‘vertically’ polarized transverse (TV), and horizontally polarized transverse (TH) waves from a semi-infinite cracklike flaw are studied. The boundary conditions on the flaw are of a type which incorporate restoring forces as well as energy dissipation, thus enabling the modelling of a number of flaw types apart from the open crack or the closed friction-free crack. These types include a thin layer of viscous incompressible fluid and a thin inclusion of a material of Maxwell or Kelvin type. It is also argued that the boundary conditions, though linear, can be adapted to serve as an approximate model, capturing at least the aspect of energy dissipation, for a closed crack under a background pressure with friction between the faces of the crack. Both the uncoupled TH case, and the more complicated L-TV case, where mode coupling enters, are solved by means of the Wiener-Hopf technique. Both the geometrical elastodynamic and the edge-diffracted body waves are computed, the latter as high frequency approximations expressed in terms of diffraction coefficients. Similarly the diffraction coefficients for body-to-surface and surface-to-body waves are computed, providing the canonical solutions needed for a GTD computation of the 2-D scattering of L or TV waves from e.g. a finite cracklike flaw of the type considered.

RECENT SURVEY AND APPLICATION OF THE simSUNDT SOFTWARE

The simSUNDT software is based on a previous developed program (SUNDT). The latest version has been customized in order to generate realistic synthetic data (including a grain noise model), compatible with a number of off-line analysis software. The software consists of a Windows®-based preprocessor and postprocessor together with a mathematical kernel (UTDefect), dealing with the actual mathematical modeling. The model employs various integral transforms and integral equation and enables simulations of the entire ultrasonic testing situation. The model is completely three-dimensional though the simulated component is two-dimensional, bounded by the scanning surface and a planar back surface as an option. It is of great importance that inspection methods that are applied are proper validated and that their capability of detection of cracks and defects are quantified. In order to achieve this, statistical methods such as Probability of Detection (POD) often are applied, with the ambition to estimate the detectability as a function of defect size. Despite the fact that the proposed procedure with the utilization of test pieces is very expensive, it also tends to introduce a number of possible misalignments between the actual NDT situation that is to be performed and the proposed experimental simulation. The presentation will describe the developed model that will enable simulation of a phased array NDT inspection and the ambition to use this simulation software to generate POD information. The paper also includes the most recent developments of the model including some initial experimental validation of the phased array probe model.

Emulation of POD curves from synthetic data of phased array ultrasound testing

Reliability of non-destructive techniques (NDT) is traditionally quantified by experimental determined probability of detection (POD). Such multi-parameter variability studies require a significant amount of experiments for each application verified, making them extremely costly. Reducing the need of experimental data by simulations requires both a verified simulation model and a procedure for effective computer experiments. Here synthetic POD curves for ultrasonic phased array testing have been generated using simSUNDT for signal amplitude simulations and a procedure to emulate response variability by predictive (meta) modeling and Monte Carlo simulations.

Application of the Geometrical Theory of Diffraction to closed cracks

The purpose of this paper is to compare the scattering of ultrasound by means of different types of smooth planar cracks in elastic solids. The boundary conditions on the flaws are of a type that incorporates interfacial forces. A crack that is partly closed by a static background pressure can thus be modeled. The Geometrical Theory of Diffraction (GTD) is used to predict the pulse-echo response from the crack. Previously obtained diffraction and reflection coefficients for cracks with interfacial forces are reviewed and some numerical difficulties are discussed. The backscattered echo amplitude is numerically calculated and compared for some different crack types and crack shapes. The presence of interfacial forces, due to background pressure, significantly influences the scattering behavior of the cracks. For a background pressure of 250 MPa, the backscattered amplitude, using our model of the interfacial forces, is typically reduced by 5–20 dB.

Pod generated by Monte Carlo simulation using a meta-model based on the simSUNDT software

A recent developed numerical procedure for simulation of POD is used to identify the most influential parameters and test the effect of their interaction and variability with different statistical distributions. With a multi-parameter prediction model, based on the NDT simulation software simSUNDT, a qualified ultrasonic procedure of personnel within Swedish nuclear power plants is investigated. The stochastical computations are compared to experimentally based POD and conclusions are drawn for both fatigue and stress corrosion cracks.

The Potential in Simulation and Metamodeling for the Understanding and Development of NDE

Abstract By combining detailed mathematical modeling of the physics involved in NDE with a broader and robust engineering approach based on the sequential steps of screening, modeling and optimization, it is possible to generate metamodels that can support NDE engineering efforts to evaluate the applicability of NDE in a wider context, as a complement to the repeatability, reproducibility and capability studies normally performed. The aim of the initial screening phase is to effectively evaluate and prioritize NDE control parameters from a wider perspective regarding the demands of a specific application and to prioritize parameters of lesser importance for the outcome on the basis of economic and practical considerations. The aim of the second and third steps is to study the influence of the important parameters and to perform sensitivity analyses of reproducibility and repeatability, for example, followed by procedure development, respectively. The methodology is straightforward when it comes to smooth response surfaces of lower order (up to second or third order). Generally, the recommendation for the screening phase is ‘to be bold’ for the definition of the experimental range for each parameter – meaning to make them as wide as possibly relevant for the specific application. For NDE applications not following the Berens assumption for POD studies, e.g., large cracks yield large response signals, such as the varying signal amplitudes from surface breaking notches in ultrasonic testing, the mentioned recommendation of ‘be-bold’ screening phase may lead to incorrect prioritization of parameters. In this publication, this is illustrated by how the width of the experimental range for the control parameters tested during screening actually influences the screening results. Two basic ultrasonic testing set-ups have been compared using the SimSUNDT simulation software package: surface breaking notch (SBN) and side drilled hole (SDH). Even though the results were anticipated, they pointed out the need to further develop the screening methodology supporting NDE engineering, especially when it comes to addressing the issue of applicability. Does the data collected tell us what we actually want to know about the tested application? Or does it only tell us something about the NDE method?

2-D Elastodynamic Scattering from a Finite Closed Crack

In the present paper the problem of 2-D elastodynamic scattering of horizontally polarized transverse waves from a finite planar or nonplanar closed crack is studied. The boundary conditions on the flaw are of a type which incorporate restoring forces (as well as energy dissipation), and this enables the modelling of a crack which is partly closed under a static background pressure. Given an incident plane wave and the crack geometry we calculate the backscattered far field in the time-harmonic case. In this study there are also a numerical comparison between two well known theoretical methods for 2-D scattering of ultrasonic sound by flaws in elastic solids. The methods are the GTD (Geometrical Theory of Diffraction) method that gives an asymptotic solution for high frequencies and the nullfield approach that yields an “exact” numerical solution. The boundary conditions for the partly closed crack are proposed by Bostrom and Wickham [1]. For a thorough description of the details of the GTD method as applied to scattering problems in elastodynamics, the reader is referred to the book by Achenbach, Gautesen, and McMaken [2]. The nullfield approach has previously been used for treating 3-D planar and nonplanar cracks with similar boundary conditions [3], the same ideas will here be used in the treatment of the 2-D case. The backscattered far field amplitude is numerically calculated and compared between the two methods.