Vij D.R. Handbook of Applied Solid State Spectroscopy

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8. Resonance Acoustic Spectroscopy

This study shows that RAS is potentially capable of detecting the cladding

delamination in a clad rod. It also demonstrates how the spring model can be

used for evaluating the quality of the material bond.

Figure 8.22 Form function of the Epon -815-clad steel rod after breaking the bond at the core-

cladding interface. a) Experimentally measured, b) Numerically calculated with

2.3 10

KK u N/m

[75].

8.5.6 Characterization of Cladding Delamination

This section demonstrates how RAS can detect incipient cladding damage on

a clad rod in an on-line system [75]. A piece of a copper-clad aluminum rod

b) Numerically calculated [75].

Figure 8.21 Form function of the Epon-815-clad steel rod. a) Experimentally measured.

388

on which separation of the cladding from the core had initiated was scanned

along its axis. At 1-cm intervals, the backscattered echoes from the rod were

measured and their corresponding form functions were evaluated. Figure 8.23

shows the image obtained by plotting these measured form functions as a

function of position of the probe along the rod axis. Grey color intensity on

the image indicates the relative amplitude of the form function. Darker areas

have lower amplitude compared to the lighter areas. The dark horizontal strips

on the figure represent resonance dips on the form function.

For a good sample, these horizontal strips must be straight and uniform

along the rod, i.e., the resonance frequencies should be the same at all axial

positions. When a defect appears on the sample, some of these dark horizontal

strips become distorted, hence indicating the existence of a problem.

Delamination of the cladding starts at approximately the 11-cm position on

the horizontal axis where a noticeable shift in the dark strip at approximately

530 kHz is observed. This clearly indicates that damage in a clad rod can be

detected by monitoring the variations of the form function along the rod

during the manufacturing process.

Figure 8.23 Scanned image of a copper-clad aluminum rod on which the delamination of the

cladding has initiated [75].

8.5 Experimental and Numerical Results

389

8. Resonance Acoustic Spectroscopy

Clad Rods by RAS

The applicability of RAS to the NDE of explosively welded clad rods is

investigated in this section [86]. The focus is on copper-clad aluminum rods

used as electrical conductors in high current applications. Any breakdown of

the core/cladding interface may lead to hot spots, accelerated material

degradation, or complete failure of the conductor. These clad rods are

manufactured by explosive welding. Explosive welding is a solid-phase

joining technique in which two or more metal components are driven together

by a controlled explosion to form a very strong metallurgical bond [87, 88].

One of the limitations of traditional applications of resonance acoustic

spectroscopy is the assumption of a perfect bond (continuity of all stress and

displacement components) at material interfaces. This runs contrary to the

experimental observation that a poor explosively welded specimen may

feature bond discontinuities or the presence of interfacial contaminants

consisting of bimetallic compounds.

8.5.7.1 Mathematical Model of the Interface

For the copper-clad aluminum rods, the interfacial transition zones are not

always very sharp; they have finite mass and thickness, and their features

must be included in the mathematical model to achieve an accurate result.

The thickness of the interlayer is still significantly smaller than one

wavelength, such that the two surfaces of the interlayer move approximately

in phase with each other when ultrasonic waves strike the cylinder. Under

these circumstances, a spring-mass system is an appropriate first-order

approximation for representing the thin interfacial layer. Thus, each rod is

modeled as a two-layered cylinder with a spring-mass system to represent a

thin interfacial layer containing the weld. At the core/cladding interface

br , the boundary conditions are [76]

1 ș 2 ș

ș 2ș 1ș

1ș 2ș

2 ș 1 ș

(ıı)

(),

()

ıı Ȧ ,

(ıı)

(),

()

ıı Ȧ ,

rr rr

rr r

rr rr

Ku u







 







 

(8.102)

390

8.5.7 Nondestructive Evaluation (NDE) of Explosively Welded

where m is mass per unit area at the interface, and

K and

K are the

boundary stiffness constants. When

șr

KK f and 0om the boundary

conditions correspond to a perfect bond with a vanishingly thin transition

layer. The opposite extreme of

KK corresponds to total debonding.

By applying the boundary conditions and taking the definition of form

function defined in Section 3, the scattered pressure field can be evaluated.

Details of the mathematical model can be found in [86].

8.5.7.2 Experimental Specimens

The explosive welding process can be described with the aid of the diagram

shown in Figure 8.24. A copper tube is located concentrically around the

aluminum core, the bore of the tube is so dimensioned that a small annular

standoff gap exists between the

two surfaces which are to be bonded. A plastic

tube is located concentrically around the cylindrical components. Its diameter

is carefully selected such that there remains a further annular gap into which

explosive powder is poured. A detonator initiates the explosion at one end of

the tube.

Figure 8.24 Arrangement for explosive welding of an aluminum core and a copper sleeve (all

dimensions in mm) [86].

