Ultrasonic Non-destructive Evaluation of Titanium Diffusion Bonds

Transcription

1 J Nondestruct Eval (2011) 30: DOI /s y Ultrasonic Non-destructive Evaluation of Titanium Diffusion Bonds K. Milne P. Cawley P.B. Nagy D.C. Wright A. Dunhill Received: 9 April 2011 / Accepted: 4 July 2011 / Published online: 28 July 2011 Springer Science+Business Media, LLC 2011 Abstract Diffusion bonds offer several advantages over alternative welding methods, including the ability to produce near-net shapes and achieve almost parent metal strength. However, voids remnant from the joining process can be tens of microns in their lateral dimension, making them difficult to detect with conventional pulse-echo immersion inspection at any significant metal depth. In titanium the inspection is particularly challenging; the anisotropic microstructure is highly scattering and the diffusion bond itself forms an interface between regions of preferred crystallographic orientation (macrozones), which can act as a weak spatially coherent reflector. A simple interfacial spring model predicts that, for partial bonds (sub-wavelength voids distributed on the bond line) and at certain frequencies, the phase of the signal can be used to separate the component of the signal due to the change in texture at the interface and the component due to the flaw. Here it is shown that the phase of the signal from an interface is also affected by the anisotropic microtexture of Ti 6Al 4V. Good separation between wellbonded and partially bonded samples was achieved using a symmetric inspection, where the magnitude and phase of the reflection coefficient were calculated for normal incidence from opposite sides of the diffusion bond. K. Milne ( ) P. Cawley P.B. Nagy RCNDE, Department of Mechanical Engineering, Imperial College London, London, SW7 2AZ, UK katy.milne@the-mtc.org P.B. Nagy School of Aerospace Systems, University of Cincinnati, Cincinnati, OH , USA K. Milne D.C. Wright A. Dunhill Rolls-Royce plc, PO Box 31, Derby, DE24 8BJ, UK Keywords Diffusion bond Partial bond Titanium Imperfect interface Interfacial stiffness Ultrasonic reflection coefficient Phase 1 Introduction Diffusion bonding can generate joins with almost parent metal strength in near net shapes [1]. If the bonding pressure, temperature or time has been insufficient, voids will be remnant on the diffusion bond line. Their size is related to the roughness of the joined surfaces [2 4] and so their lateral dimension may be in the order of micrometres. A partial bond is defined as an array of these voids that are not resolved individually by the interrogating ultrasonic beam [5]. For the conventional pulse-echo inspection of forgings, low MHz range frequencies are used to allow inspection up to metal paths of 100 mm [6]. Thus the size of individual defects is generally smaller than either the ultrasonic beam diameter or the wavelength. In titanium, the sensitivity of a pulse-echo inspection is limited, since noise backscattered by the anisotropic microstructure can mask reflections from the defects. Furthermore, a diffusion bond between pieces of titanium creates a planar interface between macrozones regions where the grains have a preferred crystallographic orientation [7 9]. While a typical grain diameter is 50 µm for forged titanium, a macrozone may be several millimetres in diameter. This interface acts as a weak but spatially coherent reflector, analogous to that between two dissimilar materials, which may also mask reflections from defects. In this paper, both the magnitude and the phase of the frequency dependent reflection coefficient are measured for low MHz range ultrasound normally incident on the diffusion bond plane in Ti 6Al 4V samples. Theory on the reflection coefficient for ultrasound normally incident on a

2 226 J Nondestruct Eval (2011) 30: partial diffusion bond is discussed in the remainder of this section. It is suggested that the phase of the reflection coefficient can be used to differentiate between the component of the reflection due to the acoustic impedance change at the interface and the component of the reflection due to subwavelength sized voids distributed across the interface. The experimental method for determining the phase and magnitude of the reflection coefficient is described. Factors affecting the measured value of the magnitude and the phase of a signal reflected from an interface are investigated in Sect. 2. Finally, experimental results are presented for the reflection coefficient measured for ultrasound normally incident from both sides of the diffusion bond plane. These two reflection coefficients are combined to obtain a single symmetric reflection coefficient. transverse direction. Below the diffusion bond line the orientation appears random. The average acoustic impedance for wave propagation orthogonal to the diffusion bond plane is different for each macrozone. An ultrasonic B-scan for the same sample, scanned in pulse-echo immersion with a longitudinal wave probe, is showninfig.3. There is a weak, spatially coherent reflection at the bond depth, which is thought to be due to the planar interface between macrozones. The region highlighted with the white dashed line corresponds to that highlighted in Fig. 1. The sample was generated by a hot isostatic press, using parameters selected to give a good weld. The sample was polished and etched to show the microstructure at the same section as the ultrasonic B-scan in Fig. 3. No defects