In today’s world where new materials are developed and older materials and bonding methods are subjected to higher pressures and loads, NDT ensures that materials can continue to operate to their highest capacity with the assurance that they will not fail within predetermined time limits. NDT is not limited to just flaw detection but a wide range of uses. It can be used to ensure the quality right from raw material stage through fabrication and processing to pre-service and in-service inspection.
Apart from ensuring the structural integrity, quality and reliability of components and plants, NDT today finds extensive applications for condition monitoring and residual life assessment amongst others. There are many different methods of NDT which can be deployed for different materials and situations. Here we list some of the lost popular for completeness, and we will then begin to focus in on the ones of interest.
- Volumetric Examination Method
- Ultrasonic Testing
- Radiography Testing
- Surface Examination Method
- Visual Inspection
- Liquid Penetrant
- Eddy Current
- Magnetic Flux Leakage (MFL)/Magnetic Particle
- Integrity Examination Method
- Leak Testing
- Acoustic Emission Testing
- Condition Monitoring Method
- Thermography – Infrared Testing
- Vibration Analysis
- Special MethodsThere are 4 primary factors in deciding which of these methods to use. They are:
- Material Type
- Defect Type
- Defect Size
- Defect Location
These factors may favour a Volumetric technique like Ultrasonic which uses high frequency sound waves to detect imperfections or changes in properties within the materials. It can also be used to measure the thickness of a wide range of metallic and non-metallic materials where access from one side only is available.
Radiography uses an x-ray device, or radioactive isotope as a source of radiation which passes through the material and is captured on film or digital device. After processing the film an image of varying density is obtained. Possible imperfections are identified through density changes.
In this blog we will concentrate on the surface examination methods Eddy Current and Magnetic Flux Leakage.
The most commonly deployed techniques are liquid-penetrant and Magnetic Flux Leakage, accounting for around 50% of NDT usage. Ultrasonic and X-ray account for around another 30%, and Eddy Current around 10%. Magnetic Flux Leakage is used for defect detection, but Eddy Current testing is sensitive enough to be used for gauging as well.
Magnetic Flux Leakage Testing
Or MFL relies on the specimen being ferromagnetic, and is used to identify surface and near surface discontinuities in steel and iron. The technique uses the principle that magnetic lines of force (flux) will be distorted by the presence of a discontinuity. Discontinuities (for example, cracks) are located from the flux distortion following the application of fine magnetic particles to the area under test.
Eddy Current Testing
Relies on the specimen being conductive since electrical currents are generated in a conductive material by an induced magnetic field. Distortions in the flow of the electric current (eddy currents) caused by imperfections or changes in a material’s conductive properties will cause changes in the induced magnetic field.
Finite element analysis can complement and partially replace experimental Electromagnetic Non-Destructive Testing design processes. Firstly, the simulation allows for generating scenarios with a full control over all input variables, such as material properties, dimensions, and signals strengths and frequencies. Secondly, it is impractical to measure all results quantities of interest at all points over the field of interest, especially in a solid medium. Thirdly, FEA tends to be more economic than experiment, especially for the what-if scenarios, which take seconds to generate and solve using simulation.
But FEA cannot complete replace testing – it assists in preparation of test scenarios – showing where sensors are best placed, for example.
Conventional Eddy Current testing is based on the fact that when a coil excited by an alternating current is brought in proximity to an electrically conducting material, eddy currents are induced and the impedance measured at the terminals of the coil changes. The magnetic field associated with the current flowing in the coil (primary field) generates eddy currents within the conducting specimen; according to Lenz’s law, the direction of the induced currents, and of the secondary magnetic field created by these currents, is such as to oppose the change in the primary field. This causes a decrease in the flux linkage associated with the coil, and therefore a decrease in the coil inductance if the test material is nonmagnetic, whereas the higher permeability of ferromagnetic materials generally accounts for increases in the coil inductance. Accompanying this change in inductance is usually an increase in resistance, due to the eddy current losses incurred within the specimen.