The detonator initiates the powder explosive and provides a detonation

front. This travels down the length of the assembly and progressively swages

the copper tube down upon the outer surface of the aluminum core. The

explosion velocity,

Ȟ , is controlled by the addition of a suitable inert

diluting agent to the selected explosive powder. During the interval of time

that any point A of the tube is traveling inward over the gap at a velocity

to collide at the collision front, the detonation front will have moved on to

reach a point B (see Figure 8.24). Thus, the copper tube collides at an angle E

with the aluminum core. As can be deduced from the diagram, the tangent of

the angle E is . It is this angle that controls the topography of the

8.5 Experimental and Numerical Results

391

Ȟ /Ȟ

8. Resonance Acoustic Spectroscopy

interface. From the relationship

tanȕȞ/Ȟ , it can be seen that a high

detonation velocity will give a relatively large value of angle E, thereby

creating a strongly turbulent system of solid waves at the aluminum-copper

interface. Such waves have low pressure zones at the vortices that promote the

generation of highly brittle copper-aluminum compounds. In general, it is

desirable to dilute the explosive sufficiently to promote a slower explosion

propagation velocity, yielding gently undulating waves or even a flat

interface. However, excessive dilution of the explosive gives rise to frequent

misfires; therefore, a practical limit to the dilution is imposed. Consequently,

it is frequently found that the bond will be characterized by a wavy interface

of some form. The pattern of these solid waves or interfacial oscillations

provides the key to a nondestructive evaluation system for estimating

interfacial integrity on the basis of the wave topography and the associated

levels of intermetallics that can be expected. In this paper Ying et al. [86]

manufactured four copper-clad aluminum rods by explosive welding. The

sleeves were made of 99% pure copper and the core material was aluminum

6061. Initial dimensions of the Al core and Cu sleeves are shown in Figure

8.24. The detonation velocity

Ȟ was varied among the four specimens by

appropriate dilution of the explosive mixture. For samples #1– #4, the

concentration of the active explosive ingredient were 20%, 30%, 40%, and

50%, respectively. For sample #1, the value for

Ȟ was estimated at

approximately 20 mm/s.

Figure 8.25 shows (r, z)-planar cross-sections of the welds, which illustrate

the intermetallic content associated with vorticity in the waves. Figure 8.25a

features the specimen with the lowest detonation velocity, and

correspondingly the highest value of E. Consequently, the interface is the

most flat of the four samples and contains no intermetallics. By contrast,

sample #2 (Figure 8.25b) contains moderate amounts of these compounds,

while samples #3 and #4 (Figures 8.25c and 8.25d) show prominent waviness

in the weld profile and significant amounts of intermetallics associated with

the wave vortices. These intermetallics contain microcracks due to their

brittleness and the effects of rapid cooling through the dissipation of heat

from the weld to the surrounding metal mass in the immediate post-bonding

period. A highly magnified image of this phenomenon is shown in Figure

8.26. Shear stresses may also arise from the welding process, due to a

differential in the elastic recovery of the two metals; this effect also

contributes to cracking. In extreme cases, the combined effects of these two

factors in the immediate post-bonding period can entirely destroy the bond.

8.25d can also lead to problems should any fabrication process be imposed

upon the welded specimen, such as drawing down of the rod to produce

smaller diameters.

392

The presence of intermetallics in the amounts seen in Figures 8.25c and

Figure 8.25 SEM results showing a cross-section of the welded area of explosively welded

specimens: (a) sample #1 (20% explosive mixture); (b) sample #2 (30% explosive mixture); (c)

sample #3 (40% explosive mixture); (d) sample #4 (50% explosive mixture). In (b), (c), and

(d), intermetallic regions appear as semi-shaded gray areas between the bulk copper and

aluminum [86].

Figure 8.26 SEM result showing a magnified cross-section of the welded area of sample #4

(50% explosive mixture). Cracks can be seen clearly within the intermetallic region [86].

8.5 Experimental and Numerical Results

393

8. Resonance Acoustic Spectroscopy

8.5.7.3 Resonance Acoustic Spectroscopy Results

The RAS form functions are shown in Figure 8.27 [86]. It was found that the

form function showed minimal variation along the axis of each individual rod.

Also shown in Figure 8.27 are the results of the numerical calculations of the

and

K . Their

values are

Figure 8.27 Calculated and measured form functions, (a), (b), (c), and (d) for samples #1, #2,

#3, and #4, respectively, the solid lines for calculated and dotted lines for measured [86].

394

form functions. The numerical solutions required parameters char

cterizing the interfacial region as inputs, namely, values of the interphase

thickness t and interfacial spring constants

given in Table 8.4.

Table 8.4 Spring constants and average interlayer thickness for each specimen [86].

