ultrasonic measu rement of material properties

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Ultrasonic measurement of material properties

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Chapter 1. Introduction to UltrasonicTesting . . . . . . . . . . . . . . . . . . . . . 1

Part 1. Nondestructive Testing . . . . . 2Part 2. Management of Ultrasonic

Testing . . . . . . . . . . . . . . . 13Part 3. History of Ultrasonic

Testing . . . . . . . . . . . . . . . 24Part 4. Measurement Units for

Ultrasonic Testing . . . . . . 30References . . . . . . . . . . . . . . . . . . . . 33

Chapter 2. Ultrasonic WavePropagation . . . . . . . . . . . . . . . . 35

Part 1. Introduction to WavePropagation . . . . . . . . . . . 36

Part 2. Wave Propagation inIsotropic Materials . . . . . . 41

Part 3. Extensions to Other Typesof Surface Waves . . . . . . . 46

Part 4. Reflection at PlaneBoundary in Stress FreeMedia . . . . . . . . . . . . . . . . 52

References . . . . . . . . . . . . . . . . . . . . 57

Chapter 3. Generation and Detectionof Ultrasound . . . . . . . . . . . . . . . 61

Part 1. Piezoelectricity . . . . . . . . . . 60Part 2. Transduction . . . . . . . . . . . . 68Part 3. Generation and Reception

of Ultrasound . . . . . . . . . . 78Part 4. Phased Arrays . . . . . . . . . . . 90Part 5. Focused Beam Immersion

Techniques . . . . . . . . . . . . 95Part 6. Lamb Waves . . . . . . . . . . . 100Part 7. Ultrasonic Guided

Waves . . . . . . . . . . . . . . . 101Part 8. Optical Generation

and Detection ofUltrasound . . . . . . . . . . . 107

Part 9. Electromagnetic AcousticTransduction . . . . . . . . . 115

Part 10. Air CoupledTransducers . . . . . . . . . . . 129

References . . . . . . . . . . . . . . . . . . . 133

Chapter 4. Ultrasonic SignalProcessing . . . . . . . . . . . . . . . . .143

Part 1. Signal Acquisition andProcessing . . . . . . . . . . . . 144

Part 2. Ultrasonic Spectroscopy . . 156

Part 3. Recognition Principles inUltrasonic Testing . . . . . 164

References . . . . . . . . . . . . . . . . . . . 174

Chapter 5. Instrumentation forUltrasonic Testing . . . . . . . . . . . 177

Part 1. Scanning Approaches . . . . 178Part 2. Basic Send/Receive

Instrumentation . . . . . . . 182Part 3. Special Purpose Ultrasonic

Equipment . . . . . . . . . . . 191Part 4. Calibration . . . . . . . . . . . . 194References . . . . . . . . . . . . . . . . . . . 199

Chapter 6. Ultrasonic Pulse EchoContact Techniques . . . . . . . . . 201

Part 1. Straight Beam PulseEcho Tests . . . . . . . . . . . . 202

Part 2. Angle Beam ContactTesting . . . . . . . . . . . . . . 217

Part 3. Coupling Media forContact Tests . . . . . . . . . 221

Part 4. Imaging of Butt WeldPulse Echo Tests . . . . . . . 225

Part 5. Multiple-TransducerUltrasonic Techniques . . 229

Part 6. Phased Arrays . . . . . . . . . . 238Part 7. Moving Transducers . . . . . 250References . . . . . . . . . . . . . . . . . . . 253

Chapter 7. Ultrasonic Scanning . . . . . 261Part 1. Ultrasonic Coupling . . . . . 262Part 2. Ultrasonic Test

Techniques . . . . . . . . . . . 264Part 3. Immersion Coupling

Devices . . . . . . . . . . . . . . 267Part 4. Water Couplant

Characteristics . . . . . . . . 270Part 5. Pulse Echo Immersion

Test Parameters . . . . . . . . 271Part 6. Interpretation of

Immersion UltrasonicTest Indications . . . . . . . 274

Part 7. Immersion Testing ofComposite Materials . . . 284

Part 8. Angle Beam ImmersionTechniques . . . . . . . . . . . 289

Part 9. Focused Beam ImmersionTechniques . . . . . . . . . . . 296

Part 10. Acoustical Holography . . 300References . . . . . . . . . . . . . . . . . . . 302

ixUltrasonic Testing

C O N T E N T S

Chapter 8. Ultrasonic Characterizationof Material Properties . . . . . . . .305

Part 1. Fundamentals ofMaterial PropertyCharacterization . . . . . . . 306

Part 2. Material CharacterizationMethods . . . . . . . . . . . . . 308

Part 3. Measurement of ElasticProperties . . . . . . . . . . . . 319

Part 4. Microstructure and DiffuseDiscontinuities . . . . . . . . 324

Part 5. Ultrasonic Testing forMechanical Properties . . 331

Part 6. Acoustoultrasonic Tests forMechanical Properties . . 338

References . . . . . . . . . . . . . . . . . . . 343

Chapter 9. Ultrasonic Testing ofAdvanced Materials . . . . . . . . . 357

Part 1. Ultrasonic Testing ofAdvanced StructuralCeramics . . . . . . . . . . . . . 358

Part 2. Ultrasonic Testing ofAdhesive Bonds . . . . . . . 369

Part 3. Ultrasonic Tests ofComposite Laminates . . 380

References . . . . . . . . . . . . . . . . . . . 391

Chapter 10. Metals Applications ofUltrasonic Testing . . . . . . . . . . . 399

Part 1. Ultrasonic Tests of Steeland Wrought Alloys . . . . 400

Part 2. Ultrasonic Testing ofPrimary Aluminum . . . . 406

Part 3. Multiple-TransducerUltrasonic Techniques . . 418

References . . . . . . . . . . . . . . . . . . . 423

Chapter 11. Chemical and PetroleumApplications of UltrasonicTesting . . . . . . . . . . . . . . . . . . . 427

Part 1. Chemical and PetroleumIndustry . . . . . . . . . . . . . 428

Part 2. Ultrasonic Testing inProcessing Plants . . . . . . 432

Part 3. Storage Tanks . . . . . . . . . . 439Part 4. Petroleum Pipes . . . . . . . . 441Part 5. Inservice Ultrasonic

Testing of OffshoreStructures . . . . . . . . . . . . 444

References . . . . . . . . . . . . . . . . . . . 454

Chapter 12. Electric PowerApplications of UltrasonicTesting . . . . . . . . . . . . . . . . . . . 457

Part 1. Inservice Inspection inPower Plants . . . . . . . . . . 458

Part 2. Nuclear Power Plants . . . . 461Part 3. Fossil Power Plants . . . . . . 466References . . . . . . . . . . . . . . . . . . . 473

Chapter 13. InfrastructureApplications of UltrasonicTesting . . . . . . . . . . . . . . . . . . . 475

Part 1. Ultrasonic Testing of Woodand Structural Steel . . . . 476

Part 2. Ultrasonic Testing ofStructural Concrete . . . . 481

References . . . . . . . . . . . . . . . . . . . 488

Chapter 14. Aerospace Applicationsof Ultrasonic Testing . . . . . . . . . 493

Part 1. Overview of AerospaceApplications ofUltrasonic Testing . . . . . 494

Part 2. Aerospace MaterialProduction Inspection . . 499

Part 3. Inservice Inspection ofAircraft . . . . . . . . . . . . . . 507

Part 4. Ultrasonic Testing forSpace Systems andAeronautics . . . . . . . . . . . 516

References . . . . . . . . . . . . . . . . . . . 525

Chapter 15. Special Applications ofUltrasonic Testing . . . . . . . . . . . 529

Part 1. Reliability ofNondestructiveTesting . . . . . . . . . . . . . . 530

Part 2. Ultrasonic Testing inRailroad Industry . . . . . . 535

Part 3. Ultrasonic Testing inMarine Industry . . . . . . . 541

Part 4. Acoustic Microscopy . . . . . 544References . . . . . . . . . . . . . . . . . . . 549

Chapter 16. Ultrasonic TestingGlossary . . . . . . . . . . . . . . . . . . . 555

Part 1. Terms . . . . . . . . . . . . . . . . . 556Part 2. Symbols . . . . . . . . . . . . . . . 558References . . . . . . . . . . . . . . . . . . . 569

Index . . . . . . . . . . . . . . . . . . . . . . . . . 571

Figure Acknowledgments . . . . . . . . . . 588

x Ultrasonic Testing

Alex Vary, North Olmsted, Ohio

8C H A P T E R

UltrasonicCharacterization of

Material Properties1

To different degrees, elastic moduli,material microstructure, morphologicalconditions and associated mechanicalproperties can be characterized byultrasonic testing. Elastic moduli aredetermined by speed measurements.Material microstructure can becharacterized by speed and attenuationmeasurements. Ultrasonic assessments ofmechanical properties (strength ortoughness) are indirect and depend oneither theoretical inferences or empiricalcorrelations. Four categories of ultrasonicmaterials characterization are shown inTable 1: (1) measurements that determineelastic constants such as tensile, shear andbulk moduli, (2) microstructural andmorphological factors such as grain sizeand distribution, grain aspect ratio andtexture, (3) diffuse discontinuitypopulations such as microporosity ormicrocracking and (4) mechanicalproperties such as strength, hardness andtoughness. Mechanical properties areextrinsic and depend on elastic propertiesand material microstructure andmorphology. The directly measured

quantities are ultrasonic speed andattenuation.

Rationale for UsingUltrasonic TechniquesThe usual objective in nondestructivetesting is to detect and characterize avariety of discrete hidden discontinuitiesthat can impair the integrity and reducethe service life of a structure. Suchdiscontinuities include cracks in metals,delaminations in composites andinclusions in ceramics. Although astructure may be free of distinctidentifiable discontinuities, it may still besusceptible to failure because ofinadequate or degraded mechanicalproperties. This can arise from faultymaterial processing, over aging,degradation under aggressive serviceenvironments or from the other factorslisted in Table 2. Because of poormicrostructure and morphology, a solidmay lack strength, toughness or mayexhibit degraded resistance to impact,

306 Ultrasonic Testing

PART 1. Fundamentals of Material PropertyCharacterization

TABLE 1. Ultrasonic materials characterization categories dependent on physical andgeometric constraints given in Table 3.

Elastic Microstructure Diffuse MechanicalConstantsa and Morphologyb Discontinuityb Propertiesc

Tensile modulus Mean grain size Microcracking Tensile strengthShear modulus Grain size distribution Crazing Shear strengthFlexural modulus Grain aspect ratio Microporosity Interlaminar strengthBulk modulus Texture Inclusions Yield strengthYoung's modulus Anisotropy Aggregates DuctilityPoisson's ratio Density variations Precipitates HardnessLamé constant Dispersoid variations Fiber breakage Fracture toughness

Whisker/fiber bunching Segregations Fatigue resistanceand maldistribution Porosity Impact resistance

Shock damageImpact damageFatigue damageCreep damageFiber/matrix

interface voids

a. Well established speed relations and dynamic resonance relations for simple shapes and laboratory samples. Bothare comparative when applied to complex geometries.

b. Indirect; based on scatter attenuation and speed dispersion models and theories.c. Indirect; comparative and based primarily on empirical correlations with speed and attenuation

characteristics governed by microstructural and morphological factors.

fatigue or fracture. For these reasons, it isimportant to have nondestructivemethods for characterizing local or globalanomalies in microstructure ormorphology and their associatedmechanical property deficiencies.2-5

The best approach to reliabilityassurance combines nondestructivecharacterization of discontinuities withcharacterization of material environmentsin which the discontinuities reside.Assessments of structural integrity andservice life can be improved by providingmore complete information for fractureanalysis and life prediction. This approachis needed to assess the structural reliabilityand residual life of components made ofadvanced materials in systems thatdemand efficient performance underextreme operating conditions.6

Relation to MaterialsResearchIn materials research, the term materialscharacterization is conventionallyunderstood to involve some form ofdestructive testing. However,nondestructive techniques should be usedin materials research before and duringdestructive testing. This is especially thecase for complex materials such asadvanced polymeric, metallic and ceramicmatrix composites. Application ofultrasonic and other nondestructivemethods enhances materialscharacterization, understanding of failuremechanisms and explanation of behavior.

Relation to FractureAnalysisNondestructive testing is frequently basedon the need to detect criticaldiscontinuities with dimensions specifiedby fracture analysis. Fracture analysis andthe prediction of safe service life, in turn,depend on the assumption of an accurateset of mechanical properties. Fractureanalysis presupposes discontinuity growthin materials with known moduli, ultimatestrength, fracture toughness and fatigueand creep properties. Nondestructivemethods that verify and characterize theseproperties can be used to validate fractureanalyses and life predictions. Fractureanalysis and analytical life predictionmethods should be supplemented byultrasonics and other nondestructive testtechniques that can verify properties,structural integrity and reliability.7

Relation to StructuralMaterialsA survey of ultrasonic technology ispresented below to indicate potentialapplications for nondestructivecharacterization of mechanical propertiesin structural materials. Ultrasonictechniques are covered that can be usedto monitor extrinsic properties (tensile,shear and yield strengths, fracturetoughness, hardness and ductility), elasticmoduli and underlying microstructuraland morphological factors.

The emphasis is on nondestructivetesting of structural materials that arise inapplications where high strength andtoughness, low weight and high durabilityare required under aggressive serviceconditions, such as high temperaturepower and propulsion systems. Thematerials can include structural ceramics,metallics and their composite forms, suchas particulate and whisker toughenedceramics and such as metallic,intermetallic and ceramic fiber reinforcedcomposites. The usual applications aredirected toward the evaluation of bulkproperties in engineering solids withextensions to surfaces, substrates, bondedinterfaces and protective coatings.