There are different ways of modelling conductors in Finite Element Analysis and how we couple them to external circuits. There are methods for taking account of skin depth and flaws using either surface or volume representations to circumvent possible geometry modelling issues and possible numerical issues caused by mesh aspect ratios.
Finite Element Analysis (FEA) is a numerical analysis technique. The domain is meshed using the Finite Elements of the process’s name. The mesh gives discretisation errors due to the approximations involved in the numerical solution process. These can be reduced by using more elements – mesh refinement as it is called, but they can never be completely eliminated.
To eliminate errors introduced by mesh discretisation and the finite nature of the model we run two models; one with and one without the flaw The difference, therefore, is purely the effect of the flaw, not due to any FEA artefacts. To do this, define the model such that the flaw is present as a geometric feature, therefore the material can easily be changed from air to plate with a simple re-assignment.
Solve the problem using a harmonic solution; it utilises a complex solution, so the real and imaginary components of the magnetic flux density are available directly. Magnetic flux linked by each of the pickup coils is determined by performing a series of integrals over the area of the coil at various positions. This can easily be automated using Opera’s scripting capabilities.
In Eddy Current testing the excitation of the problem will be by use of coils with, usually, an AC supply. In FEA there are different ways of modelling coils; which is most accurate and efficient can vary with the type of problem being solved.
Firstly, we can use analytic representations of fixed-current density coils. These are placed independent of the mesh – the conductors don’t form part of the mesh in the solution. Hence models can be easier to be define. But post-processing may be more challenging, requiring derivations from flux linkage calculations rather than utilising readily accessible circuit parameters.
Alternately, we can use a filamentary representation. The filaments become edges within the finite element mesh and we can make use of drive circuits. Or we can choose to mesh the coil. The coils are defined as independent volumes in the model, which, usefully, can be utilised in post-processing. Current is regarded as being uniformly distributed throughout the coil cross-section, so field patterns are smooth and accurate in the coil region. Meshed coils can be connected to circuits, allowing direct calculation of inductance and resistance from circuit parameters.
Another practical consideration when performing finite element analysis of eddy current NDT problems is skin-depth modelling. It may be impractical, resource-wise, to mesh a whole problem with finite elements discretised to the size of the skin depth of the problem. So users need a way to accurately perform calculations at the surface, but utilise a coarser representation where the numerical integration points are unnecessary. Generally speaking, the accuracy of any finite element solution will depend on having sufficient elements to describe the shape of the field, and avoiding excessive distortion or aspect ratios.
Opera FEA offers two main ways in which this sufficient integration points can be deployed in the area of interest whilst allowing a coarser mesh elsewhere. The first is a volume representation – the usual elements are present, but the mesh spacing and bias is refined to give a high mesh density at the external surface, and larger elements away from the surface of interest.
The second is a surface representation. In Opera-3d this is referred to as a Surface Impedance Boundary Condition, which is applied to the external surface of a conducting volume. The SIBC treats all current as flowing on the surface of the material and specific calculation techniques are employed to accurately capture the behaviour of the fields.
If the flaw in a specimen is very small, employing a volume mesh representation can cause unnecessarily complex geometry models. In this case we can deploy the Electric Insulating Boundary Condition, or EIBC, in Opera-3d. Instead of modelling the gap, or flaw, explicitly as a small volume it is represented as an infinitely thin break between materials by applying a surface boundary condition between two conducting volumes. This stops current crossing while enforcing correct magnetic field continuity. So it can be used to model very thin flaws more simply than with a volume representation. It is typically used in solving NDT problems, or where insulating materials are present in electrical machines such as the rotor model shown below:
For example, TEAM Problems 8 and 15 deal with benchmarks in modelling the accuracy of coils above cracks in metallic plates. We’ll took a look at these to highlight important considerations when performing electromagnetic NDT analysis.