were found on the diffusion bond. Figure 4 shows the bond 1.1 Diffusion Bond Microtexture and Backscattered Ultrasound It was recently discovered that optically homogeneous microstructures can have a preferred crystallographic orientation over regions or macrozones much larger than the mean grain diameter [7 9]. Macrozones have been observed by Electron Backscattered Diffraction (EBSD) [7 9] and by mapping the surface wave velocity [10]. Figure 1a shows a surface wave velocity map for a diffusion bonded Ti 6Al 4V sample generated for this study. Regions of similar surface wave velocity, indicating preferred crystallographic orientation, are apparent. Figure 1b shows a 2 mm thick 20 mm long band obtained by scanning with a finer step size. The diffusion bond can be observed as a planar interface between macrozones halfway down Fig. 1b. A 0.7 mm wide 0.5 mm tall area (see box in Fig. 1b) of the sample was mapped with EBSD. The crystal orientation map (Fig. 2) shows that there is a sharp microtexture above the diffusion bond line; the main axis of the hexagonal close packed unit cell is strongly aligned with the sample Fig. 1 Surface wave velocity map of diffusion bonded Ti 6Al 4V sample #2 obtained using optical-scanning acoustic microscope (O-SAM) at University of Nottingham [11]. (a) The surface wave velocity was measured over a length of 100 µm with 100 µm steps in the direction normal to the diffusion bond line (top-to-bottom of image). Macrozones are apparent either side of the bond line. (b) Enlarged image of bond line region with step size of 25 µm. The area scanned using electron backscatter diffraction to generate the map shown in Fig. 2 is indicated. The region highlighted by the white dashed lines corresponds to that highlighted in Fig. 3 Fig. 2 Crystal orientation map for 0.7 mm wide by 0.5 mm tall area of sample #2 (see Fig. 1b) with µm resolution with respect to sample transverse direction (left to right). The colour map indicates which plane is oriented closest to the sample transverse direction for α-phase Ti 6Al 4V

3 J Nondestruct Eval (2011) 30: Fig. 4 Micrograph at 200 magnification of sample #2. The section corresponds to the ultrasonic B-scan in Fig. 3. This image corresponds to x = 30 mm Fig. 3. Theblack regions between grains are fine platelets of secondary alpha Fig. 3 Ultrasonic B-scan (amplitude vs. time of flight and lateral position, x) of sample #2 captured using 10.9 MHz centre frequency, 160 mm focal length, 19 mm diameter longitudinal wave probe focused at the bond line depth. A coherent bond line reflection is apparent. The scan pitch is 0.25 mm. The greyscale is linear and indicates % of oscilloscope screen height. The region highlighted by the white dashed lines corresponds to that highlighted in Fig. 1 line at 200 magnification at the position corresponding to x = 30 mm in Fig Reflection of Ultrasound from an Imperfect Interface The magnitude of the reflection coefficient is commonly used to evaluate interfaces [3, 12 27]. For low frequencies, where the wavelength is long compared to the defect size and separation [15, 25, 27], imperfect interfaces have been modelled as a spring layer with an interfacial stiffness, K. For the simple case of a longitudinal or transverse wave normally incident on a bond line, which is thin relative to the wavelength so that the mass of defects is negligible, the reflection coefficient R 12 can be related to the interfacial spring stiffness by [5, 13 15, 25, 27, 28]: R 12 (ω) = Z 1 Z 2 + iω(z 1 Z 2 /K) Z 1 + Z 2 + iω(z 1 Z 2 /K), (1) where ω is the angular frequency, i is 1 and Z 1 and Z 2 are the acoustic impedances of the bonded media. For a perfect interface, the interfacial stiffness is infinite and the frequency dependent term disappears. The magnitude of the reflection coefficient is frequency independent and related only to the difference in acoustic impedance between the two materials. The reflected wave is either in phase with the incident wave (Z 2 >Z 1 ) or π radians out of phase (Z 1 > Z 2 ). For an imperfect interface between two media with the same acoustic impedance, Z 1 = Z 2 = Z [5]: iω R(ω) = 1 + iω, (2) Fig. 5 (a) Magnitude and (b) phase angle of reflection coefficient, R(ω), for an imperfect interface, calculated using spring model (2)and (3) for an interface between similar materials with acoustic impedance, Z = 27.3 MRayls, which is a typical value for a titanium alloy where is the characteristic frequency: = 2K Z. (3) Figure 5 shows the magnitude and phase of the reflection coefficient for an imperfect interface with various interfacial stiffnesses, K,between two pieces of material with the same acoustic impedance. As the magnitude of the reflection coefficient increases with frequency towards unity, the phase tends towards π radians. When ω, the magnitude is linearly proportional to frequency and the phase is π/2 radians. For an imperfect interface between two media with different acoustic impedances, if the component of the reflection coefficient, R bond, due to the flaw, R bond,flaw,issmall relative to the component due to the acoustic impedance mismatch, R bond,imp, detection using the magnitude of the reflection coefficient becomes difficult [12, 26, 29]. However, for the regime ω there is a π/2 radian separation in phase between R bond,imp and R bond,flaw. It may therefore be possible to separate well bonded and partially bonded titanium samples by also measuring the phase of the reflection coefficient.