307Ultrasonic Characterization of Material Properties

TABLE 2. Causes of material failure that can becharacterized and assessed by ultrasonic nondestructivetesting.

Processing Faults Service Degradation

Texture and anisotropy Altered microstructureWrong phase composition Corrosion or chemical attackInclusions, agglomerates Excessive deformationEmbrittling impurities Excessive residual stressWrong grain structure Overheating, decompositionFaulty heat treatment Fatigue or creep damageFaulty case hardening DecarburizationFaulty surface treatment Stress corrosionIncomplete polymerization Radiation damageWrong fiber fraction Gas embrittlementHigh microvoid content Moisture damage, absorptionFiber bunching, segregation Matrix softening, crazingFiber or ply misalignments Impact or shock damage

There are a variety of mechanical wavetechniques suitable for nondestructivematerials characterization, including sonicand dynamic vibration methods. Acousticemission testing is also included herebecause of its ability to reveal crucialmaterial variables. Pulse echo,through-transmission and other ultrasonicinterrogation techniques are discussed,along with signal analysis.

Although methods for global propertyevaluation are described, the emphasis ison methods that deal with smallervolumes within components at a giventime. These methods include acousticmicroscopy and analytical ultrasonics forquantitative characterization of materialsdown to the microstructural level. Inmaterials research, such methods are usedto monitor and characterize materialresponse and microstructural behavior.

Sonic and DynamicVibration Techniques

Sonic AnalysisSonic tests are among the oldest forms ofnondestructive testing. They typicallyinvolve striking (coin tapping) an objectto determine if it rings true.8 In sometypes of instrumented sonic testing, thesignals are inaudible and must beacquired electronically.

Sonic analysis tests are nondestructiveif strain amplitudes are quite small andleave the material unaltered. They may beapplied to simple laboratory specimensand also to structural components havingcomplex shapes. Automated signatureanalysis is used to infer the integrity andinternal condition of a range of structuralcomponents.9

Dynamic ResonanceDynamic resonance testing assessesphysical and mechanical properties ofcertain materials by evaluating theresonant vibration frequency.10 If excitedproperly, most solids exhibit sonicresonances, typically in the frequencyrange below 20 kHz. Elastic moduli can becalculated if the dimensions, density andresonant frequency are known.

There are direct empirical relationsbetween tensile moduli and resonantfrequencies of structural components. It ispossible to quickly confirm mechanicalproperties of a test object by comparing itwith a known reference standard havingthe same shape and dimensions. Theunderlying relation is that the resonantfrequency is the product of a shape factorand a physical factor. The shape factorincludes length, width and thickness. Thephysical factor is a combination ofmodulus, density and Poisson’s ratio.

Damping MeasurementAlthough dynamic resonance testing usessustained forced vibrations, dampingmeasurement uses the vibration’s freedecay.11-13 The test object is isolated fromexternal forces after excitation and eitherof two quantities can be measured: (1) thespecific damping capacity or internalfriction of the material or (2) acomparative structural damping factor ofactual components.

Specific damping capacity D is afunction of the logarithmic decrement dexpressed in terms of the amplitude losssuffered by successive oscillations of afreely vibrating sample. The relationbetween D and d is:

(1)

where AN is the amplitude of the Nthcycle (volts) and AN+1 is the amplitude ofthe next cycle (volts).14

Structural damping is not as sensitiveas dynamic resonance to size, shape andother geometric factors. Although thereare exceptions, damping values D tend tobe small in most engineering materials.9Damping measurements are generallysensitive to discontinuities and damage,provided that extraneous damping fromsupports and fixtures is minimized. Withsimple excitation methods (pointimpulse), several simultaneous vibrationalmodes can be excited. These can beanalyzed separately by computer for allfrequency components and modes.

D dA

AN

N

= =+

2 21

ln


PART 2. Material Characterization Methods

Applications of Dynamic SonicVibrationDynamic sonic vibration techniques aresuitable for studying microstructuredependent properties. Damping andresonant frequency measurements can beused to monitor phase transformations,plastic deformation, hardening, coldworking and alloy composition effects.15

Dynamic sonic and damping methods areused to evaluate porosity and density inceramics, fiber-to-resin ratios incomposites, bond strength in laminates,16

nodularity and texture in metals17 andstrengthening by dispersoids in alloys.18

In its basic form, dynamic resonanceaffords a quick and convenient check fordetermining whether an object hasappropriate mechanical properties or hasundergone loss of elasticity or tensilestrength. Elastic moduli and dynamicconstants of structural materials can beassessed for predicting dynamic response,as discussed below.

Acoustic EmissionTechniquesAcoustic emission is a passivephenomenon relying on spontaneous,transient, usually inaudible ultrasonicsignals such as those released duringmechanical deformation or thermalstressing (see the Nondestructive TestingHandbook: Acoustic Emission Testing).Acoustic emission frequencies range fromthe audible (sonic) to several megahertz(ultrasonic). Acoustic emission can arisewhen a material undergoes metallurgicaltransformations (twinning) or dislocationmovements, plastic yielding ormicrocracking.19

Passive sensors are fixed to the surfaceof a test object and are selected to ensuresensitivity to signals generated at somedistance by microdisturbances and otherweak sources. Operational methodsinclude event counts, ringdown counts,energy or amplitude distribution analysis,waveform analysis and frequencyspectrum analysis.20,21

ApplicationsThe objective of acoustic emission testingis the detection and location of incipientdiscontinuities. The spontaneous stresswaves that constitute acoustic emissioncan be analyzed to obtain informationconcerning discontinuities’ characteristics,location, abundance and distributionsduring the loading or proof testing ofstructures.22,23 Acoustic emission testingmonitors the presence and severity ofgrowing cracks, plastic deformation ordelaminations.

The acoustic emission technique alsoaffords a means for monitoring structuralintegrity and dynamic response and forinferring the current internal condition orstate of degradation in structuralcomponents. Examples of in-processmonitoring of materials are available inthe literature,24,25 especially forsolidification processes such as spotwelding and heavy section welding.

Another objective of acoustic emissiontesting is source characterization.26 This ishampered by signal modifications intransducers, instrumentation andespecially the material. Signalmodification by material microstructure,texture, diffuse discontinuity populations,mode conversions and reflections atboundary surfaces make it inherentlydifficult to quantitatively infer the exactnature of emitting sources.27 Becausesource characteristics are usuallyunknown, acoustic emission is not usedfor quantitative characterization ofmicrostructure or material properties.

Pulse Echo TechniqueThe ultrasonic pulse echo technique is akey method for materials characterization.It is widely used for making precisemeasurements of ultrasonic speed andattenuation. These two measurements arethe bases for accurately evaluating elasticmoduli, characterizing microstructure andfor assessing mechanical properties.

The pulse echo technique uses a broadband, buffered piezo transducer that emitsand collects ultrasonic signals. Thetransducer is held in contact with the testobject at normal incidence. Contact withthe test object is generally preferred overseparation by a liquid buffer or immersioncoupling medium. A solid buffer rod withlow attenuation (usually quartz or fusedsilica) is integrated into the transducercase and provides the means for isolatinga series of back echoes. The buffer delaysfront surface echoes and prevents themfrom becoming confused withreverberations in the piezoelectric crystal.The length of the buffer is dictated by thetest object thickness and the number ofechoes that need to be included withinthe buffer time delay. The frequency rangefor most engineering solids is from about300 kHz to about 400 MHz.

Constraints on Pulse EchoTechniqueIdeally, the test object must have smooth,flat, parallel opposing surfaces and shouldmeet the constraints for precise signalanalysis prescribed in Table 3. In addition,sufficient force on the transducer isrequired to squeeze out excess couplant


between it and the test object.28,29 Thetransducer collects a set of echoesreturned by the front and back surfaces ofthe test object. Signal acquisition,processing and analysis methods aredescribed in this volume and in theliterature.4,30-34

Many kinds of test objects areappropriate for pulse echo ultrasonics,including rectangular components, sheetstock, bar stock and cylindrical rods. Forcomplex objects, the need forperpendicular alignment of thetransducer’s axis with a test object’ssurface may demand certain designaccommodations to satisfy the constraintsin Table 3.

Note that direct, normal incidencereflections may not occur even if testobject shape and boundaries meet theconditions given in Table 3. If thematerial is anisotropic, is orthotropic orcontains microstructural gradients,4 theremay be multiple skewed quasilongitudinaland quasitransverse wave paths.

Pulse Echo Signal ProcessingFor speed measurements, the objective isto establish the exact time interval neededfor a signal to travel between the frontand back surface of a test object. Signalanalysis yields the group speed andfrequency dependent phase speeds (thespeed dispersion characteristics of thematerial). For attenuation measurements,the objective is to determine the energyloss experienced by signals that traverse atest object. Signal analysis yields theattenuation coefficient as a function offrequency (the attenuation spectrumunique to the material). Using computers,both measurements can be made at onceby collecting a series of echoes returnedby the back surface of the test object.

Signal analysis can be done in eitherthe time domain or the frequency domaindepending on need and convenience. Thesimplest and usually least accuratemeasurements use time domain records ofvoltage (A-scans). Either analog ordigitized records can be used forestimating speed and attenuation. Thepreferred method is to use digital fouriertransforms to determine the frequencydependence of speed and attenuation overa broad frequency range. Generally, dataneeded for materials characterization arelikely to be deficient unless they are basedon broad band phase speed andattenuation spectrum analysis.

Speed MeasurementThe four primary approaches to speedmeasurement using the pulse echotechnique are the peak detection andecho overlap methods30 or the crosscorrelation and phase measurementmethods.35

Peak detection and echo overlap aresufficiently accurate if the echoes are notseriously distorted by dispersion effects.The cross correlation method gives groupspeed and is most useful with noisysignals such as those found in coarsematerials and fiber reinforced composites.The phase method is used to determinethe phase speed as a function offrequency.35-38

The cross correlation or group speed ofthe first two echoes B1 and B2 is given by:

(2)

where X is the test object thickness(meter) and τ is the time shift (second).

vX= 2

0τ


TABLE 3. Constraints on the test object necessary to ensure precise ultrasonicattenuation and speed measurements.

Recommended Constraints Ambiguities Eliminated

Normal incidence probing Miscalculation of texture, anisotropy or wave pathsClean, smooth surfaces Poor transducer coupling and couplant reverberationsFlat, parallel surfaces Deflected or distorted signals and oblique signal pathsGeometrically simple shapes Signal path untraceabilityMinimum thickness and length Excess attenuation losses and low signal-to-noise ratiosPrecise physical dimensions Significant attenuation and speed measurement errorsLarge test object-to-transducer area Sidewall and edge effectsAccessibility of key areasa Inability to characterize critical zones or volumesAbsence of overt discontinuitiesb Spurious signals unrelated to material properties

a. Actual test objects may not lend themselves to precise characterization unless design accommodations are madeto facilitate testing.

b. It is assumed that appropriate nondestructive testing has been applied to screen out objects with overtdiscontinuities that can interfere with materials characterization.

The value of τ in Eq. 3 is –∞ ≤ τ ≤ ∞ andis determined by the maximum value ofEq. 3:

(3)

The phase speed is given by:

(4)

where:

(5)

(6)

(7)

where f is frequency (hertz), Im is animaginary number and Re is a realnumber.

Attenuation MeasurementThe quantities B1, B2, I1, I2 and R arefunctions of frequency (fourier transformsof corresponding time domain quantities).The quantities B1, B2, I1 and I2 are spectraof corresponding waveforms. Thereflection coefficient R of the front surfaceis generally also a function of frequency.

The reflection coefficient can bedefined either in terms of energy(intensity) or amplitude (pressure).39

Taking R as the reflection coefficient andT as the transmission coefficient across aninterface from medium 1 to medium 2,the definition for energy is:

(8)

(9)

(10)

where z1 and z2 are acoustic impedancesof media 1 and 2:

(11)

(12)

where ρ1 and ρ2 are densities (kilogramper cubic meter) and v1 and v2 are phasespeeds in the media (meter per second).

The preceding equations for reflectionand transmission apply to ideal interfacesthat have no thickness. When there is afinite thickness that greatly exceeds thetransmitted ultrasonic wavelengths, thetransmission and reflection coefficientsare frequency dependent.40 In general, thereflection coefficient as a function offrequency can be determined:

(13)

where the fourier spectra of echoes fromthe end of the buffer are F1(f ) and F2(f ),with and without coupling to the testobject, respectively.41

The reflection coefficient is unity (1) atthe free back surface of the test object.Internal echo I1 is the source of the signalB1. A part of the energy of I1 is reflectedand appears as the second internal echo I2giving the reduced echo B2, thus:

(14)

(15)

The quantity H represents a transferfunction of the material defined in termsof the attenuation suffered by a pulsetraveling twice the test object thickness X:

(16)

where α is the attenuation coefficient.Like B1, B2, G, R and T, α is a function offrequency and plots of α versus f aresometimes termed attenuation spectra.

The quantity G is a combination oftransfer functions associated withinstrumentation, signal transduction andother aspects of the signal acquisitionsystem. In the pulse echo technique, Gdrops out of the expression for theattenuation coefficient found by solvingthe preceding equations. For example, theattenuation coefficient may be writtenas:30,34

(17)

This equation is the deconvolution ofecho B1 with respect to B2 as modified bythe reflection coefficient function R.