The probe consists of three coils: a drive coil and two smaller pickup coils, which allows us to examine the real and imaginary part of the differential magnetic flux.
Firstly, we need model only half of the problem – the boundary condition on the centre-line will infer the existence of the other half of the plate. In Finite Element Analysis, this is standard practice to cut down on computing resource requirements. Secondly, only the drive coil is included, the existence of the pickup coils will be implied in the post-processing. Here we have used a tetrahedral mesh, as specified in the problem definition. We could, in Opera, alternately, use a hexahedral mesh for accuracy.
The drive coil is operated at 500 Hz, giving a skin depth of 19 mm for the material used. You can, in practice, layer the mesh away from the surface of the material to accurately account for the skin depth of the material. The coil is re-positioned along the centre-line to create a series of static snap-shots for the harmonic electromagnetic solver. Velocity effects are not considered in this case.
The difference in the real and imaginary flux linked by the two pickup coils is calculated at positions 10 mm apart as per the benchmark specification. Here we see the Opera model for TEAM problem 8, for the case where the flaw is parallel to the motion of the coil.
Which is a requirement if we want to eliminate mesh discretisation errors for the most accurate results. We can create a number of solution cases in a single database, so we generate one database for the plate with the flaw, then re-assign materials and create a second database for the plate without a flaw.
Here we see the results for the different coil positions specified in TEAM Problem 8, for the plate with no crack, and the plate with a crack parallel to the direction of motion.
In an actual NDT device there would be 2, or even 3 probes measuring the return signal. From the relative shapes of the signal not only can the presence of a flaw be detected but also some information about its relative orientation. Flaws in different directions will have differing levels of severity – depending on how the structure is stressed.
This benchmark has been defined to look at how users might practically account for skin depth. It may be impractical, resource-wise, to mesh a whole problem with finite elements discretised to the size of the skin depth of the problem. For the lower frequency we will use volume elements, layered to better model the eddy currents near the surface of the plate. For the higher frequency we will use a surface modelling method, SIBC, because of the very small skin depth. In this benchmark the flaw is very small, so employing a volume mesh representation can cause unnecessarily complex modelling issues. In this case we can deploy the Electric Insulating Boundary Condition, or EIBC, in Opera-3d. As in the earlier benchmark, the coil is being driven at a fixed frequency, so we will be making use of the harmonic solution capability within Opera’s Dynamic solver module. We couple the meshed windings into an Opera circuit, which allows us to recover the resistive and inductive impedance in post-processing. Circuits can, generally, contain both active and passive components including resistors, inductors and capacitors, current and voltage supplies, diodes and switches besides the meshed coils.
If we ignore capacitance, the inductance and resistance can be calculated using the formulae given. The problem is solved twice, again, first with the flaw present and then missing. Then the difference between the two is calculated. The required output parameters can be calculated directly in the software post-processor.
The TEAM benchmarks are not limited to simple AC problems with surface flaws. TEAM Problem 27 uses a transient excitation, and a series of flaws buried within the sample. The sample is a cylinder of aluminium with a hole down the centre. Three shapes of flaw are simulated; these are located on the inner surface of the cylinder. The extent of the flaws is modelled explicitly. All three flaws are physically present in each simulation – the “active” flaw is determined by setting the material properties of the corresponding region to those of air. A fourth model is also used in which no flaw is present. This method allows us to use the same mesh for each model and thereby exclude mesh-related numerical inaccuracies. The probe is a coil of wire and a pair of Hall Effect sensors. The coil is positioned co-axially with the sample. The probes are located level with the base of the drive coil, at a distance of 5mm from the axis. One sensor is directly above the flaw; the other is diametrically opposite. The current in the coil is switched off suddenly, and the sensors detect the magnetic flux density from the induced eddy currents. The probes themselves are not explicitly modelled – we simply sample the field components at the appropriate locations in the model. We use a Biot-Savart coil – this provides a drive to the model but does not form a part of the mesh. The model uses reflection symmetry in the plane passing through the centre of the flaw (and through both Hall Effect sensors), with magnetic fields set to be tangential to this plane. This allows us to reduce the resource requirements for model solution.