4 228 J Nondestruct Eval (2011) 30: Fig. 6 Vector decomposition for complex reflection coefficients, R 12 and R 21, at a single frequency ω for an imperfect interface where Z 1 >Z 2 (a) with components due to acoustic impedance, R imp,the flaw, R flaw, and backscattered noise, R noise.(b) Spatially averaged signal with components due to acoustic impedance, R imp,andtheflaw, R flaw. The backscattered noise has cancelled Figure 6 shows a schematic of the components of the reflection coefficient, R bond, for an imperfect interface at one frequency in the regime ω. If a normal incidence pulse-echo inspection is possible from both sides of the diffusion bond, then two reflection coefficients can be obtained: R 12 and R 21. Figure 6a illustrates the scenario for one position on the diffusion bond for the case where Z 1 >Z 2. For normal incidence inspection from one side of the diffusion bond, the component due to the impedance mismatch, R 12,imp,isπ radians out of phase with the incident wave. The phase is the same as that for a reference signal from a titanium-water interface. For inspection from the opposite side of the diffusion bond, the component due to impedance mismatch R 21,imp, is in phase with the incident wave. Therefore, relative to a reference signal from a titanium-water interface, Re(R 12 ) = R 12,imp and Re(R 21,imp ) = R 21,imp.Re(R 12 ) and Re(R 21 ) are expected to have the same magnitude but be opposite in sign i.e. the components due to the acoustic impedance mismatch exhibit odd symmetry for normal incidence inspection from opposite sides of the diffusion bond. The components due to the flaw, R 12,flaw and R 21,flaw, are both π/2 out of phase with the incident wave. Therefore, relative to a reference signal from a titanium-water interface, Im(R 12 ) = R 12,flaw and Im(R 21 ) = R 21,flaw.Im(R 12 ) and Im(R 21 ) are expected to have the same magnitude and the same sign i.e. the components due to the flaw exhibit even symmetry. For a real material and due to gating of the signal, there will also be a component due to backscattered noise, R noise, from the microstructure immediately before and after the diffusion bond. The phase is random and different for inspection from opposite sides of the diffusion bond. The phase of R noise varies with position and so R noise can be reduced by spatial averaging. The notation denotes a spatial average here. Figure 6b shows the spatially averaged signal; only the components due to the acoustic impedance mismatch, R imp, and due to the flaw, R flaw, remain. 1.3 Magnitude and True Phase of the Reflection Coefficient The magnitude H(t w ; ω) and phase spectrum ϕ(t w ; ω) of a signal h(t) can be extracted from the Fourier transform, H : H(t w ; ω) e iω(t w;ω) = tw +T w /2 t w T w /2 w(t t w )h(t)e iω(t t w) dt, (4) where w is a windowing function and t w indicates the centre of the window relative to an absolute time scale, t, which is started at the excitation pulse. T w is the width of the window. If the window is rectangular and long such that it does not distort the waveform, the phase, ϕ, at a given angular frequency, ω, will depend upon the arrival time of the pulse relative to the window centre, t w. Figure 7a shows a broadband pulse with 12 MHz centre frequency, which has been shifted twice in 0.02 µs steps in software. The magnitude spectra are the same for all three signals. The phase spectra are shown in Fig. 7b. The phase at the centre frequency, f 0, changes depending upon the position of the signal relative to the centre of the window. Pilant et al. showed that, if a line is fitted through the frequency dependent phase spectrum over a frequency range around the centre frequency of the broadband pulse, ω 0, and the line is extrapolated to zero, as shown in Fig. 7b, the phase at the zero-crossing is independent of the arrival time of the wave [30]. Instanes et al. termed this the true phase, ϕ true [31]: ϕ = ϕ true + βω. (5) β is the slope of the best-fit line and is directly proportional to the time lag between the half-energy point of the bandlimited pulse and the window centre. If the windowing function distorts the pulse then it will affect ϕ(t w ; ω) and also ϕ true [31]. The experimental set-up used for the measurement of the magnitude, R bond, and phase, ϕ bond, of the reflection coefficient for the diffusion bonded samples in this study is illustrated in Fig. 8a. The samples were ultrasonically scanned in