α =⎛⎝⎜

⎞⎠⎟

12

1

2XR

BB

ln

H X= −( )exp 2 α

B GHR R I2 11= −( )

B G R I1 11= −( )

R fF f

F f( ) =

( )( )

2

1

z v2 2 2= ρ

z v1 1 1= ρ

Tz z

z z=

+( )4 1 2

1 22

Rz zz z

=−+

⎛⎝⎜

⎞⎠⎟

1 2

1 2

2

R T+ = 1

B fI B f

R B f21 2

2

( ) =( )⎡⎣ ⎤⎦( )⎡⎣ ⎤⎦

−tane

m

B fI B f

R B f11 1

1

( ) =( )⎡⎣ ⎤⎦( )⎡⎣ ⎤⎦

−tane

m

Δ B B B= −2 1

v fX f

B( ) = 4 π

Δ

τ τn B t B t dt= ( ) −( )−∞

+∞

∫ 1 2


Expressions for the attenuationcoefficient can be derived by consideringvarious energy loss mechanisms.Examples of the attenuation coefficientfor different loss mechanisms are given inTable 4 for typical polycrystalline solids.

Pulse Echo ApplicationsThe pulse echo technique is preferred forprecise measurements of attenuation andvelocity spectra that can in turn be usedfor quantitative characterization ofmicrostructure and assessment of materialproperties. Mechanical properties andmorphological conditions that can beevaluated by the pulse echo method arelisted in Table 5.5 The variables R, T, B1, B2and hence attenuation and velocityspectra are affected by the properties of

bulk microstructures, interfaces, bonds,substrates, coatings and like factors thatgovern material response and integrity(see the discussion of microstructure anddiffuse discontinuities, below).

Backscatter TechniqueThe backscattering of ultrasonic waves iscaused by discontinuities in density andspeed, that is, by the jump in acousticimpedance Δρv encountered at phase andgrain boundaries in metals or fiber matrixinterfaces in composites. In thebackscatter technique, the appearance ofrandom stochastic reflections (between B1and B2 or between the front surface echoand B1) is of interest. The two keyparameters that govern the nature andmagnitude of scattering are Δρv and a·λ–1.These include changes in acousticimpedance and ratio of scatterer size a towavelength λ used to characterizemicrostructure. By using time domainwaveforms or frequency domain spectra,it is possible to infer mean grain size,presence and distribution of inclusions.

The usual application of backscatteringmeasurements is for nondestructive grainsize determination.42-44 The backscatterapproach has also proved useful formeasuring global heterogeneities such asthose from segregations and inclusions inmetals and ceramics. In addition,backscatter measurements can be appliedto surfaces and substrates to determinerelative roughness,45 to measure casehardening depth,46 to rank adhesive bondquality47 and to monitor texture andporosity in metals and composites.48,49

Dual-TransducerTechniquesDual-transducer techniques involvetransducer pairs that are usuallypositioned so that signals are directedalong well defined paths. Either contact orimmersion coupling may be used atnormal or oblique incidence. As in thecase of the pulse echo technique, there areconstraints that need to be met toproduce and acquire meaningful signals.Three dual-transducer techniques formaterials characterization are describedhere: (1) through-transmission, (2) pitchcatch and (3) acoustoultrasonic.

Through-Transmission TechniqueThrough-transmission techniques use twotransducers (sending and receiving)usually facing each other on oppositesides of a test object. The object thatoccupies the space between the


TABLE 4. Theoretical ultrasonic attenuation coefficientsfor semilinear elastic polycrystalline solids.

AttenuationWavelength Attenuation Coefficient

Relation Mechanism (Np·m–1)

— True absorption αa = Cafλ >> πD Rayleigh scatter αr = CrD3f 4

λ ≅ πD Phase scatter αp = CpDf 2

λ << πD Diffusion scatter αd = CdD–1

D = nominal or mean grain size (µm)λ = wavelength (m)f = frequency (Hz)

α = attenuation coefficient (Np·m–1)C = experimental constants (may include grain, geometric anisotropy, elastic

anisotropy, density, longitudinal speed and transverse speed)

TABLE 5. Properties and conditions that can be monitoredwith ultrasonic techniques. (Ultrasonic measurementsgive indirect indications of mechanical propertyvariations and morphological conditions. Empiricalcorrelations and calibrations must be established foreach material even where theoretical bases exist.)

Mechanical Properties Morphological Conditions

Tensile modulus Texture and anisotropyShear modulus Grain size and distributionBulk modulus Microvoid or porosity distributionLame constant Phase compositionTensile strength Case hardening depthShear strength Precipitation hardeningYield strength Residual stressesInterlaminar bond strength Overaging effectsHardness and ductility Undercuring and cure stateImpact resistance Fatigue and impact damageImpact strength Fiber or whisker alignmentFracture resistance Degree of recrystallizationFracture toughness Alloy matrix supersaturationAdhesive bond strength Composite matrix crazing

transducers is either in contact with themor is separated by immersion in a fluidcoupling medium. The acoustic beam isdirected at normal incidence to test objectsurfaces that meet the constraintssuggested in Table 3. Alternatively, withimmersion coupling, the test object canbe rotated between the transducers.Oblique incidence can be used tocharacterize material properties withtransverse waves or surface (rayleigh)waves that are generated when fluidborne longitudinal waves meet a surfaceat an angle.

Through-transmission techniques areoften used for making comparativeproperty measurements withtime-of-flight speed measurements andrelative attenuation measurements.30

Single-transit, through transmission isused if there is high signal attenuationbecause of test object thickness. Thistechnique is often used in a comparatorconfiguration where the test object’stransit time delay is compared with thetransit time delay in a reference standard,as when measuring relative changes inelastic moduli.

To ensure precise attenuationmeasurements in a through-transmissiontechnique, the transducer pair must beperfectly matched or fully characterized.Signal modulation properties of theinstrumentation, transducers andinterfaces must be eliminatedexperimentally or taken into account withsignal processing. This can be avoided byusing the single-transducer pulse echomethod where transducer related couplingand impedance mismatch factors can bebetter accounted for in analyticalexpressions.

Through transmission also lends itselfto forward scattering measurements. Thetransducer on the opposite side of the testobject collects wave energy scattered outof the main beam. Inverse analysis is usedto infer size and distribution data.50

Pitch Catch TechniqueThe dual-transducer pitch catch techniqueuses a pair of transducers displaced fromeach other by a fixed distance, on thesame side or opposite sides of a testobject, as in the leaky lamb wave method(Fig. 1). The transducers may be in directcontact at either normal or obliquealignment. In the latter case, thetransducers may be coupled by anglebeam fixtures to excite transverse orrayleigh waves.

In a fluid medium, the pitch catchtechnique can be accomplished with asingle focused transducer operating withself-generated and self-interceptedrayleigh waves (see Fig. 2).

The usual objective with pitch catchtesting is discontinuity location andcharacterization. The technique can alsocharacterize material properties. In eithercase, the positions of the transducers arecalculated to recover specific signals thathave traversed well defined paths alongthe surface or in the bulk. The pathsusually involve simple reflections fromthe back surface or surface waves that areintercepted by the strategically placedreceiving transducer. The pitch catchtechnique often uses surface waves andguided waves, such as rayleigh waves andplate waves, respectively. Lamb waves and


FIGURE 1. Pitch catch dual-transducertechnique using leaky lamb wave effect.

TransmitterReceiver

PlateFluid

Fluid

Null zone Leaky wave

FIGURE 2. Pitch catch technique using focused transducer:(a) wave from rim of lens hits test object surface at criticalangle producing surface waves that return to lens;(b) resulting waveform.

Lens

Water

1

2

1 2

Test Object

0.1 µs

Time

Volta

ge

Legend1. Direct reflection.2. Rayleigh wave.

(a)

(b)

leaky lamb waves are used to evaluatebonds and interfaces by using angle beamimmersion tests.51 Variations in bondingare observed through variations in thespacing of null zones over a range offrequencies.

AcoustoultrasonicsThe word Acoustoultrasonics may be takenas a contraction of acoustic emissionsimulation with ultrasonic sources. Incontrast to acoustic emission techniques,the idea in acoustoultrasonic testing is tokeep the nature and location of the sourceof ultrasonic radiation known and fixed.The idea is to introduce stress waves inthe material and establish the change inwaveform. The test is not concerned withsource location and characterization butwith characterization of the materialmedium between the source and receiver.The acoustoultrasonic approach usesanalysis of simulated stress waves fordetecting and mapping variations and thecollective effects of diffuse discontinuitiesand material anomalies.52,53

Unlike the through-transmission orpitch catch technique, theacoustoultrasonic technique imposes nodemand on having particularly welldefined propagation paths. Indeed, typicalapplications are with materials that are soheterogeneous and anisotropic that itwould be futile to demand well definedsignal trajectories. The usual applicationsare with laminated fiber composites andcoarse grained, highly textured materials.

The source may be any means forperiodically exciting ultrasonic waves,usually a piezo transducer. A secondtransducer receives the signals. Both thesender and receiver are coupled to the testobject surface at normal incidence.Although this arrangement resembles thepitch catch technique, the underlyingapproach is considerably different. Oncelaunched in the test object, ultrasonicwaves are modified by multiple reflectionsand stochastic processes. In this respectthe acoustoultrasonic method mostresembles the forward scatter technique.The acoustoultrasonic approach simulatesthe propagation of stress waves that mightnormally arise under acoustic emissiontesting.

Laser TechniquesDual-transducer techniques increasinglyuse laser ultrasonics. Laser ultrasonictesting involves laser-in, laser-outexcitation and detection without contactor immersion in a coupling medium. Itallows high speed scanning andconvenient test object contour following.Laser ultrasonic techniques provide good

attenuation and speed measurements formaterials characterization.54,55

ApplicationsThere exists a wide range of applicationsfor materials characterization usingdual-transducer techniques. These includemonitoring of metallurgical processes,55

assessment of porosity,56 measurement ofelastic constants,57 evaluation of fatiguedamage,58 interlaminar strength,59

adhesive bond strength60,61 and curestate.62,63

Ultrasonic SpectroscopyUltrasonic spectroscopy is done withsingle-transducer or dual-transducerconfigurations. The objective is to analyzemodulations of ultrasonic waves causedby variations in microstructure andmorphology. Ultrasonic spectroscopypresupposes unique signal modulations bythe material. The pulse echo techniquedescribed above uses a form ofspectroscopy in that a pair of back echoesare deconvolved to obtain an attenuationspectrum (attenuation as a function offrequency). The deconvolution step is notalways necessary nor readilyaccomplished. As an alternative, thespectrum of a once-through signal (as inthrough-transmission) may be analyzed.The resulting spectral signature can becompared with that taken from areference standard.

Spectrum analysis is an excellentapproach for comparing subtle and oftensignificant variations in materialmicrostructures. Digital fast fouriertransform methods are necessary toobtain quantitative results.64-67 Ultrasonicspectrum analysis is used routinely inpulse echo, acoustoultrasonic and relatedtesting techniques. Appropriate analyticalprocedures include spectrum analysis,spectral partitioning, regression analysisand the method of moments.53,68 Thelatter uses statistical parameters todescribe spectral signatures. Additionaldata processing techniques includepattern recognition and adaptive learningnetwork theory.52,69-77

Ultrasonic spectroscopy is comparativeand relies on a repertoire of spectralsignatures for a wide range of materialand boundary conditions.

Applications of UltrasonicSpectroscopyUltrasonic spectroscopy has been widelyused for both qualitative and quantitativemicrostructure characterization.45,78

Attenuation spectra provide a powerfulway to assess mean grain size in


polycrystalline solids.32,34,79,80 In addition,porosity and other morphological factorscan be assessed with ultrasonicspectroscopy.81

Analysis of ultrasonic spectral featurescan yield quantitative correlations withmaterial properties that are governed inturn by microstructure. These correlationsinclude the ultimate strength andinterlaminar strength of compositelaminates82,83 and toughness inmetals.84,85

Ultrasonic ImagingTechniquesSeveral ultrasonic imaging techniqueshave a major role in materialscharacterization: (1) immersionmacroscanning, (2) acoustic microscopyand (3) multiparametric scanning.

Acoustic microscopy andmultiparametric scanning imposerestrictions on the size and geometry ofthe test objects. These restrictions areoften similar to those imposed inconventional optical microscopy inassociation with test object size, shapeand mode of preparation. Magnifiedimages, at very high resolution tosubmicrometer levels, can be formed withacoustic microscopy in the megahertz andgigahertz range by scanning minute areasof a surface or substrate.

Immersion MacroscanningFor large test objects, immersion scanningis the standard C-scan method, usingassorted pulse echo, through-transmissionor pitch catch configurations. Thefrequency range for immersionmacroscanning is usually from 0.5 toabout 25 MHz. It is universally applied fordiscontinuity detection but can be used tomap relative global variations in materialproperties.

These variations can be related tomaterial microstructure, texture or otherextrinsic properties provided that thereturn signals are not also subject tochanges in surface properties or thickness,curvature and similar boundary orgeometric factors.

Acoustic MicroscopyAcoustic microscopy reveals density,texture and microelastic variations.86

Images are generated by pulsed orcontinuous wave ultrasound, usually inthe range from 50 MHz to 1 GHz. Theimages are produced either by pulse echoor thorough-transmission techniques.There are a number of acousticmicroscopy methods, each with specificapplications, including: (1) scanning

acoustic microscopy, (2) scanning laseracoustic microscopy, (3) scanning electronacoustic microscopy and(4) photoacoustic microscopy.