The problem definition is to observe the difference in horizontal flux at the two sensors following the turn-off of the coil currents, so we use a transient electromagnetic solution, rather than harmonic. The initial 35ms allows any transients induced by the turn-on of the coil to decay away, so the testcase measurements begin at 35ms. The solution begins at time=0 with a DC current of 1.5A in the coil. Modelling the first time-point as DC allows us to skip the initial 35ms, as we are only interested in the effects of the current turnoff, not the turn-on. After this initial solution, the current is switched off. We use an adaptive time-step method to accurately capture the effects of this sharp transient.
Moving away from Eddy Current testing now, and onto Magnetic Flux Leakage. The MFL measurement principle is based on the fact that when strongly magnetizing a steel tube, some of the flux will leak out of the tube. Flaws in the tube that reduce the wall cross-section alter the leakage pattern. The shape of the flux leakage, therefore is dependent upon the defect’s geometry. The presence of the leakage field at the surface of the material can then be detected by sensors such as coils or Hall probes or it can be observed visually using magnetic particles. The specimen to be tested is usually magnetised by applying a direct current, with the form of the coil dependent on the application, or using permanent magnets.
Let’s now take a look at some features of Finite Element Analysis which are crucial in successful, efficient use for solving magnetic flux leakage simulation. Because the method relies on inducing a high magnetic flux density in the pipe accurate nonlinear material modelling is a must. Sometimes, this is achieved with permanent magnets, so accurate magnetisation modelling is also a must.
High-speed non-destructive inspection systems using the MFL method are in great demand for online inspection and defect characterisation, especially in pipeline maintenance. Such schemes aim to deduce the shape and dimensions of a flaw, from the voltage induced in a pick-up coil moving relatively quickly along the structure. MFL simulated with purely a velocity effect gives rise to an additional difficulty, in both signal interpretation and modelling, due to the formation of eddy currents when an excitation source moves over or inside a metallic pipeline. Numerical approaches to this problem include two schemes. Firstly it can be solved quasi-statically, with an extra movement component added to the formulation. The formulation in Opera, which we will come onto later, avoids the numerical difficulties, ie inaccuracy and non-convergence associated with increasing relative velocity and material’s magnetic permeability. Or, secondly, the relative movement of the probe and pipe can be analysed over several time-steps with the problem automatically repositioning and re-meshing at the solution progresses.
Competing goals and constraints such as those mentioned earlier mean that an automated Optimizer can often be the only way to achieve an optimal design. Static MFL methodology (or Magnetic Particle Inspection) involves magnetizing a portion of a structure and recording the flux at the surface. Usually a local magnetization close to saturation is required, because a leakage flux amplitude is generally proportional to the magnetization level. For something like a bulk liquid storage tank a magnetizing field of 1.5 to 2T is commonly used. This allows for scanning on both sides of the wall. Using a lower field might require multiple passes to fully determine the location of the flaw, and this can be difficult because of residual magnetism in the steel after passing over the MFL scanner.
The most common sources of a magnetizing field, electromagnets or yokes with permanent magnets, are used. The solution of such a problem is relatively simple with FEA – the material nonlinearities present provide no challenge to a solver such as Opera provided the B-H curve data is suitably accurate and smooth.
This type of device is commonly used on structures such as storage tanks where the walls or floor are subject to corrosion. Constraints on the design may revolve around physical sizes of access hatches, or static load limits, so an Optimizer such as Opera’s can be useful in achieving the required flux density from a given size and weight of device.