5 J Nondestruct Eval (2011) 30: Fig. 7 (a) Original signal is shifted forward in time by 0.02 µs twice to create two new signals. (b) Phase spectra for the three signals in (a). The phase angle, ϕ, depends upon the arrival time of the wave relative to the window centre, t w. A true phase, ϕ true, can be obtained that is independent of pulse arrival time was obtained using the same inspection parameters from a titanium-water interface at the same metal path as the diffusion bond, as illustrated in Fig. 8b. A window with finite length, T w, was used to isolate the diffusion bond signal, h bond (t), and the reference signal, h ref (t). Some noise backscattered from the microstructure immediately before and after the interface was therefore included. The error introduced in the magnitude and phase of the reflection coefficient is related to the relative amplitude of the interface signal and the backscattered noise [33]. The centre of the window, t w, was fixed relative to the front wall reflection using an interface gate. The arrival time of the diffusion bond signal can vary due to variations in the thickness of the block and due to crystallographic anisotropy [33]. For h ref (t), the signal to noise ratio is high and therefore a window significantly longer than the pulse length plus any variation in arrival time (T w = 1.2 µs) could be used. For h bond (t), the window length is a trade-off between a short window that would distort the reflection from the diffusion bond and a long window, which would increase the component due to backscattered noise. T w = 0.48 µs was used. The frequency range, f, that corresponds to a 1 db drop in H ref (f ) either side of the centre frequency was determined. The average magnitude of the frequency spectra, H ref and H bond were determined over the same frequency range, f. The magnitude of the reflection coefficient is then: R bond = H bond H ref. (6) Fig. 8 Experimental set-up to capture (a) reflection from diffusion bond, h bond (t) (b) reflection from back wall of reference block, h ref (t) pulse-echo immersion using a 10.9 MHz centre frequency, 160 mm focal length and 19 mm diameter probe, with the probe axis normal to the diffusion bond plane and the beam focused at the diffusion bond depth (water path = 79 mm). Full waveform data sampled at 250 MS/s was captured. In order to determine the magnitude and true phase of the reflection coefficient, R bond, the magnitude and the true phase of the signal from the diffusion bond was determined relative to those of a reference signal. The reference signal To find the true phase of the reference signal, ϕ ref, a straight line was fitted to the phase spectrum, ϕ ref (f ), across f and extrapolated to zero frequency. ϕ ref will not be π radians, as would be expected from (1) when Z 1 >Z 2, since the system (filters, amplifiers, transducers, etc.) has a frequency dependent phase delay [31]. To find the true phase of the diffusion bond signal, ϕ bond, a straight line was fitted to the phase spectrum, ϕ bond (f ), across f and extrapolated to zero frequency. The true phase of the diffusion bond reflection signal, ϕ bond, is then corrected as follows: ϕ bond = ϕ bond ϕ ref + π (7) so that a back wall reflection has a true phase angle of π radians. In the next section of this paper, it is shown that the reference true phase, ϕ ref, also depends upon beam focusing and upon the microtexture of the titanium sample through which it has propagated.