Scanning acoustic microscopy can takeeither of two forms. The first is simply aminiature C-scan or C-scanning acousticmicroscopic technique that uses a focusedtransducer, a stepper driven scanner and asmall immersion tank containing the testobject (Fig. 3). The second form uses araster vibrated scanning acousticmicroscopic focused transducer coupled tothe test object with a bead of fluid. Bothmethods operate in the focused pulseecho reflection mode with the option ofusing rayleigh wave imaging of surfacefeatures.87

C-scanning acoustic microscopyusually operates in the 50 to 200 MHzrange whereas vibrated scanning acousticmicroscopy operates in the 1 to 2 GHzrange and requires metallographicallypolished surfaces. Either of these twoforms of scanning acoustic microscopy isuseful for imaging the elasticmicrostructure at surfaces and substrates.Pulse echo or rayleigh wave modes areused to reveal microstructure to depths ofabout 4 µm (at frequencies of about4 GHz) to about 4 mm (at frequencies of50 to 400 MHz). The field of view is 100to 700 µm2 for vibrated scanning acousticmicroscopy and 2 to 15 mm2 forC-scanning acoustic microscopy, givingimage magnifications from roughly 2500×to 100×.

Scanning laser acoustic microscopyuses through-transmission continuouswaves at specific frequencies, usually in


FIGURE 3. Scanning acoustic microscopy system for C-scanimaging.

Piezoelectric crystal

Mechanical XY scan

Focal plane

Test object surface

Lens Water

Computer controlledscan generator

Computer data acquisitionand storage

Imagingsystem

Receiver

Pulser

the 30 to 100 MHz range as dictated bythe material attenuation and test objectthickness.88,89 Waves that pass throughthe test object set up perturbations on theopposite surface that are read by a rasterscanning laser beam (Fig. 4). Reflectedlaser energy is sensed by a photoopticaldetector to generate a video image. Thisrequires the scanned surface to bespecularly reflective or coupled to areflective cover slip. For typical metal andceramic test objects, the thickness may beseveral millimeters. The scanning laseracoustic microscopic image revealsmicrostructural variations in the volumeilluminated by the piezo transducer(usually about 4 mm2 in area). The imageis magnified about 100 times on the videomonitor.

Scanning electron acoustic microscopyis accomplished by electron beam heatingof the test object surface (Fig. 5). Thisrequires that the test object be enclosed ina vacuum chamber. In fact, scanningelectron acoustic microscopy is done withslightly modified scanning electronmicroscopy equipment and shares thescanning electron microscopy envelope.

The scanning electron microscopyelectron beam is modulated (chopped)while it raster scans a small area that istypically a few millimeters square.90-92

Acoustic signals generated at each pointheated by the beam are sensed by apiezoelectric transducer attached to thebottom of the test object. The result ofthe raster scanning is displayed on a videoscreen. Both a conventional scanningelectron microscopic and a scanningelectron acoustic microscopy image canbe viewed for the same area on the testobject. As in the case of scanning acousticmicroscopy, microelastic variations can beimaged using scanning electron acousticmicroscopy. The scanning electronacoustic microscopy imaging depthdepends on thermal diffusion length inthe solid.

Photoacoustic microscopy uses a rasterscanning laser beam to thermally exciteacoustic waves (Fig. 6). The test object isenclosed in a pressure tight cell thatcontains a window through which thelaser beam impinges on the testobject.88,89,93 Thermally generated acousticwaves are picked up by a miniaturemicrophone in the cell. Images are createdby displaying the intensity of the soundwaves against the current coordinates ofthe laser beam. In an alternativeconfiguration, a piezoelectric crystal isattached to the test object. In either case,the acoustic wave intensity values areused to image microstructural variationswithin the volume scanned (usuallyseveral millimeters in area and to depthsof several millimeters, depending on thethermal diffusion length of the material).


FIGURE 4. Diagram of scanning laser acoustic microscopysystem.

Laser Beamscanners

Mirrors Demodulator andphotodetector

Acousticsignal

processor

Opticalsignal

processor

Acousticimagedisplay

Opticalimagedisplay

Test object

Imagingoptics

Mirrored coverslip

Acousticfrequencygenerator

Ultrasonic transducer

FIGURE 5. Essential features of scanning electron acousticmicroscope with typical parameters showing representativewavelengths.

Scanning electronmicroscopy enclosure

Scanning electron beammodulated at 1 MHz

5 µm wavelength

Microstructuralfeature

5 mm wavelength

Piezoelectric crystal

To image intensity modulator

Acoustic waves

Thermal waves

Test object surface

FIGURE 6. Diagram of photoacoustic microscopy system.

LaserMirror

Chopper

Scandevice Microphone

Sample

Preamplifier

Window

Isolation cell

Lock-inamplifier

AB

Ratiometer

Photodiode

A·B–1

XYrecorder

Reference

Multiparametric ScanningMultiparametric scanning goes beyondproducing images of materialmicrostructure and microelastic domains.The goal is to collect an assortment of rawultrasonic data and analyze them to givenumerical values to a wide range ofparameters. Selected parameters that canbe mapped against the test object imageinclude phase and group speeds,attenuation at selected frequencies,surface and internal reflection coefficients,and elasticity and stress values.Multiparametrics also comprisesmeasurement of ultrasonic interactionswith other forms of energy (thermal ormagnetic).

Immersion noncontact C-scanapproaches are fairly common formultiparametric mapping.94 Contactscanning with a single-pulse echotransducer affords a means for obtainingmore precise multiparametric data. Inboth cases, the test object is systematicallyscanned to collect sets of broad band(usually several hundred megahertz) echowaveforms.95 When scanning is done witha contact transducer, the test object musthave a flat, polished surface so that thetransducer can be readily moved about.This movement is done by intermittentlyrelaxing the coupling pressure as thetransducer slides to the next position,using the couplant as lubricant. Althoughthere are practical limits, large areas maybe scanned with this method if theconstraints in Table 3 are met.

Front surface and back surface echoesare collected for each of several hundredto several thousand equally spaced gridpoints on the test object. The data arestored and retrieved under computercontrol to generate attenuation and speedspectra for each point. The test objectshould have uniform thickness so that thespeed and attenuation measurements canbe compared from point to point.Mapping of attenuation and speedvariations at selected frequencies can begenerated from stored waveform data forthe test object area being tested (Figs. 7and 8).

Applications of Ultrasonic ImagingTechniquesFor materials characterization, acousticmicroscopy (particularly scanning acousticmicroscopy) has capabilities thatcomplement optical microscopy. Acousticmicroscopy reveals grain, grain boundaryand subgrain details without the need forspecial techniques such as etching toenhance contrast. In addition, acousticmicroscopy can image subsurfacemicrostructure features. Because ultrasonicwaves are used, the image contains

microelasticity information that does notappear in photomicrographs.

Scanning electron acoustic microscopycomplements scanning electronmicroscopy because the former is basedon thermal waves that penetrate belowthe surface to reveal subsurface features.Scanning laser acoustic microscopyimages are projections of internal featuresimprinted on the laser scanned surfaceand therefore contain information oninternal microelastic variations and otherinternal heterogeneities. Acousticmicroscopy and multiparametric scanningcan be applied to laboratory test objectsfor characterizing microstructure andelastic properties. Potential research andindustrial applications include assessmentof elastic anisotropy; surface and internalstress states; and mechanical, thermal andchemical damage.

Although C-scan imaging is widelyused for materials characterization, thepotential of acoustic microscopy andmultiparametric scanning is still beingdeveloped. The applicability of acousticmicroscopy techniques has beendemonstrated on metals, ceramics andcomposites for evaluating grain structure,texture, porosity, fatigue damage, solidstate weld bonding and fiber/matrixinterface quality.87-89,95,96


FIGURE 7. Mapping speed variations in monolithic siliconcarbide disk: (a) image; (b) speed profile along diameter.

Spee

d(k

m·s

–1)

Diameter (relative scale)

12.7

12.0

11.3

10 mm

(a)

(b)

Analytical versus ImagingTechniquesAlthough the distinctions may not alwaysbe clear, there are differences betweenanalytical and imaging ultrasonic testing.Analytical ultrasonic testing addresses theneed to quantify factors such as speed andattenuation and their interrelation withmaterial properties. Imaging ultrasonictesting is usually dedicated to revealingdiscontinuities, their location, orientationand microstructure. Imaging alsoaddresses the spatial distribution ofdiscontinuity populations and materialanomalies such as porosity, texture anddensity variations.

Analytical and imaging ultrasonictesting are combined in multiparametricscanning where quantities like reflectioncoefficient, attenuation coefficient andphase speed are spatially mapped againsta test object’s outline.


FIGURE 8. Mapping of attenuation variations in monolithicsilicon carbide disk: (a) disk with areas of interest;(b) porosity for area 1; (c) porosity for area 2; (d) grainstructure for area 1; (e) grain structure for area 2.

(a)

(b)

(c)

(d)

(e)

10 mm

1 2

25 µm

25 µm

10 µm

10 µm

Fundamental ElasticProperty RelationsThe measurement of elastic properties isbasic to understanding and predicting thebehavior of engineering materials.Ultrasonic wave propagationmeasurements afford a nondestructivemeans for determining elastic constants,texture and stress states. This can be doneby introducing longitudinal andtransverse waves in test objects andmeasuring the corresponding wavespeeds.57 Interrelations among thesespeeds and elastic moduli are shown inTable 6.

Anisotropic MaterialsReal materials, even when they havesimple shapes, rarely exhibit uniform andlinear elastic properties assumed in theequations given for elastic moduli.Internal variations exist because ofthermomechanical processing(solidification, densification and coldworking) that can cause anisotropy andtexture.4 The distribution of tougheningparticles, whiskers and fibers can varyconsiderably (but not necessarilyconspicuously) in ceramic and metalmatrix composites. These factors lead tothe need for measuring elastic propertiesthat are direction dependent and thatvary globally in the material volume.

Porous SolidsIf solids are porous as in the case of castmetals, ceramics and most composites,

then relations between elastic moduli andspeed are more complex than indicated inTable 6. As discussed below, even if thesolids are linearly elastic and isotropic, themoduli become functions of pore size,shape and orientation.97 Moreover, othermicrostructural factors such as grainshape, grain boundaries, texture andprecipitates can have pronounced effectson relations between speed and moduli.

Dynamic Resonance

Vibrational ModesWhen determining elastic moduli ofsolids from resonance frequencies, thetype of vibration may be longitudinal(extensional), transverse (flexural) ortorsional.10 The first two modes giveYoung’s modulus and the last gives theshear modulus.

The way to obtain the best test resultsis to choose a geometry, such as arectangle or cylinder, with simpleboundary conditions. The dynamicresonance method is based on thestanding waves in an object. If the objectis undergoing longitudinal or torsionalvibration, its length � contains an integralnumber n of half wavelengths, 0.5 λ:

(18)

and the wave speed is:

(19)

where fr is the resonant frequency. Theequation does not apply to flexuralresonance.

Longitudinal VibrationIf the object is a cylindrical rod orrectangular bar, Young’s modulus E inpascal can be approximated fromlongitudinal resonances for n = 1:

(20) E Gfn

G v

= ( ) ⎛⎝⎜

⎞⎠⎟

=

ρ

ρ

�

�

�2

2

2

r

v ff

n= =λ λ

r 2

� = nλ2


PART 3. Measurement of Elastic Properties

TABLE 6. Relations among elastic constants and ultrasonicwave speeds in fully dense linear elastic isotropic solids.

Elastic Constant (Pa) Relation

Longitudinal modulus L = ρv�2

Shear modulus S = ρvt2

Bulk modulus K = L – 4S/3Young's modulus E = 3S – S2(L – S)Lamé constant λ = L – 2S

v� = longitudinal speed (meter per second)vt = transverse speed (meter per second)ρ = density (kilograms per cubic meter)

where ρ is density (kilogram per cubicmeter) and G� is a geometric factorcontaining object size and shape andPoisson’s ratio.

Flexural VibrationFlexural vibrations are easier to generatethan longitudinal vibrations, especiallyfor thin objects. Flexural vibration modesare more practical and more widely usedfor determining Young’s modulus from:

(21)

where Gf is a factor that contains testobject size, shape, Poisson’s ratio, radiusof gyration and a mode of vibrationconstant.

Torsional VibrationThe general equation that relates shearmodulus S and torsional resonantfrequency is:

(22)

where Gt is a shape factor that depends onthe test object’s shape and cross section.The value of n is 1 for the fundamentalmode and 2 for the first overtone.

Speed and Elastic ModuliDynamic resonance is an approach tomeasuring ultrasonic propagation speedby means of resonant frequencies — thatis, by the �fr factor in the previousequations. This approach is useful forcalculating moduli and for inferringglobal changes in elastic moduli andassociated mechanical properties.Applications of dynamic resonance are fortest objects that do not lend themselves todirect measurement of speed because ofinconvenience, geometric complexity orlow signal-to-noise ratios (highattenuation).

Ultrasonic MeasurementsDirect measurement of longitudinal v� andtransverse vt speeds give the fundamentallongitudinal L and shear S moduli,respectively. Young’s modulus is obtainedfrom combinations of L and S given inTable 6:

(23)

and:

(24)

These relations assume that speedmeasurements are on test objects withdimensions much greater than thewavelength of the ultrasound. Otherwise,when wavelengths are comparable todimensions, frequency dependent modesare generated.

