TABLE OF CONTENTS

Introduction Acceptability requirements Physical interaction for the crack detection Practical applications and experimental verification of the model Inclined notch, Inner crack Geometrical and physical properties of the crack Conclusion References

1. Introduction

The tremendous efforts for the validation of various NDT methods - especially of those applied within nuclear power plants - promoted the search for simplified and cost-effective procedures to cheque the performance of the used NDT methods. Since for inservice inspections the main goal of the applied NDT methods is the reliable crack detection and if possible also their sizing, there is a special interest to judge the crack detectability and the sizing performance.

Most of the actually discussed procedures for the validation of this performance e.g. the ENIQ procedure or the ASME -Code, Section XI , Appendix VIII are proposing demonstration measurements on testblocks in an open or blind trial arrangement. At the end the performance is judged on a more or less statistical basis. It is possible to reduce the amount of time and work be spended for such demonstration trials by the use of technical justifications. One essential for those justifications is the concentration on testreflectors representing the different worst case conditions for the detection and the sizing of dangerous defects e.g. cracks in the case of an inservice inspection. But the definition of a worst case condition depends not only on the cracks but also on the used detection and sizing method especially the physical interaction between the crack and the ultrasonic waves. In the following we will try to discuss the major requirements for the crack detection and some examples for the principal limiting influences on the detectability of cracks.

For the ultrasonic methods the limiting influences on the crack detectability will be discussed considering three different aspects: Acceptability requirements for cracks Physical interactions used for the detection Geometrical and physical properties of the crack

2. Acceptability requirements

Critical Crack Size and NDT Acceptance Criteria

In figure 1 a general scheme for the definition of recording thresholds and acceptability levels for an NDT method is shown. The upper limit for an unstable crack growth can be defined on the basis of a fracture mechanical analysis. The relationship between a fracture mechanical analysis and the NDT is shown in figure 2. There are two major connections between those two disciplines: A fracture mechanical analysis can define the detectability threshold of a method, e.g. the needed recording and acceptance levels of an ultrasonic technique in terms of equivalent flaw sizes. The result of a NDT may deliver quantitative data of the defect depth extension, the defect length and the ligament between surface and defect or between different defects as a basis for further fracture mechanical evaluations to define the remaining safety margins and operation conditions.

But in most common cases the safety margin between unstable crack growth and the over all quality produced by a specific fabrication or welding procedure is large enough to allow the definition of acceptance criteria oriented on the achievable quality including a specific degree of absence of larger cracks. This is the case of an inherent basic safety with a certain tolerance against defects including e.g. smaller cracks. This procedure is the unspoken basis of the definition of the most common acceptance criteria for welds in steel components. But in cases where the difference between the allowable crack size due to unstable crack growth and the noise from spurious indications (based on structure geometry) is to small, e.g. in the case of ceramic components the requirement for the crack detectability are so severe that most of the NDT techniques are operating on their limits. This is the case for many structures based on ceramics or other materials with a limited toughness. In such cases the limitation for the crack detectability is based on both, the content of impurities and inhomogeneities within the material and the toughness limits.

3. Physical interaction for the crack detection

For the ultrasonic waves a crack is an object where the waves are diffracted or reflected. There is basically no difference between diffraction and reflection, but for a pragmatic classification it seems to be useful to distinguish cases with a strong specular geometric reflection - e.g. for large planar defects - from those with a weak diffraction - e.g. for crack tips.

Since the surface roughness of a crack is in most cases smaller than the wave length of an ultrasonic wave, the roughness influence on the amplitude is considered as to be a less important parameter for the limitation of the detectability. Smooth planar surfaces of cracks are much more limiting the detectability under the influence of misorientations between the incoming beam and the crack surface than rough surface structures do. In order to guarantee a minimum crack detectability most of the actually applied specifications for the ultrasonic weld-inspection are based on the beam reflection at the defect. The use of this strong interaction between the ultrasonic wave and the defect is traditionally justified with the well known interactions and the possibility to predict possible worst cases like misorientations etc. But this requires a careful adaptation of the orientation of the beam to the possible crack surface orientations. The case of surface breaking cracks represents a more severe requirement for the ultrasonic inspection, especially the orientation dependency is more difficult to predict than for the case of an inner volume crack. For the corner effect a lot of studies have been carried out and many models are available. In connection with this contribution an approximate model for notch type reflectors used at the BAM is described within the following [13]: Figure 3 shows the basic ingredients of this model.