6 230 J Nondestruct Eval (2011) 30: Fig. 9 Propagation of a focused beam in (a) a homogeneous nickel block and (b) a Ti 6Al 4V block with inhomogeneous microscopic texture 2 Factors Affecting Magnitude and True Phase of the Reference Signal A nickel block and a Ti 6Al 4V block both with thickness 19 mm were ultrasonically inspected in pulse-echo, as showninfig.9. The ultrasonic probe described in Sect. 1.3 was used. A C-scan was carried out for a mm area with a scan pitch of 0.25 mm in both lateral directions. The Ti 6Al 4V block was cut from a forged segment. The stock nickel was manufactured by hot isostatic press from powder and so the sample has a fine and homogeneous microstructure. At each scan position, the magnitude, H, and true phase, ϕ true, of the signal reflected from the back wall of the block were determined, as described in Sect This was done for a range of water paths (distance between transducer element and the front wall of the block), so that the focal depth of the ultrasonic beam in the block was varied. The same window length was used for all water paths; T w = 1.2 µs. The true phase of the back wall reflection averaged across the scanned area is plotted against water path in Fig. 10a. The mean true phase varies with water path for both the titanium and the nickel block. When the back wall of the block intersects the nearfield of the probe (water paths <79 mm) where the beam is formed by constructive and destructive interference the mean true phase fluctuates erratically. When the back wall of the block intersects the farfield of the probe (water paths >79 mm) the mean true phase changes steadily. The nearfield-farfield transition or N point [6]was determined by finding the maximum amplitude reflection from a ball target along the central beam of the transducer. This change in mean true phase with increasing distance from the focal plane is attributed to wavefront curvature. The true phase of the received signal will be that of each ray arriving back at the probe, integrated over the area of the element. At different water paths the back wall of the blocks Fig. 10 (a) Mean and (b) standard deviation in true phase angle (radians) calculated over scanned area against water path between probe face and front wall of block for Ti 6Al 4V and nickel block. The true phase angle, ϕ true, is found by fitting a straight line over the frequency range, f, and finding ϕ (f = 0 MHz). f is the frequency range corresponding to a 1 db decrease in the magnitude of the frequency spectrum. The focal plane for the Ti 6Al 4V block is 79 mm intersects a different plane of the ultrasonic beam, as shown in Fig. 9a, and so the measured phase changes. The standard deviation in true phase against water path for both blocks is plotted in Fig. 10b. For both blocks the standard deviation is lowest at the focal plane. It increases quickly in the nearfield (water path <79 mm) and slower in the farfield (water path >79 mm). The standard deviation for the Ti 6Al 4V block is significantly higher than for the nickel alloy block at all water paths. In the Ti 6Al 4V block the microtexture of the material causes distortion of the propagating wavefront, as illustrated in Fig. 9b and indicated by the variation in the amplitude [32, 33] and the arrival time of the back wall echo [33]. The phase of the ultrasonic rays arriving back at the transducer depends upon the volume of microtexture that the beam has passed through and so the position of the probe over the block. In summary, wavefront curvature in focused beams and wavefront distortion for propagation through crystallographically anisotropic materials are both thought to affect the measured value of true phase.

7 J Nondestruct Eval (2011) 30: Table 1 Combination of blanks cut from forged (FORG ) Ti 6Al 4V used to make diffusion bonded samples #1 #13 Well bonded Partially bonded Sample# FORG FORG Fig. 11 Longitudinal wave velocity of forged reference samples, FORG01-09, in through-thickness direction. Acoustic impedance in through-thickness direction, Z = ρc,where ρ is the densityof the samples (4410 kg/m 3 )andc is the longitudinal wave velocity (m/s) The diffusion bonded samples described in the next section were generated by joining blanks cut at nine radial positions (FORG01-09) from segments of forged Ti 6Al 4V (see Table 1). Blanks cut from the same radial position in the forged segments were used as reference blocks. It was assumed that the microtexture, and therefore the attenuation and ultrasonic backscatter, for blocks cut from the same radial position in a forging is similar. However, this is not necessarily correct; the microstructure produced in forgings is often banded; different quadrants of the forging have different levels of backscattered ultrasonic noise [34]. The longitudinal wave velocity in the through-thickness direction was measured using a 0.25 diameter contact probe with nominally 10 MHz centre frequency for each block and is plotted in Fig. 11. The time of flight was calculated by measuring time between positive maxima of 1st and 2nd backwall reflections. Measurement was made in 5 different positions and an average was taken. The standard deviation in these values is plotted on the graph. The mean and standard deviation of the true phase across the scanned area are plotted for each block in Fig. 12 forawaterpath of 79 mm. The standard deviation in true phase is higher for blocks FORG03-06 than for the others. This is thought to be related to the various microtextures of the blocks [33], however more work is required to confirm this. The reference true phase therefore varies with location. To