For linear elastic isotropic solids, themoduli L and S are sufficient tocompletely define elastic behavior, giveninterconnecting relations with othermoduli. Anisotropic solids present a morecomplicated situation because theprincipal moduli assume different valuesaccording to the direction of wavepropagation. In general, the elasticcharacterization of a solid depends onnine separate speed measurements.2Transversely isotropic materials such asfiber reinforced lamina need fiveindependent speed measurements.98

Effect of PorosityThere is considerable variability in theeffects of porosity (and impurities) on theelastic properties of structural materialssuch as ceramics and composites.Expressions interrelating elastic properties,ultrasonic speed and porosity have beenmostly empirical. Numerous theoreticaland semitheoretical expressions have beenderived to incorporate the effects of poresize, shape orientation and distributionconditions on various moduli (bulk, shearand Young’s).97 For example, the effect ofporosity on Young’s modulus has beenexpressed as:

(25)

or

(26)

where b is an adjustable porosity factor, E0is Young’s modulus with no porosity (fulldensity) and P is volume fraction ofporosity.

The first equation is for P values lessthan 50 percent. Equation 26 is for Pvalues greater than 50 percent.

The consequence of porosity is thatspeed is no longer a simple decreasingfunction of density as implied by theprevious equations for L and S. Instead,speed is related to the porosity factors andalso to grain size, shape and orientationfactors peculiar to a given material. Formost porous solids, speed is found to bean increasing function of density.99

Mechanical strength and fracture behaviorof structural ceramics have an important

E E b P= − − −( )⎡⎣ ⎤⎦{ }0 1 1exp

E E bP= −( )0 exp

S v= ρ t2

L v= ρ �2

S Gf

n=

( )4

2

ρ tr�

E G f= ( )ρ πf r2 2 2�


and complicated dependence on porosity,impurities and grain structure.

Elastic Moduli and TemperatureSpeed and elastic moduli are functions oftemperature. This temperaturedependence is important because elasticmoduli are related to interatomic forcesthat determine embrittlement at lowtemperatures. At cryogenic temperatures,the temperature variation of thelongitudinal modulus L and shearmodulus S tend to follow the relation:

(27)

where c is the value of L or S as Tapproaches 0 K and T is the absolutetemperature (kelvin).100

Variables c, s and t are adjustableparameters that depend on the material.The longitudinal and shear moduliusually vary linearly with temperature atroom temperature. Empiricalinvestigations have been conducted onboth low (cryogenic) and hightemperature variations of elastic moduliusing ultrasonic speed.101,102

AcoustoelasticityAcoustoelasticity is the term applied tochanges in speed or attenuation wroughtby applied or residual stress.103-105 Inpractice, it is easier to measure speedchanges although speed is a weakfunction of stress.

Effect of StressRelative changes in wave speed of only10–5 per megapascal are typical for steeland aluminum so that precise speedmeasurements are needed. The simplestcase can be represented by the linearexpression:

(28)

where A is the acoustoelastic constant, v0is speed in the absence of stress (meter persecond) and Δv = (v0 – vσ) where σ is theinduced stress.

Fundamentally, acoustoelasticconstants apply to single crystals butempirical relations exist connectingacoustoelastic constants to polycrystallineaggregates. In most engineering solids,nonlinear relations between Δv·v–1 and σmay arise because of anisotropy ortexture.106

BirefringenceGenerally, there are two transverse wavespeeds vtx and vty polarized in twoperpendicular directions corresponding totwo principal stresses, σx and σy, so that:

(29)

The birefringent coefficient Bt is related tothe second and third order elasticconstants of the unstressed solid in whichthe transverse speed is vt0.

105 Speed alongthe axes of principal stress are equal onlyif the principal stresses are equal andthere is no texture.

Effect of TextureIn orthotropic and most polycrystallinesolids there is an initial birefringence fromanisotropy and texture such asnonrandom grain orientation. Induced orresidual stresses result in secondarybirefringence. For isotropic untexturedmaterials, the initial, unstressedbirefringence is zero. For slightlyorthotropic solids, the birefringence isgiven by:

(30)

The birefringent constant Bt depends onthe original (unstressed) anisotropy. Insome materials, the initial birefringencecaused by texture may be greater thanthat due to stresses as great as yield.107-109

The previous expressions may be valid fordetermining stresses in an elasticallydeformed body but might produce largeerrors in residual stress measurements.104

Effect of TemperatureIt has been established that ultrasonicspeed varies linearly with temperatureand, as indicated above, tends to varylinearly with stress. Externally inducedelastic stress also affects the temperaturedependence of ultrasonic speed. Therelation is expressed by:

(31)

where dv·(dT)0–1 is the temperature

dependence of ultrasonic speed at zerostress, dv·(dT)σ

–1 is the temperaturedependence at an induced stress of σ andK is a material constant.110

dvdT

dvdT

dvdT

K

⎛⎝⎜

⎞⎠⎟

−⎛⎝⎜

⎞⎠⎟

⎛⎝⎜

⎞⎠⎟

=0

0

σ σ±

Δvv

B B0

0= + −( )t x yσ σ

Δvv

v v

vBx y

x y0 0

=−

= −( )t t

tt σ σ

Δvv

A0

= σ

L Sc s

tT

or = −

−exp 1


Effect of MagnetizationAcoustoelastic speed changes can bemagnetically induced in ferromagneticmaterials. When an ultrasonic wavepropagates through a ferromagneticmaterial, there is rotational vibration ofmagnetic domains due to magnetoelasticinteractions that affect speed:

(32)

where c is the overall strain due to σu, ce isthe ordinary elastic strain, cm is themagnetostrictive strain, ve is the purelyacoustoelastic value of speed obtained inthe absence of magnetostrictive strain(meter per second), ρ is material density(kilogram per cubic meter) and σu is thestress of the ultrasonic wave (pascal).111

The speed in a ferromagnetic materialat zero magnetic field and zero stress issmaller than the purely elastic value byabout ve·cm·(2ce)–1. The speed firstincreases rapidly with application of amagnetic field and then approaches thepurely elastic value for high fields.

Application of SpeedMeasurementsThe practical use of speed to determineelastic constants and stresses is hamperedby two factors: (1) the effects of test objectgeometry and (2) the effects of texture,porosity and other microstructuralvariations. Geometric simplicity is neededfor valid and accurate measurements ofspeed and speed changes wrought bytemperature and acoustoelasticfactors.112,113

Calibration reference standards canopen possibilities for using speed andacoustoelastic effects to assessmicrostructural anomalies andnonuniformities such as those associatedwith porosity and texture. Ultrasonicspeed measurements can detect volumeand surface stresses but the problem is toseparate the influence of texture andother microstructural factors.106

Elastic ConstantsBecause they are related to interatomicforces, elastic moduli indicate maximumattainable strengths. Elastic moduli alsoappear in equations for strain energyrelease rate and are related to stress wavepropagation properties associated withimpact shock, crack growth and fracture.7There are incentives for convenient,nondestructive means for measuringelastic constants, especially for materialsat extreme conditions and test objects not

amenable to conventional mechanicalinspection methods.

Brittle materials present a specialproblem for measuring elastic constantsby conventional means such as tensile orbending tests. Ceramics in particular areamenable to the use of ultrasonics forelasticity measurements. Other testmethods produce poor results becauseceramics and other brittle solids arevulnerable to fracture from very smallstrains.

Elastic constants at extremetemperatures are most readily determinedwith speed measurements. Longitudinal,shear modulus, bulk modulus andPoisson’s ratio have been measured for aseries of stainless steels down to 5 K.114

Laser ultrasonic techniques have beenused to determine elastic constants ofcermets to temperatures from 500 to1000 °C (900 to 1800 °F).102 Ultrasonicmeasurement of elastic constants forrefractory metals to near melting pointhave been determined using self-heatedwires.115

Stress and TextureIt is convenient to measure stress statesand texture with birefringence because itrequires only the measurement of transittime differences and is independent oferrors in length measurements. Thesemeasurements can be aided byindependent ultrasonic techniques fordetermining texture and anisotropy.116-118

The frequency dependence oftransverse wave birefringence, ultrasonicattenuation and thermoelastic effects canbe used to characterize grain structure andthus separate effects due to texture andanisotropy.103 Experimental evidenceindicates independent correlationsbetween ultrasonic attenuation and stressin aluminum crystals subjected touniaxial compression.4 The temperaturedependence of longitudinal andtransverse waves has been used to producecalibration curves for measuring inducedstress in steel.119 It has also been shownthat stress and texture can beindependently inferred from the angulardependence of polarized plate modespeeds.120

In ferromagnetic materials, an externalmagnetic field can help unambiguouslydetermine the stress dependence of speedchanges.121-122 Magnetically inducedspeed changes can be used to measure theeffects of internal stresses by longitudinalor transverse waves and surface stresses bysurface waves. Magnetoelasticity can beused to determine magnitude, sign anddirection of tensile and compressive orresidual stresses.111

Practical uses of acoustoelasticity forstress state measurements have been

vc

vc

c= =

σρ

ue

m

e

1 –2


applied to stainless steel sheet, plate andpiping106,123 and to railroad wheels, railsand aircraft landing gear.124,125 However,extraordinary precision is required tomeasure changes in acoustoelastic wavespeeds. Because of this, it is advantageousto combine instrumentation with digitalprocessing of the ultrasonic data.66 Fouriertransform techniques greatly improve notonly speed but accuracy in speed phasedelay measurements for residual stressdetermination.126,127


Overview ofMicrostructure andUltrasonic Methods

Microstructure and MorphologyMechanical properties are controlled bycomposition, microstructure andmorphology. Because these factors alsoinfluence ultrasonic wave propagation,ultrasonic characterization of materialproperties is possible. Modulations ofultrasonic waves by material variablesdetermine ultrasonic correlations withstrength, hardness, toughness and othermechanical properties governed by thesame variables.

Diffuse Discontinuity PopulationsThe need for nondestructive materialscharacterization arises when the presence,identity and distribution of minutediscontinuities can only be assessedstatistically. In some materials,discontinuities can be so microscopic,numerous and widely dispersed that it isimpractical to resolve them individually.Porosity in ceramics, crazing incomposites, fatigue and creep damage inmetals are examples of such anomalies.

Large populations of subcriticalmicroscopic discontinuities in associationwith morphological anomalies producedegraded bulk mechanical properties andstrength deficiencies. Although structuresmay be free of single criticaldiscontinuities, they may still besusceptible to failure because ofinadequate or degraded mechanicalproperties.

FundamentalMicrostructure Quantities

Mean Grain SizeA universally cited quantity forcharacterizing polycrystallinemicrostructures is the mean grain size.This quantity is used despite difficultiesinherent in measuring or assigning valuesto it, especially in materials that exhibitcomplex microstructures (subgrains,

second phases or precipitates). Moreover,heating and forming processes tend toresult in nonuniform grain sizes and innonrandom crystallographic orientationssuch as columnar grain growth. Therefore,most real polycrystalline solids possesswhat is known as texturing.4

There are many polycrystallineaggregates having microstructures withreadily defined mean grain sizes.128 Forexample, single-phase polycrystallineaggregates with uniform microstructurestend to exhibit a well defined mean grainsize. In these cases, mean grain size can bedetermined from grain size distributionfunctions (histograms) based onphotooptical (metallographic) analyses byusing standard computer basedtechniques.128,129

Grain BoundariesFrom a purely physical standpoint, graininterfaces, facets and surface areas shouldinfluence mechanical properties ofpolycrystalline and noncrystallineaggregate solids. This is certainly true ofproperties that depend on the surfaceenergy of grains, properties affected bythe grain boundary thickness, propertiesfor which grain boundaries are obstaclesand properties connected with grain andphase boundary migrations andobliterations.

Generally, grain boundaries ofpolycrystalline solids exhibit an abruptchange in acoustic impedance because thecrystallites have different speeds indifferent principal directions. Similarchanges in acoustic impedance and wavepropagation occur in particulatetoughened and fiber reinforced materials,such as those at fiber matrix or whiskermatrix interfaces in ceramic and metalmatrix composites.

Elastic AnisotropyElastic anisotropy and the impedancemismatch at grain boundaries influencewave propagation and scattering. Elasticanisotropy K for cubic crystallites is:

(33) Kc c

c=

−⎛

⎝⎜

⎞

⎠⎟

11 11

11

2


PART 4. Microstructure and DiffuseDiscontinuities

where c is the elastic tensor coefficient(compression modulus); and ⟨c⟩ is itsaverage value.

For cubic crystallites, the elasticanisotropy may also be expressed in termsof acoustic impedance:

(34)

where the acoustic impedances z = ρv arebased on principal longitudinal speeds.The equation is exactly the same for thereflection coefficient R at the boundarybetween two materials as described above.

Speed and AttenuationChanges in wave propagation speed andenergy losses from interactions withmaterial microstructure are the two keyfactors in ultrasonic determination ofmaterial properties. Ultrasonic speed andattenuation measurements are basic.Relatively small variations of speed andattenuation are often associated withsignificant variations in microstructuralcharacteristics and mechanical properties.

Single-frequency, continuous waveultrasound is used in those cases whereunique relations exist at a specificfrequency but speed and attenuation areboth functions of frequency. Withtransducers that emit broad band pulsedultrasound, signals have a wide frequencyspectrum. Generally, each spectralcomponent is affected differently as theultrasound propagates in a material.

In polycrystalline solids, eachfrequency component and wavelength isaffected differently according to grain size,morphology, inclusions, texture andelastic anisotropy. Frequency dependenceof speed and attenuation are veryimportant in the ultrasoniccharacterization of materialmicrostructures, porosity and diffusediscontinuities. It is precisely because ofthese interrelations that ultrasonicmeasurement can assess elastic,microstructural and hence mechanicalproperties of materials.