When analysing a moving MFL system, you can make use of two different analysis types. Firstly, you can model a moving conductor in static field by merely applying a loading, and assume that the cross section of moving and conducting media are uniform. You might use this to check the saturation of the flux into the specimen. It will not predict the signal generated by a particular type or shape of flaw. For that, you would need to use a transient analysis, whereby the pieces move relative to one another, and the problem transiently re-meshes as the solution progresses.
Naturally, the former type of analysis takes less resources to perform. We’ll now look at these two analysis types, and what they might be used for. When running a problem whereby the mesh is constant, and the relative motion is applied as a velocity loading in a standard FEA solver you will risk non-convergence of the solution. The main reason is that diagonals of conventional FEA equations approach zero, or even negative, when the velocity increases. The Opera-3d solver used in this instance, on the other hand, makes use of a technique called upwinding.
Numerical solutions without upwinding display oscillation of current distribution where the oscillation is non-physical. This phenomena is quantified by the Peclet number, which is proportional to permeability, conductivity, velocity and element size. Opera-3d introduced upwinding by modifying the FEA weight function to rectify the problem; it’s a Streamline Upwinding with Petrov-Galerkin method (SUPG) in vector form. This has allowed greater speeds to be defined without the need for overly-refined meshes, and hence the solution times have been greatly improved.
Velocity loading can be applied to linear structures but maybe it is easier to visualise on a circular structure. Here we have two discs sandwiching coils and soft magnetic material, as shown in the model on the left. It produces a static field as shown on the right. Using the velocity loading we can spin the discs. The geometry doesn’t move, the mesh doesn’t move, the coil doesn’t move. We just, mathematically, tell the solver that the discs are spinning with a given velocity. So let’s have a look at the results as we increase the spin-speed.
Now onto how Magnetic Flux Leakage NDT testing is carried out in the field. A common piece of hardware used for MFL detection in a pipe is a pipeline inspection gauge, or PIG. A strong magnetic field is established in the pipe wall using either magnets or by injecting electrical current into the steel. Damaged areas of the pipe can’t support as much magnetic flux as undamaged areas so magnetic flux leaks out of the pipe wall at the damaged areas. An array of sensors around the circumference of the pig detects the magnetic flux leakage and notes the area of damage.
If you Google Pipeline Inspection Gauge you’ll see an almost bewildering variety of devices. But really, in terms of Electromagnetic MFL PIGs there are two types – Magnetiser Bar (or MagBar) and Solid Core Brush design (or Sweep’s brush). A Sweep’s brush consists of magnets arranged around an annular carbon steel body, with the magnetic circuit completed by ferromagnetic bristles mounted on the magnets. The bristles transmit the magnetic flux into the wall, and act as a mechanical shock absorber/damper in the system.
A Magbar design has distinct return paths sprung-mounted around the annular body. The permanent magnets are mounted on the ends of the return paths, and hence the magnet material is mounted much closer to the pipe wall. The mounting position helps in saturating the wall, but there must be annular gaps in the design to account for the necessary radial restriction.
The purpose of performing simulation in design of a PIG is to optimize the shape and weight of the device against given performance criteria. The requirements that the tool saturate the pipe and provide maximum fluid bypass are inherently conflicting. Saturating the pipe requires a large area of steel inside the body of the tool to provide a return path for the magnetic flux. On the other hand, achieving maximum gas bypass requires a large bore in the center of the tool. Magnetic clamping forces are directly proportional to the flux magnitude and the gap; these clamping forces should be minimised so as not to adversely affect the smooth progress through the pipeline. With increasing speed, the magnetic field levels will decrease on the outer wall as the field is channelled away from the outside wall, so this must be factored into the design process.
Long pole-spacing will typically deliver lower magnetic flux densities in the pipe at low velocities, but these designs are more stable, dynamically, and provide better access for sensors, so there are a number of factors to consider in the basics of the design.