find the magnitude, R bond and the true phase, ϕ ref,of the reflection coefficient for the diffusion bonded samples, a spatially averaged magnitude, H ref was calculated for Fig. 12 Mean true phase angle of back wall of forged reference samples, FORG01-09, across the scanned area. Error bars show one standard deviation above and below the mean each of the blocks FORG01-09 and was substituted into (6). Similarly, the spatially averaged true phase angle, plotted in Fig. 12, was used as the reference true phase, ϕ ref. 3 Magnitude and True Phase of Reflection Coefficient for Diffusion Bonded Samples 3.1 Manufacture of Diffusion Bonded Samples The diffusion bonded samples were made by joining two mm Ti 6Al 4V blanks. The mm faces of the blanks were ground to a finish of 0.62 µm Ra. Gas was evacuated from the interface and the samples underwent a hot isostatic press with parameters selected to achieve a good weld. Samples #1 #9 were generated using this process. To generate partial bonds, the surface roughness of the samples was altered. Samples #10 and #11 were generated by joining Ti 6Al 4V blanks that had been scratched randomly following the grinding process. Samples #12 and #13 were generated by joining Ti 6Al 4V blanks that had only been ground to a nominal finish of 1.6 µm Ra prior to joining. 3.2 Ultrasonic Inspection and Cut-up A30 20 mm area of each of the diffusion bonded samples was ultrasonically scanned in pulse-echo with the probe focused at the diffusion bond depth (water path = 79 mm), as

8 232 J Nondestruct Eval (2011) 30: Fig. 14 Typical micrograph at 200 magnification of partiallyvoided sample #12 Fig. 13 Maximum magnitude of the reflection coefficient across entire ultrasonic scan for both well-bonded (#1 #9) and voided samples (#10 #13) described in Sect The samples were scanned from both sides to obtain two reflection coefficients, R 12 and R 21. The magnitude of the diffusion bond reflection coefficient R bond and the true phase ϕ bond were calculated at each scan position, using (6) and (7) respectively, and combined to find the complex reflection coefficient R bond = R bond exp(iϕ bond ). Finally, the complex reflection coefficient was spatially averaged over the scanned area for samples #1 #13 in order to reduce the contribution of the backscattered noise. The maximum magnitude of the reflection coefficient across the scanned area, R bond, for inspection from each side of the sample is plotted for all samples in Fig. 13. The difference in the measured reflection coefficient from either side of the sample, R 12 and R 21, is due to differences in the apparent attenuation of the signal and error in the measurement system. Following ultrasonic inspection, samples #1 #9 were sectioned normal to the diffusion bond plane and polished such that the polished face intersected the position of the highest amplitude reflection on the ultrasonic C-scan. The diffusion bond line was metallurgically examined under a binocular microscope at 200 magnification. No voids were observed. Samples #12 and #13 can be easily separated from the well bonded samples #1 #9 using the magnitude of the reflection coefficient, R bond. These samples were sectioned at one plane perpendicular to the bond line. A typical micrograph is shown in Fig. 14. Isolated voids were distributed along the bond line, separated by well-bonded regions. For samples #12 and #13, images were taken at 200 magnification under a binocular microscope at 2 mm intervals along the bond line. The mean void length and the standard deviation for each of the samples #12 and #13 are listed in Table 2. Samples #10 and #11 were sectioned perpendicular to the diffusion bond plane and then polished incrementally with 2 mm steps. 9 sections were examined on each sample. In sample #10, voids were observed ranging from µm in length on 7 out of 9 sections. In sample #11, voids were observed that ranged from µm in length, also on 7 out of 9 sections. Samples #10 and #11 were defective. However, as shown in Fig. 13, these two samples cannot be separated from the well-bonded samples #1 #9 using the maximum amplitude of the reflection coefficient, R bond,at the centre frequency of the probe. 3.3 The Magnitude of the Reflection Coefficient for Detection of Partial Bonds The interface model described by (1) predicts that for an ideal interface the reflection coefficient will be independent of frequency but that for an imperfect interface the magnitude of the reflection coefficient will increase with frequency (see Fig. 5a). For each sample, the magnitude of the reflection coefficient, R bond, was averaged over 1 MHz frequency ranges from 7 8 MHz, then 8 9 MHz etc., increasing to MHz. These frequencies cover the working bandwidth of the probe. For each frequency range, the magnitude of the reflection coefficient was calculated at every scan position. The peak strength of the interface signal S was defined as the maximum value of R bond across the scanned area. Then, over each of the eleven selected frequency bands, the signal to noise ratio for the ith specimen was obtained as SNR i = S i /S 1. Sample #1 was chosen arbitrarily from the well bonded samples to represent the level of inherent material noise. The same trends in SNR are also observed if any of the other well bonded samples is used as a reference. The signal to noise ratio (SNR) against frequency is plotted for each sample in Fig. 15. The defective samples (#10 #13) have clear frequency dependence while the well bonded samples (#1 #9) appear flatter across all frequencies, as predicted by (1). Below 13 MHz the SNR is <1 for both samples #10 and #11. These results confirm that better separation between partially bonded and well bonded samples can be achieved by moving to a higher frequency ultrasonic inspection; with increasing frequency the spatial resolution improves and, also, the magnitude of the component of the reflection coefficient due to the defect increases while the magnitude of the component due to the change in acoustic impedance at the interface remains the same. Figure 15 also suggests that the rate of change of R bond with frequency can be used to assess the quality of diffusion bonds. Jamieson had only limited success relating R bond / ω to bond quality in copper beryllium diffusion