Ultrasonic Speed andMicrostructureUltrasonic speed in many engineeringsolids (metals, ceramics or linearly elasticmaterials) is directly related to elasticconstants and density (see Table 6). Elasticproperties in turn can depend strongly onporosity and may also depend onprecipitates and other impurities.Although elastic moduli have no basicdependence on grain size, they do depend

on elastic anisotropy and therefore ongrain orientation and microstructuraltexture. Because the size, shape anddistribution of diffuse discontinuities andmicroporosity often correlate with grainsize and shape orientation, there can besecond order correlations among elasticproperties, speed, grain shape and aspectratio.

Effect of PorosityThe equations given to connectpropagation speeds with elastic moduliand density (Eqs. 23 and 24) lead to theexpectation that speed is an inversefunction of density. The converse is truein porous solids where speed increases,usually linearly, with density. Speeddepends on the elastic moduli, Poisson’sratio and density: v = f(L,S,μ,ρ). Themoduli L and S are in turn dependent onpore volume fraction and pore size, shape,orientation and spacing factors.97

Group and Phase SpeedNeither v� nor vt can be measuredunambiguously as unique quantitiesexcept in the case of a nondispersivematerial. A medium may be dispersivebecause of its geometric boundaries orinternal morphology or both. Forexample, speed dispersion occurs in wiresand thin rods or plates when thewavelength nearly equals the thickness.

The bandwidth or main frequencycontent of a pulse traversing a dispersivemedium is altered and may carryinformation on the medium’smacrostructure and microstructure. Inmost solids, the speed dispersion isusually less than a few percent. Byaccounting for phase speed dispersion,measurements of subtle propertyvariations can be made.30,130

For each phase or frequencycomponent of an ultrasonic pulse, there isa particular phase speed v. The pulse(energy) travels with a group speed u.

(35)

and

(36)

where f is frequency (hertz) and λ iswavelength (meter).

The group speed u varies withfrequency depending on the particularvalues assumed by df·dλ–1, which is inturn a function of the phase speed v.Dispersion or variation of speed withfrequency occurs in the case of lamb or

u ff

, λ λλ

( ) = ∂∂

2

v f f, λ λ( ) =

Kz zz z

=−+

⎛⎝⎜

⎞⎠⎟

2 1

2 1

2


plate waves and with guided waveswhenever wavelengths are comparable tothe plate or waveguide dimensions.Techniques of measuring group and phasespeeds are described below andelsewhere.36

Ultrasonic Attenuation andMicrostructureAttenuation measurements are pivotal forestablishing correlations betweenmicrostructure and mechanical properties.Mechanical property characterizationdepends on precise attenuationmeasurements.131,132

Scattering and absorption are theenergy loss mechanisms that governultrasonic attenuation in the frequencyranges of interest for characterizing mostengineering solids. Diffusion, rayleigh andstochastic (phase) scattering losses areextrinsic whereas absorption losses fromdislocation damping, anelastic hysteresis,relaxation and thermoelastic effects areintrinsic to individual grains such ascrystallites.

There are other losses associated withtechniques for measuring attenuation.These are geometric losses such as thosefrom diffraction effects and beamdivergence, which are not inherent tomaterial microstructures. These losses canbe controlled or eliminated fromattenuation measurements byexperimental and data reductionprocedures130 to get the true attenuationcoefficient as a function of frequency.

Attenuation CoefficientAttenuation from scattering and othermechanisms is measured by anattenuation coefficient α usuallyexpressed in terms of the intensity I ofsound after traversing a distance Xthrough a material:

(37)

where I0 is the initial intensity and I0 – I isthe loss in intensity over distance X.

Extrinsic MechanismsScattering usually accounts for thegreatest portion of losses in engineeringsolids. The scatter attenuation coefficientα is a function of frequency f. Inpolycrystalline aggregates (metals andceramics), there are three scatterattenuation processes defined by the ratioof mean grain size D to the dominantwavelength λ (see Table 4). For therayleigh scattering process where λ >> πD:

(38)

For the stochastic (phase) scatteringprocess where λ ≅≅ πD:

(39)

For the diffusion scattering process whereλ << πD:

(40)

The constants Cd, Cp and Cr containgeometric factors, longitudinal andtransverse speeds, density and elasticanisotropy factors.28,133-136

Intrinsic MechanismsAbsorption losses due to dislocationdamping, hysteresis and thermoelasticeffects are intrinsic to grains (crystallites)and involve direct conversion of acousticenergy to heat. These attenuationmechanisms are essentially independentof grain size, shape and volume. Forhysteresis, the absorption losses are:11,137

(41)

For thermoelastic effects, absorption lossesare:138

(42)

Hysteresis losses arise when acousticwaves cause stress-strain dampening.Hysteresis losses with a first powerfrequency dependence are usuallyobserved in single crystals, amorphoussolids and with difficulty inpolycrystalline solids.98 Frequencydependent thermodynamic losses arisewhen longitudinal waves produce heatflow from dilatation to compressionregions.

Viscous losses139 also exhibit a secondpower frequency dependence but aregenerally negligible in solids. Models forabsorption losses caused by dislocationvibrations, relaxation effects and internalfriction predict second power frequencydependence down to frequencyindependence.28,140,141 Absorption lossesdue to electrons or photons comprisespecial cases involving ferromagneticmaterials, very high frequencies orcryogenic temperatures. Magnetoelasticabsorption (due to magnetic domains)tends to occur at frequencies on the orderof 5 to 10 MHz in structural steels.142

αt t= C f 2

αh h= C f

αd d= −C D 1

αp p= C Df 2

αr r= C D f3 4

I I X= −( )0 exp α


Combined ExpressionsTotal attenuation coefficients are usuallywritten as sums of coefficients forscattering and absorption. For example,equations for hysteresis and stochasticattenuation are combined to form anexpression for the total attenuationcoefficient:

(43)

Equations for hysteresis and rayleighscattering are combined to produce:

(44)

Combined expressions are convenientfor fitting experimental data and foranalyzing the contributions ofattenuation mechanisms and underlyingmicrostructural factors.80

Scattering CentersScattering theories used to derive theprevious equations usually considerensembles of scattering centers embeddedin a featureless continuum. Currenttheories for polycrystalline materialsaccount only for scattering by equiaxedgrains, neglecting effects of texture,anisotropy and grain size variations. Wellformulated theories for attenuation existonly for: (1) the simple case ofsingle-phase polycrystalline solids withvirtually identical, equiaxed grains; and(2) frequencies that satisfy the conditionska << 1 or ka >> 1, where k is wavenumber and a is mean scatterer size.

Fourth and second power relationsgiven in the previous equations have beenexperimentally confirmed only for specialcases.143 The fourth power relation forrayleigh scattering was realized bymeasuring scattering due only to sparselydistributed scatterers or minority phases(carbon nodules and inclusions) inpolycrystalline aggregates.144-147

Grain Size DistributionFor most polycrystallines, the overallexperimentally determined frequencydependence of attenuation is not anintegral power even in the rayleigh orstochastic processes. There are a variety ofreasons for this, including the fact thatpremises underlying scatter attenuationequations are not met in engineeringsolids that tend to exhibit a widedistribution in grain size and textured,quasielastic microstructures. Variousinvestigations suggest approaches forhandling the effects of grain sizedistributions. One method is to include a

probabilistic distribution function inscatter attenuation coefficients.34,148-150

Empirical CorrelationsThere are special cases where it is possibleto fit attenuation data with expressionsthat allow the exponent of frequency tobe an experimentally determinedvariable.5,32 The simplest expressions ofthis kind are:

(45)

In Eq. 45, f1 < f < f2 and >α< denotes thatα is empirically defined only in a limitedfrequency range. The quantities c and massume noninteger values and changewith microstructural changes that affectattenuation (mean grain size or sizedistribution). Experimental results showthat the previous equation is statisticallyvalid for fitting attenuation data over afrequency range that spans the rayleighscattering process for a variety ofpolycrystalline materials.84,85,151,152

Applications inMicrostructureCharacterizationSelected examples are given below for avariety of potential applications ofultrasonics for characterizingmicrostructure. These include themeasurements of mean grain size, texture,recrystallization, cure state, porosity anddiffuse discontinuity populations. Theexamples show that simple pulse echospeed or attenuation measurements oftensuffice to establish correlations withmicrostructure.

Speed and attenuation, usually at asingle and sometimes arbitrarily selectedfrequency, correlate well with certainmicrostructural factors in some cases. Thisdoes not mean that the methodologies aresimple, as can be appreciated byconsulting the references cited. There areother cases where empirical correlationsdepend very strongly on makingultrasonic measurements with broad bandwaveforms (100 to 200 MHz bandwidths),followed by detailed comparative analysesof amplitude and phase spectra.

Mean Grain SizePerhaps the most underused yet wellproven capability of ultrasonics is theestimation of mean grain size in simplepolycrystalline solids. Literature surveysshow that there has been extensive workdedicated to ultrasonic assessment ofgrain size.79,153 Abundant data existshowing the capability of ultrasonics for

> < =α c f m

αhr h r= +C f C D f3 4

αhp h p= +C f C Df 2


assigning photomicrographicallyconfirmable values to the mean grain sizein polycrystalline solids.42-44,154-155

Strong incentives exist for in-processmonitoring of grain size andmicrostructure in materials research anddevelopment and in manufacturingenvironments.156,157 There is stronginterest in ultrasonic assessment ofmicrostructural quantities like grain sizebecause of their role in governingmechanical properties, such as strengthand toughness. Many empiricalcorrelations that demonstrate relationsbetween grain size and strength propertiescan be exploited in research andindustry.155,158

Techniques for ultrasonic grain sizedetermination use both speed andattenuation measurements. Theoreticalbases for speed correlations with grain sizeare virtually nonexistent compared withthe equations connecting attenuation andgrain size given previously. Speed dependson elastic properties that have no basicdependence on grain size.2,97 Still, in mostpolycrystalline aggregates, elasticproperties and speed are affected by grainboundary impurities and grainorientation. Consequently, there areexamples of empirical correlationsbetween speed and mean grain size inpolycrystalline solids (see Fig. 9).5

Attenuation spectrum analysis isfundamental for developing correlationswith grain structure. Pulse echo andbackscatter are methods used for

attenuation spectrum analysis.30,42,43

Excellent correlations betweenattenuation and mean grain size inpolycrystalline materials are obtained inthe rayleigh scattering frequency processusing the pulse echo technique and broadband spectrum analysis (seeFig. 10).80,147,149,153,159 In addition,noncontact laser generation and detectiontechniques have been used for measuringfrequency dependent attenuation andforward scattering to assessmicrostructure.54 Characterization ofanisotropic and textured metals andcomposites presents special problems.Directional speed variations andacoustoelasticity are appropriate formicrostructure and texturecharacterization of these materials. In thecase of texture characterization, thereremains the problem of separating thecombined effects of texture and residualstress. Surface wave birefringence, speeddispersion and speed slowness curves havebeen proposed for separating effects oftexture and stress in textured monolithicand composite materials.160-162

Tests of rolled aluminum plate haveillustrated the use of rayleigh waves formeasuring subsurface texture. The resultscompared well with various texturecoefficients obtained by X-ray polefigures.163 Columnar grain structure and


FIGURE 9. Relation between speed and grainsize at frequency of 30 MHz for titaniumalloy.184

58 62 66

Spee

d (k

m·s

–1)

Grain size (µm)

6.05

5.95

5.85

5.75

5.65

FIGURE 10. Calibration curves for mean grain size and itseffect on attenuation spectra for heat treated copper andnickel samples: (a) 99.99 percent pure copper;(b) 99.5 percent pure nickel, Unified Numbering SystemN02200.34

Att

enua

tion

coef

ficie

nt(N

p·m

–1)

Frequency (MHz)

1000

800

600

400

200

00 20 40 60 80 100

50 ±

2 µm

40 ±

2 µm

30 ±

2 µm

20 ±

2 µm

15 ±

2 µm

Att

enua

tion

coef

ficie

nt(N

p·m

–1)

Frequency (MHz)

1500

1000

500

00 20 40 60 80 100

50 ±

2 µm

25 ±

2 µm

15 ±

2 µm

(a)

(b)

elastic anisotropy in cast stainless steelhas been determined even in thick walledcomponents by speed measurements.164 Akey factor was the measurement ofultrasonic beam skewing by the crystallinetexture. The beam skewing was foundonly in columnar and not in equiaxedmicrostructures.118

Recrystallization and PrecipitationOne method for controlling metallicproperties is to apply thermomechanicalprocessing such as cold working and agingto increase strength. After cold working,there is usually a need for annealing torelieve residual stresses and to soften themetal by recrystallization. Changes in theslope (first derivatives) of broad bandattenuation spectra were found tocorrelate quite well with stages ofrecrystallization in nickel.165

In the case of rapidly solidifiedpowders, it has been shown that bothattenuation and backscattermeasurements reveal the onset ofrecrystallization and grain growth.48

Amorphous materials such as glassymetals and alloys revert to a crystallinestructure and lose advantageous propertiesunder certain thermomechanicalconditions. Clear changes in longitudinalspeed have been shown to accompanytransitions from the amorphous to thecrystalline state in metallic glass ribbonsproduced by melt spinning.55,166

Precipitation hardening or aging is alsoan important metallurgical process forimproving the strength of structuralmetals. Strength improvements dependon spacing, size, shape and distribution ofprecipitated particles. Ultrasonic speedand attenuation correspond tomicrostructural changes that increaseboth hardness and strength during theaging process of aluminum alloys.55

Porosity and DensityThe strength lowering effects of porosityaffect all structural materials, from powdermetallics to monolithic ceramics,polymers and their composites. Thepresence of porosity can be determined byspeed or attenuation measurements. Thegoals are (1) to characterize mean poresize and (2) to distinguish porosity fromgrain structure in metals or ceramics andfrom fiber content in composites.Complementary use of radiography canhelp make this distinction. In mostporous solids, speed varies linearly andinversely with porosity and directly withdensity (Fig. 11).99 For polyethylene, animportant commercial material,compressional and transverse wave speedsstrongly correlate with density, althoughthe correlation is nonlinear.167

Complementary speed and attenuationspectral measurements can also help todifferentiate density and grain structureeffects in polycrystalline solids (Fig. 12and Table 7).168 Attenuation spectra areuseful for differentiating porosityvariations from roughly 0.2 to 5 percentin an aluminum alloy.169 Spectral analysisof backscatter radiation is used tocharacterize porosity in a fiber reinforcedcomposite.67 The approach uses spectralsignal analysis to reveal both fiber relatedordered structure and random poredistribution.