a.) The probe sound fields of the model are derived from design concepts for focussing and planar probes existing at the BAM since many years [3,4,5,6 ]. Different probe characteristics can easely be investigated, even with curvature adaptation of the probe wedge.
By the modeling software the probe soundfield is described with an analytical approximation for the farfield and a special treatment of the nearfield area . This approximation contains the wavelength dependent geometrical directivity pattern of the area of the coupling surface, which is excited by the probe, and an elastodynamic point directivity pattern [1]. The nearfield is taken into account by a constant beam diameter in its area. Included is also the wave length dependent distance law along the beam axis and the assumption of a spheric shape and orientation of the wave front in each point of the space reached by the probe soundfield. (This can be modified for a better nearfield fidelity, if needed)
For both wave modes ( longitudinal and shear waves ) we are using the asymptotic approximations for the point directivity pattern according to e.g. Miller and Pursey [1]. Creeping longitudinal waves can be included with a special point directivity pattern for the longitudinal waves. Rayleigh waves are not taken into account. Focussing and the influence of curved coupling surfaces are introduced as described in several articles of the authors and others [2,3,4,5,6].
The receiving characteristic of a probe is derived from the transmitted soundfield assuming a complete reciprocity between reception and transmission.

b.) The medium of wave propagation is isotrop and homogenious. Special cases of anisotropy can be taken into account with the introduction of a special ray tracing approach and by the summation of the group time of flight contributions of all the differently oriented grains along the ray tracing path between the probe and a defect. For the case of an isotropic material the sound velocities for longitudinal and shear waves are considered to be constant and independent from the wavelength and the orientation. The attenuation is considered to be frequency dependent.

c.) The spectrum and the shape of the transmitter pulse is derived with the help of a quadrupol model of the probe using the KLM approach [6,7] and taking into account the special data of the probe construction (e.g. thickness of the transducer element, its size, material, delay path material, attenuation material, different layers of glueing and /4 -adaptations etc.)

Fig 4: Geometry of the Model for the Ultrasonic Inspection Fig 5: The Point Source Directivity at the reflector Fig 6: Test block for the Point Source Directivity Fig 7: Observation Angle

d.) The geometry is described three dimensionally. For the numerical integration, the reflector is divided into different surface elements of which the shape and size can be adapted to the defect geometry. Side-drilled holes, flat bottom-holes, elliptical or rectangular shaped cracklike reflectors with arbitrary orientation and position can be considered as well as corner effect reflectors. The three dimensional geometry of the model is for the time being limiting its application to blocks with parallel or inclined surfaces and to curved blocks with concentric surfaces.

e.) The reflection of an ultrasonic beam on an opposite or other surface (may it be planar or curved) is considered as a reflection at an unlimited mirror for an incoming beam, that means that an integration across surface elements is replaced by the assumption of a reflected ray (see Fig. 4). In case of curved surfaces or mode conversions, ray tracing with Fermat´s principle is applied. Angle dependent reflection and mode conversion factors for unlimited planar waves are taken into account for the reflection at the opposite or other surfaces.

