Håkan Wirdelius

Ultrasonic probe modeling and nondestructive crack detection

The mathematical modeling of a typical situation in ultrasonic nondestructive testing for defects is considered. The first objective is the modeling of a reasonably general type of ultrasonic probe. This is performed by prescribing the traction vector on the surface of an elastic half‐space. The effective probe area may be rectangular or elliptic and the traction may or may not include the tangential part (glued or fluid‐coupled probe, respectively). The probe can be of P, SV, or SH type and of any angle. The traction is either constant across the probe (piston‐type source) or it may taper off toward the edges. Numerical results for some representative cases are given showing snapshots of the field beneath the probe. The second objective of the paper is to include the presented probe model into a complete model of the ultrasonic testing situation. To this end the probe field is, via a series of transformations, expressed in spherical vector waves centered at the defect. The influence of the defect is give...

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.

Probe model implementation in the null field approach to crack scattering

A model of a compressional ultrasonic transducer is implemented into a T-matrix method-based solution to a crack scattering problem. The probe can act both as a receiver and as a transmitter, and it is modeled as an acoustic piston-like source. A previous solution by the null field approach is applied and is here used to model a crack that is partly closed due to an external background pressure. Numerical calculations of the signal response when the crack is penny-shaped are performed and compared with results from a program based on the Geometrical Theory of Diffraction, and the agreement is generally found to be very good.

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.

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.

Integral equation method for evaluation of eddy-current impedance of a tilted, surface-breaking crack

An integral equation method for solving the eddy-current nondestructive evaluation problem for a flat, tilted, and surface-breaking crack in a conducting half-space is presented. The method involves use of a half-space Greens tensor and the Bowler potential. This potential describes the jump in the electric field over the crack and is expanded in basis functions related to the Chebyshev polynomials, being a more analytical approach than the commonly used boundary element method. In the method, the scatterer defines a transformation operator to be applied on the incoming field. This is practical in simulations of the eddy-current inspection where this operator is independent of the position of the probe. The numerical calculations of the change in impedance due to the crack are compared to a Finite Element model of the problem and good agreement is found.

Estimation of grain orientation in an anisotropic weld by using a model of ultrasonic propagation in an inverse scheme

The initial step towards a nondestructive technique that estimates grain orientation in an anisotropic weld is presented in this paper. The purpose is to aid future forward simulations of ultrasonic NDT of this kind of weld to achieve a better result. A forward model that consists of a weld model, a transmitter model, a receiver model, and a 2D ray tracing algorithm is introduced. An inversion based on a multiobjective genetic algorithm is also presented. Experiments are conducted for both P and SV waves in order to collect enough data used in the inversion. Calculation is conducted to fulfill the estimation with both the synthetic data and the experimental data. Concluding remarks are presented at the end of the paper.

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?