Using a powder metallurgy alloy as amodel has provided a demonstration ofthe viability of both attenuation andbackscatter spectra for characterizingporosity.50 The results show that thedominant cause of attenuation andtherefore backscatter is a densedistribution (100 per cubic millimeter) ofmicropores (10 µm radius). The porosity isbeyond the ability of the technique to


FIGURE 11. Correlation between ultrasonicspeed and material density for monolithicsintered alpha silicon carbide.99

Ultr

ason

ic s

pee

d (k

m·s

–1)

Bulk density (mg·mm–3)

12.3

11.8

11.4

11.0

10.62.8 2.9 3.0 3.1 3.2

100 percent dense

FIGURE 12. Representative attenuationspectra for three samples of monolithicsilicon carbide with deliberately variedmicrostructures.168

Att

enua

tion

(Np

·m–1

)

Frequency(MHz)

300

200

100

075100 125 150

1

Grain Porosity

5 µm 5 µm

2

3

resolve individual pores. This is anexample of nonimaging analyticalultrasonics for characterizingmicroporosity.

Diffuse Discontinuity PopulationsIn a sense, diffuse discontinuitypopulations define material properties anddynamic response just as microstructuredoes. Diffuse discontinuities are eitherinherent to the material from processingor are introduced by thermomechanicaldegradation. Examples are porosity thatresults from sintering of ceramics ormicrocracking that results from fatiguingof metals and composites.

In both cases, the discontinuitiesconsist of diffuse populations of smalldiscontinuities that exist globally or inlocalized colonies and it is impractical toattempt to resolve them individually.Because no one discontinuity isdominant, it is virtually impossible tocharacterize any one as a potentialfracture origin. Instead, the problem is tocharacterize the population in terms ofmean size, number per unit volume ornature (void or inclusion).


TABLE 7. Representative speed and density data for three samples of monolithic siliconcarbide with deliberately varied microstructures (see Fig. 12).

Sintering Conditions Mean___________________________________________ Mean Grain Mean

Temperature Time Pressure Density Size SpeedSample (°C) (h) (atm) (kg·m–3) (µm) (km·s–1)

1 2300 1.0 1 3054 12 11.652 2150 4.0 1 3058 4 11.673 2200 0.5 1 3117 6 11.80

Determination of mechanical propertieslike strength and toughness isconventionally done with destructivetests. At the expense of material andmanufacturing costs, destructive testsprovide data that cannot be duplicated bynondestructive methods. Destructivetesting in the laboratory is the basis forestablishing ultrasonic correlations withmechanical properties. In-process andcontinuous monitoring of mechanicalproperties is a strong incentive fornondestructive materialscharacterization.155,157

Empirical correlations between speedand attenuation and various mechanicalproperties have been reported in theliterature. However, theoreticalfoundations for the correlations are notwell developed. In some instances, thecorrelations appear fortuitous and dependon conditions peculiar to individualmaterials. Nevertheless, theoretical modelspredict correlations between ultrasonicand mechanical properties.

Theoretical foundations and examplesof experimental validations are presentedbelow for ultrasonic assessments of severalkey mechanical properties: strengths(tensile, yield and shear), fracturetoughness and hardness. The examplesconsist primarily of laboratorydemonstrations of ultrasonicmeasurements and indicate thecapabilities of ultrasonic material propertyassessment on the basis of calibrationsderived from destructive testmeasurements.

Ultrasonics andMechanical PropertiesWave speeds are directly related tomaterial moduli (Table 6). Because moduliare in turn directly related to interatomicforces, attempts have been made to linkspeed to material strength. But materialstrength is not dependent only on modulior elastic spring constants. For example,although some alloys can be processed toincrease their fracture toughness by afactor of ten or more, elastic moduli suchas Young’s modulus remain essentiallyconstant.

In polycrystalline solids, microstructureand morphology play important roles indetermining extrinsic mechanical

properties like strength and toughness.Strength and fracture toughness areextrinsic to elastic properties of individualcrystallites or grains. Ultimate tensile andyield strength, ductility, toughness andother mechanical properties are governedby microstructural factors that includedislocation densities; grain size, aspectratio and orientation; grain interfaceproperties; impurities; phase structure;and other features in aggregate. Althoughspeed can be correlated with some ofthese factors, attenuation measurementsare much more sensitive to themicrostructural factors that governstrength, toughness and other mechanicalproperties. For example, in metallicpolycrystallines, the pivotal factors appearto be grain structure, morphology anddislocation density, all of which havestrong effects on attenuation.

To establish correlations withmicrostructural factors that governmechanical properties, precise ultrasonicmeasurements based on the pulse echoapproach are necessary. Attenuationspectra (attenuation coefficient versusfrequency curves) need to be carefullydetermined for each material. Subtle butimportant variations in the microstructureappear as changes in slope and otherparameters that define the attenuationspectrum.

The emphasis on attenuation does notpreclude speed or other basicmeasurements for obtaining correlationswith mechanical properties. Certainly, anyapproach sensitive to microstructuralvariables should be invoked and studied.For example, wave speeds have beenshown to correlate with age hardening ofsteels.55 The ductility of diffusion bondsin titanium has been assessed usingultrasonic reflection coefficients.170

Mechanical strengths of gray cast ironsand cobalt cemented tungsten carbidescan be inferred from internal frictiondamping measurements.171

Tensile and Yield Strength

Griffith ModelRelations between strength and grain sizecan be derived from the griffith criterion,which relates strength σ to crack size:


PART 5. Ultrasonic Testing for MechanicalProperties

(46)

where c is half the length of a semicircularsurface crack or notch (meter) and KIc isthe plane strain fracture toughness (pascalroot meter). Equation 46 has beenmodified to give a grain size dependenceof strength:

(47)

where A is a stress intensity constant forthe material’s grain structure (pascal rootmeter) and D is mean grain size (meter).

In this modification of the griffithcriterion, grains are assumed to act asedge or crack discontinuities. Thequantity A depends on composition,phase structure, texture and othermorphological factors. In carbon steel, Adepends on the percent of pearlite.156

Hall-Petch ModelThe hall-petch model further modifiesEq. 47 to give:

(48)

where σi is a yield stress. The hall-petchmodel assumes that dislocation motionsin a grain are arrested by grain boundariesand that any tensile stresses associatedwith dislocation pileups are sufficient tocause fracture. In this case, σi is the yieldstress of the metallic grain.172-174

Investigations have shown that yieldstrength obeys the hall-petch relation andthat yield strength has the predicteddependence on grain size for plain carbonsteels (see Fig. 13).156,158 Although tensilestrength also obeys the hall-petchrelation, it is less sensitive to grain sizeand the quantity A for tensile strength isabout half of that for yield strength. Thehall-petch relation is not necessarilylimited to tensile or yield strength. Anyproperty that depends on dislocationmotions and grain structure may inprinciple be characterized by thehall-petch relation. Such propertiesinclude hardness, fatigue limit, impactand ductile brittle transitiontemperatures.175-178

Nondestructive prediction of grain sizedependent properties is based on relationsbetween extrinsic attenuation and meangrain size (see the discussion ofmicrostructure and diffusediscontinuities). The predictions dependon attenuation measurements primarily inthe rayleigh scattering process. From

variations in attenuation spectra, it ispossible to infer mean grain size for thehall-petch equation.80,149,178,179 It shouldbe remembered that factors other thangrain structure (porosity, for instance)influence both attenuation andmechanical properties. These other factorsmay dominate both attenuation spectraand strength and lead to ambiguities inultrasonic property correlation.

Although the preceding equationsapply fairly well to polycrystalline metals,they require modification for brittlematerials. For ceramics, either maximumgrain size or discontinuity size must besubstituted for D in the griffith equationto predict flexural strength.180 That is,discontinuities rather than grain sizegovern the strength of monolithic brittlematerials. In ceramics, large numbers ofdiscontinuities may be distributedthroughout a component’s volume so thatlarge grains, microvoids or microcrackscan appear as diffuse discontinuitypopulations. In this case, meandiscontinuity size needs to be substitutedfor D in the griffith relation to predictstrength.

HardnessTensile strength, yield strength andhardness are interrelated in polycrystallinemetals. Because it is simple and essentiallynondestructive, microhardnessindentation testing is often used toestimate tensile and yield strengths.181

Hardness measurements can also beaccomplished by a resonant vibrationmethod related to microindentation. Theresonance method uses a piezoelectrictransducer mechanism to measurehardness.10

σ σ= +i

A

D

σ = A

D

σπ

=K

cIc


FIGURE 13. Measured yield strength for plain carbon steelversus yield strength calculated from hall-petch relation andmetallographically measured grain size. Standard error is15.4 MPa (2.234 × 103 lbf·in–2).158

Mea

sure

d yi

eld

stre

ngth

, M

Pa(1

03lb

f·in.

–2)

Calculated yield strength, MPa(103 lbf·in.–2)

360 (52.2)

320 (40.6)

280 (34.8)

200 (29.0)

160 (23.2)

160 200 240 280 320 360(23.2)(29.0) (34.8) (40.6) (46.4) (52.2)

Nondestructive methods forunambiguous determination of hardnessare in high demand. Ultrasonictechniques can form a basis for inferringstrength from hardness and can providecontinuous monitoring of hardness inproduction control.

Experimental evidence shows thatpulse echo speed and attenuationmeasurements can uniquely determinehardness (within limits that depend onthe material). This experiment wasconducted with variously age hardenedspecimens of an aluminum copper alloy.55

Although speed varies parabolically withhardness in the alloy, attenuation varieslinearly and inversely with hardness (Fig.14).

In another investigation, an anglebeam pulse echo backscatter method wasused to estimate case depth in hardenedsteel.46 Case hardening has also beenmeasured by dispersion of rayleigh(surface) waves.182 Depth of hardness invarious steel grades was found to relate toa break in the slopes of speed changeversus wavelength curves.

Fracture ToughnessFracture toughness is (1) an extrinsicmaterial property that depends onmicrostructure and (2) a measure of amaterial’s fracture resistance. Fracturetoughness quantifies the critical stressintensity at which a crack of particularsize becomes unstable and growscatastrophically.7 Governed by more thanmean grain size, fracture toughness isdetermined in polycrystalline solids bygrain boundaries, shapes, aspect ratios,subgrain structure, dislocation densitiesand other morphological factors.

Stress Wave Interaction ModelThe basis for ultrasonic assessment offracture toughness is the concept of stresswave participation in the fracture processduring catastrophic crack growth. Theconcept assumes that the attenuationproperties of a material microstructure areimportant in the fracture process.

A stress wave interaction model basedon this concept helps explain existingcorrelations between ultrasonicattenuation and fracture toughness.153,183

By using the stress wave interactionmodel in conjunction with fracturemechanics precepts, it is possible to deriverelations between fracture toughness andattenuation factors.184-187

Toughness and Ultrasonic FactorsThe key relation derived from the stresswave interaction model expresses the ratioof fracture toughness to yield strength asa function of speed and attenuationspectrum parameters:

(49)

where KIc is plane strain fracturetoughness (pascal root meter), M is amaterial constant, m is the exponent onfrequency f in the equation for therayleigh scattering process attenuationcoefficient α = cfm, v� is longitudinalvelocity (meter per second), σy is yieldstrength (pascal) and βδ is the derivative.

(50)

where dα·(df )–1 is evaluated at a frequencythat corresponds to a critical ultrasonicwavelength λδ in the material. Thiswavelength is defined by the criticaldimension δ, which may be the meangrain size or another feature thatparticipates in crack nucleation anddeformation processes.

The quantity (KIc·σy–1)2 is known as the

characteristic length and is also a measureof fracture toughness.188 It is proportionalto the size of the crack blunting zone atan active crack tip. This assumes amaterial in which plastic deformation orsome similar micromechanism exists forabsorbing stress wave energy at a crackfront, such as occurs in a polycrystallinemetal.