f.) Special attention is payed to the interaction between the ultrasonic waves and the defect:
For each surface element of the defect this interaction is superimposed by partial waves, each one propagating along special sound pathes or rays and being affected by reflection or mode conversion depending on the specific sound path considered. Each wave part is weighted with a geometric directivity pattern of the surface element depending on the wavelength and on the size and shape of the element and in addition with one out of four different point source directivity patterns. Those patterns (see also Fig. 5) - differentiated according to the specific case of incoming and observed wave modes and angles : trans -trans, long - long, trans - long and long - trans - are formulated according to the approximation of the physical elastodynamic [8, 9, 11] and are depending on the considered wave mode and the impinging and observation angle. The figures 6 and 7 introduce an experimental verification of the different point source directivity patterns[12]. At the test block of figure 6, an angle beam probe for long.- or shear waves excites a quasi real crack. The electrodynamic pick up receives at an observation angle the waves reflected, mode converted or diffracted at the brittle fracture crack. The results (e.g. Figure 7) showed an excellent agreement with the theory of the physical elastodynamics [12]. Each sound path between the transmitting and the receiving function of the ultrasonic probes (corresponding to the rays of a ray tracing approach) is generating a partial echo E , which contributes to the total echo amplitude. The different factors F() of those partial echos are depending on the probe soundfield, the geometry of the object and the position of the defect. Probe soundfields and the reflection factors at the different surfaces of the object are described with approximations. They are in general phase dependent , that means they are complex values and are depending on the wavelength respective the frequency. One calculates the sum of the partial echos for a sufficiently large number of frequencies, generating thus a discret spectral system function of the ultrasonic inspection arrangement under consideration. This system function is multiplied with the complex spectrum of the transmitter pulse generated by the quadrupol model which gives a frequency weighted system function. An A-scan is than obtained by an inverse Fourier transformation of this weighted function. The number of frequencies to be calculated is reduced with the help of an apriori information about the probable sound path, at which the maximum echo pulse will occur. That means that the exact position of the echo within the time domain is based on the time-of-flight of the ray corresponding to the maximum echo pulse. Based on the A-scans different kinds of gray scale or colour coded B- and TD (Time Displacement) -scans can be produced. All the results are presented in terms of A-scans, B-scans or TD-scans and are directly comparable to results gained with mechanized scanners.
We have preferred to calculate the A-scans based on frequency domain samples and an inverse Fourier transformation, because this allows a simple introduction of individual pulse spectra from different probe designs.
The theoretical results can very easily be interpreted, because the different partial echos contributing to the indication of interest can be switched on or off. The effect of such a manipulation can be observed within minutes on a computer screen, because the software allows a very fast calculation even on ordinary PC´s.

4. Practical applications and experimental verification of the model

Inclined notch
The results of this approximate model have been compared with test-block measurements for inclined notches detected by the corner effect within half a skip distance.

Fig 8:

Fig 9:

Fig 10:

Figure 8 demonstrates the different rays or soundpathes of the partial echos to be considered for inclined notches. The 30 mm thick test blocks contained 10 mm notches with a 2mm gap and inclinations between 0° and 20°. There are simple shear wave soundpathes, shear-longitudinal soundpathes with mode conversion at the defect or mode conversion at the bottom surface of the test object. There are echos produced by interactions between the defect and the bottom surface and there are echo indications from the roof of the notch with its 2 mm gap. Figure 9 compares a typical TD-scan from measurement and model calculation on an inclined notch. The pictures give an impression of the complexity of interactions to be considered in this case. ( see also [10, 11]). There are beneath the tip diffraction indications also echos from long wave contributions (to be recognized by the slightly deviating slope) and direct interactions with the bottom surface. Figure 10 demonstrates another important behaviour of an ultrasonic indication from notches. The orientation dependency can be predicted by our model with sufficient experimental agreement (Fig 10).

Inner crack
The case of a crack in the inner medium of a planar and parallel test object is demonstrated in Figure 11. Using a 45° angle beam probe for shear waves with a small transducer size (8 x 9 mm) enables the probe to receive not only the two crack-tip indications produced by the primary shear wave but also a mode converted signal for a longitudinal wave between the crack and the bottom surface generated at about 35°-38° angle of incidence at the defect surface. Figure 11 shows a typical TD-scan received by this arrangement.

But there is an other limitation not considered within this model. The applied approximation of the physical elastodynamic is not taking into account modifications at the boundary conditions close to the crack tips. Those modifications do have a very important influence. The presence of specific corrosion products or other materials close to the crack tip area can let to the transfer of acoustic forces from one crack boundary to the other. Fig 12 explains schematically this influence during the detection of underclad cracks with inclined longitudinal waves. If one changes the steplike transition between the free stress boundary conditions at the crack surface and free space condition into a smooth transition, the crack tip indications are strongly reduced, which is schematically represented by the drop of the side lobes in the reflected directivity pattern and also observed on the A-scan. This has been demonstrated with the help of the block in Fig. 13, where we have tried to reduce the crack tip indication of a fatigue crack with either stresses or with the presence of special materials within the crack tip area. We could reduce the echo indications by stresses to about 14 dB (see also Fig. 14). Further more a similar reduction had been produced by liquid penetrants at the crack tip area. In this case we could observe a drop of 18 dB for the crack tip indication.