The traditional approach to designing this tool would involve developing a concept design based on engineering rules of thumb and experience. A large artificial defect set is created by electrochemically machining defects into pipe spools. A prototype MFL tool based on the concept design is then tested in this defect set to determine its ability to generate the required magnetic flux levels and provide gas bypass.
Once the magnetic design is optimized, simulation is used to determine where the sensors should be located to best capture variations in the magnetic fields.
After manufacture of the chosen prototype sensitivity studies can easily and quickly be performed using the digital model which allows the test results to be correlated, and the tool quickly calibrated for different types of defect. Custom magnetic flux leakage (MFL) tool designs often need to be developed to ensure that inspection tools can accurately measure a wide range of pipeline defects while minimizing the degree of gas bypass necessary to continue operating the pipeline at full capacity. By reducing the time required to develop new MFL pipeline inspection tools magnetic simulation makes it practical to develop custom tools for specific applications.
For this design exercise we will use a dynamic solution whereby the relative motion is considered not to change the finite element geometry. The source fields and driving conditions are considered to be time-invariant. We will solve for only one position. So consider the PIG effectively to be moving along inside an infinitely long pipe. There is a reflective and rotational symmetry angle of 15 degrees so we will make use of that in our model to cut down on solution time. We can visualise the full 360 model in post-processing simply if we wish.
When a magnetic pig passes through a pipeline then the section of pipe will experience a change in magnetic flux and since pipe-steel is a good electrical conductor, an emf will be generated in the wall. This will give rise to eddy currents circulating in the pipe-wall and these, in turn will generate magnetic fields opposing those generated by the PIG. The greater the velocity of the pig the greater the eddy current effect will be. This motion-induced effect gives rise to smearing of the induced field, as seen in this flux density contour plot for the section of the model shown on the previous slide.
We can look at how the field is smeared along the direction of travel, and how it might influence the design if we look at a simplified PIG model, and run it through a range of relative velocities.
At higher velocities the effect of the eddy currents and induced field become most evident. Since the applied fields will always be lower on the outer wall than the inner, the sensors must be calibrated for the difference. If the PIG is run too quickly then the field levels on the outer wall may decrease to a level where reliable detection is no longer possible.
In the previous example, we were looking at the design of a PIG in order to fully magnetize the pipewall. We didn’t look at the signal generated by a flaw. If we want to look at this in detail we need to incorporate the flaw in the model, and include it’s motion through the detection system. To demonstrate a simple setup for this type of NDT analysis we’ll use a moving cable with a rectangular defect. To induce the magnetic field we are using two C-shaped formers with drive coils and then a third coil acts as the pickup.
Because the cable is moving relative to the drive coils and pickup coil, we will solve the problem using a transient technique, whereby the cable with the defect is driven between the formers and we generate output at several points in time. In between each of these time-steps, as they are called, Opera-3d will automatically re-mesh the problem to ensure we retain a quality undistorted, and hence accurate, mesh.
The moving part of the problem, in this case the cable, is controlled using the motion control script. This is defined simply using a wizard – in this case we’ll utilise a constant velocity drive function.
In order to record the voltage across the pickup coil, again we will use a defined circuit.
Once the problem has been solved there are many ways to view the results within a post-processor. For example the magnetic flux density can be viewed as contours or as vectors. Opera-3d includes simulation tools that are very effective for designing non-destructive testing equipment. Mesh-independent coils allow for easier definition of problems where the coil is moved to different positions but you want to retain the same analysis mesh.
You will need nonlinear material modelling – most EM NDT techniques rely on driving soft magnetic material well into saturation. For ease-of-modelling and accuracy you will want layering in solid meshes, or the option to go to surface representations of both skin depth and/or flaws.
Relative motion needs special formulations to avoid convergence issues and deliver the accuracy you need, with or without re-meshing. Comprehensive post-processing functionality will be required to allow the necessary calculations for characterisation of defects.
An optimizer can speed the development process of probes with conflicting goals and constraints. All of these are offered by Opera-3d.