AVG CURVE EVALUATION APPLIED TO ULTRASONIC PHASED ARRAY TESTING

Mario Certo1, G. Nardoni1

1I&T Nardoni Institute

SUMMARY Application of phased array in ultrasonic testing of component, such forged or plate component, with longitudinal wave arranged in a sectorial scan centered at zero degree can be very attractive because the possibility, due to electronic sectorial scan of the ultrasonic beam, of a complete and documented volume inspection with a less number of scan lines than using standard probe. The problem is that in such inspection technique defect estimation is done, normally, by the use of AVG set of curves. Such curves are easily available for standard probe of circular shape, but not for phased array probe whose active area is a function of the number of active elements chosen and that can be strongly rectangular. In order to avoid such difficulty, we have implemented a computer model which is capable of generating the AVG curves giving in input the actual phased array parameters. This computer model has been assessed using some calibration blocks containing flat bottom holes. The results are very encouraging showing a good performance when defects are in the far field of actual probe configuration, while in the nearfield region the generated AVG curves lead to a defect overestimation.

1. Introduction Application of phased array in ultrasonic testing of component, such forged or plate component, with longitudinal wave arranged in a sectorial scan centered at zero degree can be very attractive because the possibility, due to electronic sectorial scan of the ultrasonic beam, of a complete and documented volume inspection with a less number of scan lines than using standard probe. The problem is that in such inspection technique defect estimation is done, normally, by the use of AVG set of curves. Such curves are easily available for standard probe of circular shape, but not for phased array probe whose active area is a function of the number of active elements chosen and that can be strongly rectangular. In order to avoid such difficulty, we have implemented a computer model which is capable of generating the AVG curves giving in input the actual phased array parameters. In this paper we reports the theory developed to describe the amplitude of echoes produced by flat circular reflectors centered on probe axis and at different distance. Then we present the results of the experimental assessment of the program code, we have implemented using such theoretical model. The experimental work is carried out using some calibration blocks containing flat bottom holes; the results have been compared, also, with those obtained using a standard probe.

2. The AVG curve method

3. Theory of the Computer model for the generation of AVG curve Figure 1 shows the description of probe – reflector geometry, where it is assumed that the probe will produce a normal ultrasonic beam and the reflector disk is centered on the probe acoustical axis. The active surface of linear probe are discretized in small rectangular elements according to its phased array structure (in particular the j-index denote the j-th phased array element). Instead, disk reflector, due to its circular shape, is discretized according to the radial axis (m-index) and to the angular axis (n-index).

Figure 1: probe and flat circular reflector geometry for model implementation

The arrow denoted by j,k,m,n indicates the path of ultrasonic field produced by the (j,k) probe element on the surface of (m,n) reflector element, where j,k,m,n is the distance between the two elements. If we indicates with Aj,k,m,n the amplitude of such ultrasonic field, then the total field Cm,n produced on the (m,n) disk element is the summation of ultrasonic field produced by all the probe elements, that is: 1) where the elementary field Aj,k,m,n is expressed by the equation:

2)

and where: wj,k,m,n is a suitable weighting function, which takes account also for a finite signal

. bandwidth; f is the probe frequency; c is the ultrasound velocity;

j,k,m,n = where j,k index denote coordinate over the probe surface, while m,n index denote coordinate over the disk surface;

x, y are the linear sizes of discretized probe element; m , are the radial and angular sizes of discretized reflector disk element of index m

Using the reciprocity theorem, we can express the signal received by the probe due to back reflection by (m,n) reflector disk element as the square of the incident field Cm,n so that the total signal S back reflected by the disk reflector is the summation over (m,n) index of C 2

m,n: 3) Where S is taken as the modulus of complex value resulting from the summation. The weighting function wj,k,m,n has been assumed, with heuristic criteria, as:

4)

Equation (1), (2) (3) and (4) has been used to implement a computer program, written in Visual Basic 8.00, which accepts as input the phased array probe parameters and produces as output the numerical value, expressed in dB and normalized with respect to the maximum value, of amplitude S as a function of distance and diameter of reflector disk.

4. Computer model assessment

A first assessment of the implemented computer model has been done comparing AVG curves of a standard commercial transducer 2 MHz – 24 mm diameter, see figure 2, with the equivalent prediction of our model, see figure 3. Some small discrepancy is present for the larger disk reflector in the near field region, but this is due to the different probe geometry, in fact, the commercial probe is circular while our prediction refers to a square probe of an equivalent size 18 mm to obtain the same nearfield length. In all other case the correspondence is quite perfect.

Figure 2: AVG curve for standard probe B2S Figure 3: AVG curve of a square standard probe equivalent to the previous one

A second assessment has been done generating two set of AVG curve: one for a 32 element, 1.4 mm pitch phased array probe working at 2.25 MHz and the other for similar probe but with 16 element.

Figure 4: AVG curve for a phased array 32 element, 1.4 mm pitch working at 2.25 MHz

Figure 5: AVG curve for a phased array 16 element, 1.4 mm pitch working at 2.25 MHz

Then comparing their predictions with experiment on suitable test blocks. Figure 4 and 5 shows the AVG curve for such probe, while Table I describe the test block used in the assessment and the results obtained.

Table I: comparison of experimental results obtained with a standard probe B2S and with phased array with two element configuration

backwall depth [mm]

flat bottom hole depth

[mm]

diameter [mm]

Standard probe B2S 32 element phased array 16 element phased array

estimated diameter

dB increment with respect to

backwall

estimated diameter

dB increment with respect to

backwall

estimated diameter

dB increment with respect to backwall

545 520 9 10 +20 10 +19 527 502 6 6 +28 6 +29 100 90 3 3.2 +25 5.9 +26 3.8 +21 100 85 5 6 +14 9.8 +17 7 +11

Looking at Table I we can observe that in the probe far field, regardless it’s a standard probe or a phased array probe, size estimations are quite good and comparable each other, while if we work in the near field, as the case of 32-elements phased array probe and the last two defects, we have a mismatch consisting in an oversizing of approximately a factor 2. This behavior can be easily explained taking into account that the nearfield region is quite complex to model, especially for what concern the real effect of probe bandwidth.

5. Conclusions

The possibility to generate, by a computer model, AVG set of curves for a complex probe as a phased array probe, whose geometry changes changing active element configuration, enable us to apply such probe in inspection technique, like those for forged components and plate, based on AVG curve for the estimation of defect severity. Experimental verification has demonstrated that accuracy is quite good if defects are in the far field region of the probe. This means that, if a defect is detected in the near field region, then, in order to avoid a defect overestimation, it must be reexamined using a less number of active elements in order to reposition the defect in the probe far field.