9 J Nondestruct Eval (2011) 30: Table 2 Mean and standard deviation in void length for sample #12 and sample #13 Sample # Mean void length (µm) Standard deviation in void length (µm) Fig. 15 Signal to noise ratio (defined as maximum absolute reflection coefficient for frequency range across scanned area at each relative to the same value for sample #1) against frequency range bonds [26]. More work is required, particularly on samples containing low percentage voiding where the contribution of backscatter from the bulk material will be comparable to that of the defect. 3.4 Magnitude and True Phase of the Reflection Coefficient for Detection of Partial Bonds The interface model described by (1) predicts that, in the regime ω, the component of the reflection due to acoustic impedance mismatch at an interface will either be in phase with the incident wave or π radians out of phase. However, for an imperfect interface the reflection coefficient will always be π/2 radians out of phase. For an ultrasonic pulse with centre frequency of 10.9 MHz, this corresponds to interfacial stiffnesses in the order of N/m and above (see Fig. 5). Voids observed in the partially bonded samples #10 #13 were in the order of tens of microns long (Table 2), which is much less than the acoustic wavelength in titanium at the centre frequency of the probe used ( 600 µm). We therefore assumed that we were working in this long wavelength regime for the partially bonded samples and that the phase could be used to discriminate good and partial bonds. Unlike the separation in magnitude, the separation in phase does not decrease as the frequency is decreased. Therefore, measurement of the phase could form the basis for a low frequency technique, which could be applied for inspections at greater metal paths. Using the convention illustrated in Fig. 6b, the component of the bond line reflection coefficient due to a change in acoustic impedance at the interface is expected to be real for both well-bonded and partially bonded samples. For inspection from opposite sides of the diffusion bond, the real parts of the spatially averaged reflection coefficient, Fig. 16 Real component of spatially averaged complex reflection coefficient for both well-bonded (#1 #9) and voided samples (#10 #13). The samples were scanned from each side to obtain R 12 and R 21 Re(R 12 ) and Re(R 21 ) are expected to exhibit odd symmetry i.e. have the same magnitude but be opposite in sign. Re(R 12 ) and Re(R 21 ) are plotted in Fig. 16 for samples #1 #13. For samples #1 #9, which are thought to be well bonded, and samples #10 and #11, which have low percentage voiding, Re(R 12 ) and Re(R 21 ) exhibit odd symmetry, as expected. Re(R 12 ) and Re(R 21 ) for samples #12 and #13 are, however, both positive. For both these samples, the imaginary components Im(R 12 ) and Im(R 21 ) are larger than the real components Re(R 12 ) and Re(R 21 ) (see Fig. 17), due to the dominance of the response from the flaw. Thus a relatively small systematic error in the phase measurement could cause this result. Assuming that (1) is applicable to these distributed microvoids, that ω and using the convention illustrated in Fig. 6b, the component of the bond line reflection coefficient due to flaws is expected to be imaginary for partially bonded samples and zero for well-bonded samples. For inspection from opposite sides of the diffusion bond the imaginary parts of the spatially averaged reflection coefficient, Im(R 12 ) and Im(R 21 ), are expected to be similar in mag-

10 234 J Nondestruct Eval (2011) 30: Fig. 17 Imaginary component of spatially averaged complex reflection coefficient for both well-bonded (#1 #9) and voided samples (#10 #13). The samples were scanned from each side to obtain R 12 and R 21 Fig. 18 (a) Real component of spatially averaged symmetric reflection coefficient for both well-bonded (#1 #9) and voided samples (#10 #13). The samples were scanned from each side to obtain R 12 and R 21 nitude and both negative. Im(R 12 ) and Im(R 21 ) are plotted in Fig. 17 for all samples. For partially bonded samples #10 #13, Im(R 12 ) and Im(R 21 ) are similar in magnitude and both negative as expected. Im(R 12 ) and Im(R 21 ), for the well-bonded samples #1 #9 is expected to be zero, as the backscattered noise should cancel. However, the imaginary component for the well-bonded samples is non-zero. For sample #4, Im(R 21 ) is lower than the imaginary component for samples #10 and #11. The outcome is that, while the results for the partially bonded samples fit with the theory, the imaginary component of the spatially averaged reflection coefficient cannot be used to separate the well bonded samples from the partially bonded samples as had been hoped. The difference between theory and the experimental results suggests that either some of the well-bonded samples are defective or that there is error in the calculated magnitude or phase of the reflection coefficient. Possible sources or error include: 1. Differences between the through-thickness acoustic velocity of the diffusion bonded blank and the reference block. As discussed in Sect. 2, for a focused beam the true phase for an interface depends upon the position of the interface along the beam axis due to wavefront curvature. 