Fig 15: Comparison of Indications from Underclad Cracks produced by a TRL-Probe and by a SLIC 50 Probe Fig 16: Near Surface Probes with Different Concepts Fig 17: Diffraction at a different Reflector Types Fig 18: Signal/Noise-Ratio at Underclad Test-Reflectors Fig 19: ROC-curves for the SLIC 50 and the TRL probe

This example demonstrates, that detection methods based on idealized crack tip conditions may fail if special conditions are to be expected in the area of the crack tip. Fig. 15 demonstrates the importance of this consideration with the example of two different techniques for under clad crack detection at steel components with austenitic claddings. The example is refering to underclad cracks with a depth extension of about 3 mm and a length of 5 mm. A 70° T/R longitudinal wave probe, trying to pick up the reflected wave at the surface of the crack has a good chance to produce a well detectable amplitude of this crack. Whereas a so called SLIC probe using shear- and longitudinal waves with smaller incidence angles (see Fig. 16 for the probe design ) fails to produce detectable amplitudes of the crack tips.

There are other reasons for a diminished crack tip indication demonstrated at Fig. 17, where the diffracted energy from different reflector types are compared. The orientation of the diffracting border line and its shape do have an important influence. This can be seen in a comparison of the SLIC probe and the standard 70° TRL probes in Fig 18. The SLIC probes has no problems with the side drilled holes, but again it fails at a 3 mmØ flat bottomed hole. This remarquable difference is also present in a ROC performance evaluation in Fig. 19, but in this case for an ensemble of 30 different cladding defects. The special ability of defect sizing is for the SLIC probe based on a tip diffraction which is not the best approach for detection. Inversely the 70° TRL-Probe owns a good detectability but is fairly weak for crack sizing purposes.

Fig 20: Fig 21:

Figure 20 gives an interesting example for the suppression of diffraction based crack tip echos and the accentuation of the surface reflection at a special test block. This block had been used to qualify the so called tandem replacement LLT-technique, using phased array probes to detect defects perpendicular to the surface. In order to validate this technique we have applied test blocks whith inclined notches in order to reduce the diffracted portion of the signal received by the probe.

The comparison between the reflected surface echo of the crack and the diffracted crack indication is one of the reasons of the controverse debate concerning the TOFD technique, which has been propagated since some years in Europe. The basic principle of the TOFD technique from Maurice Silk [14] is demonstrated with the help of Fig 21, where a theoretically calculated time-of-flight-diffraction pattern, a socalled TD-scan is presented. The different types of waves interacting to produce this TD-scan are analysed and characterized in this figure. Some well known limitations of this technique are given in cases of cracks close to the surfaces. There are other limitations due to the restricted possibilities to tune and adapt the technique for situations where the diffracted energy from crack tips is reduced by the described influences (stress, corrossion products within the crack borders, misorientation and shape of the border line) . A typical property of the TOFD technique is the fact that the evaluation is based on the characterization of images. Those images can be disturbed by a lot of spureous indications and inclusions e.g. in the case for weldments on components with inclusions within the base material.

Concerning the trend to apply the TOFD approach also as a replacement of standard weld inspection techniques one should remember the following:
The debate about advantages and drawbacks of the application of the TOFD approach for ultrasonic weld inspection should not forgot the original reasons for the introduction of the ultrasonic weld inspection during the 60th of this century.