Sample #

Average thickness

from SEM (m)

Thickness used

for numerical

simulation (m)

Longitudinal spring

constant per unit

area K

(N/m

)

Shear spring constant per

unit area K

(N/m

)

No intermetallics

0 thickness

32±7

60±15

80±18

6.5E16

6.5E15

1.0E15

5.0E14

2.5E16

2.5E15

4.0E14

2.0E14

They were selected for each rod by an iterative process to achieve the best

possible match between resonance frequencies of numerical and experimental

results in the four graphs of Figure 8.27. Examination of these four graphs

(1) By suitable selection of the input parameters to the numerical algorithm,

excellent agreement was achieved between experimental and calculated

values of the resonant frequencies.

(2) The form function shown in Figure 8.27a corresponds to the specimen

manufactured at the lowest explosion propagation velocity. As seen in Figure

8.27a, no turbulence and intermetallic compounds are seen at this relatively

smooth interface. For this specimen, extremely large spring constants and

vanishingly small interphase thickness produced the best match between

numerical and experimental results.

(3) For the three clad rods manufactured at higher explosion speeds,

imperfections at the Cu–Al interface caused significant perturbations to the

form functions (Figure 8.27b–d). This is readily apparent by noting the

downshift in resonant frequencies, as compared to their values in Figure

8.27a. This downshift becomes increasingly apparent at higher values of

ka ,

where the thickness of the interfacial region is of the same order as the

ultrasonic wavelength.

Relatively low values of interfacial spring constants were required in order

to achieve a good match between experimental and calculated resonant

frequencies in specimens 2, 3, and 4. In addition, the calculated thickness t of

the interlayer was larger than that for sample #1, as shown in Table 8.4.

8.5.8 Nondestructive Evaluation of Fiber-Reinforced

Composite Rods

Application of RAS to the NDE of cylindrical components made from

transversely isotropic materials is demonstrated in this section. Transverse

isotropy is strongly evident in rods and wires made from fiber-reinforced

composite materials. For such samples, the axial and transverse properties are

significantly different and, therefore, characterization of both sets of

properties is of interest.

8.5 Experimental and Numerical Results

395

revealed the following:

8. Resonance Acoustic Spectroscopy

RAS is able to characterize the sample in both axial and transverse

directions. This is because some of the resonances are highly sensitive to axial

properties of the cylinder while others are primarily sensitive to transverse

properties. Rayleigh and whispering gallery waves are mostly dependent on

the transverse properties, while guided waves show high sensitivity to the

axial properties of the cylinder. Figure 8.28 shows the effect of a 5% increase

in the Young's modulus E

of a continuous fiber aluminum matrix composite

(CF-AMC) rod with the following elastic properties (the G

and G

are shear

modulus values):

11 22 33

13 23 12 31

E E 130 GPa, E 309 GPa

GG50GPa, Ȟ 0.36, Ȟ 0.20,

where direction 3 is along the axis and directions 1 and 2 are in the transverse

plane. The matrix of this composite material is aluminum and the reinforcing

fibers are Nextel

™

610 Ceramic Fiber. Nextel

™

610 Ceramic Fiber is a high

purity (above 99%) fine grain alumina fiber with high strength (2.7–3.4 GPa)

In Figure 8.28, the letters R, W, and G designate the resonance modes

associated with Rayleigh, whispering gallery and guided waves, respectively.

From Figure 8.28 it is clear that a 5% increase in E

has primarily affected

the R and W resonances, while resonances associated with guided waves G

have remained almost unchanged. Figure 8.29 shows the effect of a 5%

increase in the Young’s modulus E

and Figure 8.30 shows the effect of a 5%

increase in the shear modulus G

. These two elastic constants have a strong

influence on waves propagating along the axis and, therefore, it can be

observed that in these cases the G modes are most sensitive and R and W

modes remain almost unchanged. It is also noticed that the sensitivity of G

resonances to variations of E

is less than their sensitivity to G

. This is

because the guided waves are mostly of a shear type and, therefore, more

sensitive to variations of the shear modulus.

Figure 8.28 Solid line: Form function of the CF-AMC rod. Dashed line: 5% increase in

Young’s modulus in the transverse direction E

[75].

396

and high stiffness (400 GPa) [75].

Figure 8.29 Solid line: Form function of the CF-AMC rod. Dashed line: 5% increase in

Young’s modulus in the transverse direction E

[75].

Figure 8.30 Solid line: Form function of the CF-AMC rod. Dashed line: 5% increase in shear

modulus G

[75].

To show the practical applicability of the mathematical model in the case

of a transversely isotropic material, experimental results obtained from a CF-

AMC rod are presented here. The length of the rod was 300 mm, and its

surface was machined to a diameter of 1.52 mm. The density of the material

was measured to be

ȡ 3220 kg /m . The elements of the stiffness matrix

and the constants of equation (8.103) are related. The stiffness matrix for

the material was calculated to be [76]

8.5 Experimental and Numerical Results

397