2. The effect of wavefront distortion on the measured amplitude. The amplitude of the back wall reflection for the Ti 6Al 4V reference blocks was observed to change with scan position [33]. Therefore the spatially averaged reference amplitude, H ref, used in the calculation of the reflection coefficient is not correct for every scan position. 3. The effect of wavefront distortion during propagation on the measured true phase. The true phase of the back wall reflection for the reference blocks was observed to change with scan position particularly for anisotropic Ti 6Al 4V (see Fig. 12). Therefore the spatially averaged reference true phase, ϕ ref, used in the calculation of the reflection coefficient is not correct for every scan position. 4. The contribution of backscattered noise to the measured magnitude, H bond, and true phase of the signal, ϕ bond. The error is related to the relative amplitude of the interface signal to the backscattered noise [33]. More work is required to understand the error introduced by these various factors. If these errors could be reduced then a low frequency one sided inspection, which uses the imaginary component of the complex reflection coefficient to differentiate between well-bonded and partially bonded samples, could be possible. It is likely that these factors would have less effect in the inspection of solid-state welds between materials where the microtexture is not as dominant as in Ti 6Al 4V. 3.5 Symmetric Reflection Technique Nagy and Adler [12] suggested the use of the symmetric reflection coefficient, R s, for the inspection of welds between dissimilar materials. From (1), the symmetric reflection coefficient is: R s (ω) = R 12 + R 21 2 iω Z = 1 +Z 2 ( Z 1Z 2 K ) 1 + iω (8) ). Z 1 +Z 2 ( Z 1Z 2 K In Sect. 3.3, it was observed that the real components of the spatially averaged reflection coefficients for inspection from opposite sides of the diffusion bond exhibit odd symmetry (equal in magnitude and opposite in sign) for 11 of the 13 samples. For the well-bonded samples, there was also odd symmetry in the imaginary component of the spatially averaged reflection coefficient. In the symmetric reflection coefficient, these components cancel out. In this section, the real and imaginary components of the spatially averaged symmetric reflection coefficient are calculated for each of the forged diffusion bonded samples #1 #13. In order to calculate the symmetric reflection coefficient, the same region of the diffusion bond must be inspected from both sides and the complex reflection coefficients for

11 J Nondestruct Eval (2011) 30: Fig. 19 (a) Imaginary component of spatially averaged symmetric reflection coefficient for both well-bonded (#1 #9) and voided samples (#10 #13). The samples were scanned from each side to obtain R 12 and R 21 each point summed. An image correlation method was used to ensure that the reflection coefficient was calculated over an identical area of the diffusion bond for scans from both sides and to align the points [33]. The real component of the spatially averaged symmetric reflection coefficient Re(R s ) is plotted in Fig. 18. Re(R s ) is near zero for samples #1 #11, as predicted. More work is required to understand the non-zero value of Re(R s ) for samples #12 and #13. The imaginary component of the spatially averaged symmetric reflection coefficient, Im(R s ), is plotted in Fig. 19. There is now good separation between the well-bonded samples and all of the partially bonded samples. 4 Conclusion By testing diffusion bonded blocks of forged Ti 6Al 4V, it was shown that the interface created between macrozones acts as a weak reflector that can limit the sensitivity of the ultrasonic inspection to partial bonding (sub-wavelength voids distributed across the bond line). Higher frequencies were shown to give better separation between well-bonded and partially bonded samples, or between the component of the reflection due to the interface and the component due to the flaws. A simple interfacial spring model was used to predict that there would be π/2 radians separation in phase between the component of the reflection coefficient due to the interface and the component due to the flaw, for partially bonded samples inspected at low frequencies. The true phase of the signal was measured. The measured value was shown to depend upon wavefront curvature, due to beam focusing, and wavefront distortion, due to microtexture within the material. Separation between well-bonded samples and samples containing even low percentage voiding was achieved using the symmetric reflection technique where the reflection coefficient was calculated for normal incidence from both sides of the diffusion bond. Separation between wellbonded and partially bonded samples was not possible using the reflection coefficient for normal incidence from only one side of the diffusion bond; the microtexture of Ti 6Al 4V resulted in significant error in the measured reflection coefficient. If the errors in the single sided technique could be overcome it would become attractive, allowing diffusion bond inspection at lower ultrasonic frequencies and thus at deeper metal paths. The final application drove the choice of Ti 6Al 4V as a material during this investigation. 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