The mayor advantage at that time had been the better crack detection potential of the ultrasonic method against x-ray techniques in view of an increased use of steels and welding technologies with a remarquarble risc of diverse cracking phenonema (e.g. cold cracking, transverse cracks etc. ). An ultrasonic technique based on the matching between the orientation of the beam and possible crack surfaces and/or based on the corner effect together with a suitable choice of the amplitude related sensitivity had been the back bone for the successful application of the ultrasonic weld inspection. The above mentioned interactions are using a reflection rather than a diffraction at the defect that means the zero-th order diffraction instead of higher order diffractions. This is an important fact because the reflection (=zero-th order diffraction) can be reduced to fairly simple basic physical laws enabling us to predict the response from cracklike or other defects with reliable assumptions. Especially worst case conditions that means the influences reducing the echo answers from cracks can be taken into account (e.g. misorientation, mode conversions etc.). This is a distinct advantage against all other techniques using weaker interactions based on higher order diffractions, because in most cases they can only be calculated for idealized conditions like e.g. the response from a crack tip. Residual stress conditions, corrosion products between the crack boundaries or crack branching having a tremendous influence on the crack tip diffraction can only be estimated from experimental data but not be predicted and therefore not be taken into account during a sensitivity setting procedure or the choice of suitable angles of incidence. This is until today the mayor reason why TOFD approaches will have difficulties to guarantee under worst case assumptions the reliable detection of cracks in the before mentioned steel and welding technology combination with a certain risc of cracking. In addition also for the TOFD the dependency of an indication from the possible misorientation and shape of linear diffraction sources have to be considered.
Fortunately modern welding procedures have in the past strongly reduced the probability of cracking bringing into the foreground again conventional quality deficiencies in welds like slags, lack of fusion and porosity. For this situation the TOFD methods may be a valuable tool because they can easely detect corresponding defects. This explains partly the obvious success of NDE vendors applying TOFD and should be considered during the application of TOFD. But one should not oversee the limitations for a reliable crack detection, which could result in severe riscs, if this technique will be used for welds with a somehow increased potential of cracks. Such a situation can nowadays not be excluded given the fact that a global economy orders welded products every where, even on places, where the experience with the cracking potential is not always present.
The possibility of TOFD methods to size crack dimensions once they are detected is not discussed here. This is of course an important advantage of all crack tip based sizing approaches and is not specific to the TOFD technique.

5. Geometrical and physical properties of the crack

The examples of the precedent chapters have shown that much is depending on the geometrical situation of the crack (close to the surface or surface breaking or within the volume), on its orientation and also on the shape of the crack conture. The conture influences are especially of interest in cases of the application of TOFD approaches or approaches where the diffracted energy is mainly used for the detection.The extended linear diffraction source of a rectangular reflector can well be detected by crack tip sensitive techniques like the TOFD technique, but there are difficulties to guarantee the detection of those defects if they have curved tip lines, which is the case for the circular shaped reflector.

Another typical physical limitation for the crack detection is the presence of links between the seperating crack boundaries, e.g. due to corrosion products or due to a limited separation, e.g. in case of cold fusion in welding procedures. In those cases the distance of both crack boundaries can acoustically be close to zero and the reflectivity may be very limited. We have to take into account such crack behaviour in some forgings and in welds e.g. spot welds and some resistance butt welds.

6. Conclusion

The three major groups which have to be considered for the limitation of the crack detectability with ultrasonic methods are:
• acceptability requirements
• physical interactions between the ultrasonic wave and the crack
• geometrical and physical properties of the crack

The consideration of the limiting influences listed above may help to design test blocks which can represent the most important worst case conditions with simple technical means.

References

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13. H. Wuestenberg, R. Boehm Simulation of an Ultrasonic Inspection "http://www.ultrasonic.de" Copyright 1. Nov 1996
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15. H. Wuestenberg, A. Erhard Approximative Modeling for the Practical Application at Ultrasonic Inspections Copyright 1. May 1997

Authors:

H. Wuestenberg, A. Erhard, R. Boehm
BAM-Berlin, Fachgruppe VIII.4 Acoustical and Electrical methods of NDT
E-mail: Hermann.Wuestenberg@bam-berlin.de
BAM Berlin - NDT Department VIII.4
The Federal Institute of Materials Research and Testing (BAM) is a scientific-technological institute under the authority of the Federal Minister of Economics. In accordance with a decree of the Federal Minister of Economics from 1995 the BAM promotes the development of German industry by carrying out research on safety and reliability related problems in chemistry and in materials technology and by further developing the concerned testing techniques. The institute collects and makes the results of its own and others' scientific work available to the general public in suitable form.