The preceding equation forcharacteristic length can be rewritten as:

β αδ

δ

= dd f

KM

vm

Ic

yσβδ

⎛

⎝⎜

⎞

⎠⎟ =

2

�


FIGURE 14. Linear correlation of ultrasonicattenuation with age hardening of samplesof Unified Numbering System A92024 heattreatable wrought aluminum alloy,temper 351.55

Har

dnes

s (r

ockw

ell B

)

Ultrasonic attenuation (dB·m–1)

85

80

75

70

65

60355 360 365 370 375 380

(51)

where αδ is specific (phase) attenuationfor the critical microstructural feature.132

It is true that this critical feature and itsmean size δ must be presupposed toevaluate the characteristic length in eitherof the preceding equations. However, intheory δ can be deduced from attenuationspectra because it is defined in terms ofthe mean (phase) wavelength at which

stochastic scattering begins.80,149,179,184 Asecond relation that can be derived fromthe stress wave interaction model is:

(52)

where A, B and C are material constants.The ultrasonic factor β1 is the slope of theattenuation a versus frequency f curveevaluated at α = 1.84,184

Experimental ResultsThe foregoing relations between fracturetoughness, yield strength and ultrasonicspeed and attenuation have beenverified.84,85,189 As expected, even largechanges in fracture toughness producedonly slight changes in speed. By contrast,fracture toughness, yield strength andcharacteristic length (KIc·σy

–1)2 appear tobe strongly influenced by stress waveattenuation properties of the testedmaterials. As a practical matter for somepolycrystalline materials, it is unnecessaryto determine the critical microstructuralfeature δ to calculate βδ. This is becausecorrelations with fracture toughness canusually be obtained by directly comparingit to the attenuation coefficient measuredat the highest frequency within rayleighor stochastic scattering, at 100 MHz forexample (see Figs. 15 and 16).152

Figures 17 and 18 show results for twomaraging steels and a titanium alloywhere the critical microstructural factor δ

σ βy AK B C= + +Ic 1

KMIc

yσδα δ

⎛

⎝⎜

⎞

⎠⎟ =

2


FIGURE 15. Correlation between ultrasonicattenuation factor and toughness for threeheats of low carbon steel; photomicrographsshow decreasing grain size associated withincreased toughness and attenuation.132

Ultr

ason

ic a

tten

uatio

nat

30

MH

z (N

p·m

–1)

Toughness according to dropweight tear test (percent)

300

250

200

150

10050 60 70 80 90 100

40 µm

FIGURE 16. Correlation between ultrasonicattenuation factor and toughness for cobaltcemented tungsten carbide.Photomicrographs show that toughness andattenuation increase with cobalt bindercontent. Toughness measured by palmquisttechnique is directly proportional to fracturetoughness.152

Ultr

ason

ic a

tten

uatio

nat

100

MH

z (N

p·m

–1)

Toughness (kg·mm–1)

800

600

400

200

00 200 400 600 800 1000

5 percentcobalt

10 percentcobalt

16 percentcobalt

FIGURE 17. Experimental results showing predictedcorrelation of ultrasonic attenuation factor and fracturetoughness characteristic length factor for two maragingsteels and titanium alloy.84

Ultr

ason

ic a

tten

uatio

n fa

ctor

(Vl·β

δ·m

–1)

Characteristic length, mm (in.)

6

1

0.1

0.011 10 20

(0.04) (0.4) (0.8)

Legend= Unified Numbering System K92820 nickel alloy maraging steel= Unified Numbering System K92890 nickel alloy maraging steel= titanium beta alloy (8Mo, 8V, 6Cr, 4Mo, 4Zr)

was determined from photomicrographsusing the ASTM line intercept method.Figure 18 shows that the well knowninverse relation between fracturetoughness and yield strength becomesmore coherent when yield strength iscompared with the expression:

(53)

which is based on Eq. 52. The slopes ofthe lines in Fig. 18a depend on whetherthe material fractures in a brittle orductile manner.184

In the case of a titanium alloy with atwo phase alpha/beta subgrain structure,there are several possible critical features.As demonstrated in Fig. 19, regressionanalysis of the data indicates that the betaphase component has the greaterdislocation density and is the criticalmicrostructural feature. The alpha phase

component is comparable to the betacomponent but has a smaller correlationcoefficient.85 Although the ultrasonic datashow the beta component to be criticalfor plastic yielding, the ultrasonic data donot conflict with fractographic dataindicating that the alpha component addsto toughness by increasing crack pathdeflections. The results in Fig. 19 arebased on using photomicrographicallymeasured alpha and beta phase plateletthicknesses for a series of test objects heattreated to achieve different toughnesses.The phase thicknesses were taken as thecritical microstructural dimensions forcalculating βδ.

These results infer that higherattenuation leads to greater toughness.But the results predicted by Eqs. 49 and51 and shown in Figs. 17 and 19 apply tomaterials that exhibit plastic deformation.In brittle materials (ceramics) that do notprovide for plastic absorption of stresswave energy, higher attenuationcorresponds to lower toughness.

a BAB

K= +1 Ic


FIGURE 18. Experimental results showingpredicted relations among yield strengthand ultrasonic factor incorporating fracturetoughness and attenuation for titanium alloyand maraging steel: (a) yield strength versusthe ultrasonic factor β1 + (A·B –1)Klc(toughness modified by attenuation)(b) conventional plot of yield strength versustoughness.184

Yiel

d st

reng

th,

MPa

(103

lbf·i

n.–2

)

Ultrasonic factor (µs·mm–1)

1600

1400

1200

1000–4 –2 0 2 4

Fracture toughness, MPa root meter(103 lbf·in.–2 root in.)

Legend= Unified Numbering System nickel alloy steel

(Ni 200)= titanium beta alloy (8Mo, 8V, 6Cr, 4Mo, 4Zr)

Yiel

d st

reng

th,

MPa

(103

lbf·i

n.–2

)

1600

1400

1200

1000

(a)

(b)

40 60 80 100 120(36) (55) (73) (91) (109)

FIGURE 19. Comparison of toughness (characteristic length =[Klc /σy]2) and attenuation factors for critical microstructuralfactors in a two-phase titanium alloy. Best correlation is withthe beta phase which, along with the alpha phase, governsfracture toughness: (a) alpha phase thickness with correlationfactor of 0.977; (b) beta phase thickness with correlationfactor of 0.998.85

Cha

ract

eris

tic le

ngth

,m

m(in

.)

Ultrasonic attenuation factor(v�·βδ·m–1)

10 (0.4)

1 (0.04)

0.1 (0.004)100 101 102

(a)

(b)

Cha

ract

eris

tic le

ngth

,m

m(in

.)

Ultrasonic attenuation factor(v�·βδ·m–1)

10 (0.4)

1 (0.04)

0.1 (0.004)100 101 102

Interrelated FactorsFigure 19 exemplifies an important idea inthe nondestructive testing of mechanicalproperties and microstructure. Anyevaluation is incomplete unless threecomplementary factors are tied together:ultrasonic nondestructive testingmeasurements, microstructurecharacteristics and mechanical properties.Conventional destructive methods inmaterials characterization usually attemptto uncover only correlations betweenmicrostructure and destructive test results.

It has been shown that ultrasonictesting is an alternative means formicrostructure characterization. Moreover,the results cited above indicate thatultrasonic measurements can not onlycorrelate with destructively measuredmechanical properties but can also helpidentify microstructural features thatgovern those properties. Figure 19 is anexample of a case where three factors aretied together by means of ultrasonictesting.132

General ApplicabilityThese examples of ultrasonic tests ofmechanical properties are special casesthat require constraints on the test objectas itemized in Table 3. The closecorrelations found between ultrasonicmeasurements and mechanical propertiesdepend on high precision in thedetermination of speed and attenuationspectra. This is not universally possibleeven when monolithic materials andcomposite materials add furtherdifficulties.

Precision ultrasonic methods are notalways necessary. Typically, continuousfiber reinforced and woven fibercomposites are highly attenuating andheterogeneous. They do not typically lendthemselves to precise ultrasonicmeasurements in the appropriatefrequency ranges. Therefore, somealternative approaches have beendeveloped, including theacoustoultrasonic method. With thismethod, precision measurements ofabsolute attenuation and speed are notnecessary. Instead, relative stochastic wavepropagation effects are used to assessmechanical properties.52

Composite and BondStrengthsThe relations among grain size, strengthand toughness properties do not apply tofiber reinforced composites or fibermatrix, laminated and bonded interfaces.Theoretical foundations are beingdeveloped to better explain correlations

between ultrasonic measurements andmechanical properties of compositematerials and bonded interfaces. For fiberreinforced composites, the efficiency ofstress wave energy propagation appears tounderlie strength correlations.53

The concept is that more efficientstress wave energy transfer (higher speed,lower attenuation) leads to bettertransmission of dynamic strain, betterload distribution and consequently togreater strength, impact resistance andfracture resistance. This generalizationleads to ultrasonic methods that placeemphasis on waveform analysis to extractinformation relating to the combinedeffect of microstructural factors anddiffuse discontinuity populations thatinfluence mechanical strength, toughnessand dynamic response (as in compositesand structures with bonded interfaces).Examples of methods that use thisconcept are given below.

Interface and Bond StrengthsUltrasonic assessment of cohesive andadhesive bond and interface strengths isgenerally based on interface reflectivityvariations associated with bond quality.47

Assuming good mechanical or chemicalbonding, there is no overt discontinuitybut there is usually a definite jump inacoustic impedance. This results indifferent reflection coefficients accordingto the nature of the joined materials andthe bond quality. If the bond line is offinite thickness, it may containmicroporosity or other diffusemicrostructural discontinuities that causelower strength.

A theoretical basis for ultrasonic bondstrength assessment has been proposed inwhich transverse waves are used to testthe cohesive shear strength of the bondline or interface adhesive strength.62 Thisrequires the introduction of interface orguided lamb waves using obliqueincidence pitch catch techniques.Interface waves arise when bondedadherent thicknesses are much greaterthan the wavelengths used. Guided lambwave modes arise when the bond line oradherent thicknesses are comparable tothe wavelengths used. One approach is touse speed measurements to estimate shearstrength from shear modulus. Anotherapproach uses attenuation measurementsto estimate strength by sensingmorphological variations in bondlines.

Composite StrengthsUltrasonic tests can form the basis formeasuring energy transfer efficiency andfor ranking composite componentsaccording to strength. Ultrasonicattenuation and speed vary with the


combined effects of fiber matrix interfacequality, matrix porosity, fiber and plyorientation and other microstructuralfactors.

These same factors govern mechanicalproperties (ultimate tensile strength,interlaminar strength, impact strengthand toughness). Ultrasonic attenuation inpolymer matrix composite laminatescorrelates with ultimate strength,interlaminar shear strength and stiffness.The measurements can be accomplishedby through-transmission, pulse echobackscatter and acoustoultrasonicmethods.51,52,61,190-192


The acoustoultrasonic approach tocharacterization of composite and bondstrengths is highlighted below. Examplesare given of applications to compositepanels and adhesive bonds. In both cases,the acoustoultrasonic signal consistsprimarily of the superposition of multiplereverberations of waves reflected bybounding surfaces and internal interfaces.The waveforms usually result fromstochastic interactions and have thegeneral nature of burst waveforms foundin acoustic emission.19

In the acoustoultrasonic method, thestress wave factor is used to quantify thesignal. Lower values of the stress wavefactor generally correspond to higherattenuation.

The stress wave factor may be definedin a variety of ways based primarily onacoustic emission practice: ringdowncount, peak voltage or root mean squareenergy of the time domain signal (seeFig. 20).20,53,61 Spectral analysis andpartitioning of acoustoultrasonic signalsare additional means for assigning valuesto the stress wave factor and forcomparing the relative strength ofcomposite test objects(Fig. 21).52,59,74,75,190,191,193,194

Typical acoustoultrasonic waveformsare shown in Fig. 22 for twounidirectional composite panels andtransducers to illustrate the effect of fiber


PART 6. Acoustoultrasonic Tests for MechanicalProperties

FIGURE 20. Diagram of two basic techniquesfor quantifying of acoustoultrasonic stresswave factor: (a) peak voltage (SWF) =Ev = Vmax; (b) ringdown count Ec = PRC,corresponding to positive thresholdcrossings.20

Peak voltage Threshold

Ringdown count = 7

(a)

(b)

LegendC = ringdown countP = pulse rateR = reset time

SWF = stress wave factor

Am

plit

ude

(rel

ativ

e sc

ale)

Time (relative scale)

FIGURE 21. Alternative approaches to acoustoultrasonic stress wave factor quantification.53

Time domainanalysis

Acoustoultrasonicwaveform

Frequency domainanalysis

Ringdown count

Peak voltage

Energy

Amplitude root mean square

Waveform partitioningand regression analysis

Power spectrum

Spectrum root mean square

Spectrum partitioningand regression analysis

Energy distribution by method of momentsand pattern recognition analysis

Signal analysis techniques Stress wave factor

direction relative to the sending andreceiving transducer. It is apparent thatsignificant changes in the waveform occuras ply orientation changes from axial totransverse. The changes in waveforminclude signal strength, shape, speed andfrequency content. The net change canoften be quantified by a simple ringdowncount to calculate stress wave factorvalues parallel and perpendicular to thefiber direction.

The stress wave factor measurementswere made on a series of laminatedcomposite panels with a variety of plyorientations (various fiber directions). Theresults in Fig. 23 show that thenormalized stress wave factor correlateswith ultimate tensile strength as governedby ply orientation.82

Interlaminar ShearStrengthThere are other means for evaluating thestress wave factor when simple ringdowncounts produce poor correlations.Information contained in theacoustoultrasonic signal can be exploitedby alternative analysis methods. One ofthese is waveform (or spectrum)partitioning in which that part of thewaveform (or spectrum) that best

correlates with a particular property isdetermined by regression analysis.59

The result given in Fig. 24 is an exampleof this approach, where regressionanalysis showed the partition of theacoustoultrasonic waveform giving thebest correlation with interlaminar shearstrength. In this case, a relative stresswave factor was defined as:

(54)

This is the integral of voltage squared overthe time zone of the partition t1 to t2.

SWF = ∫V dtt

t

2

1

2


FIGURE 22. Typical waveforms foracoustoultrasonic signals that have traveledin unidirectional composite panels:(a) waveform for travel parallel to fibers;(b) waveform for travel perpendicular tofibers.

(a)

(b)

LegendS = sending piezotransducer coupled to panel surfaceR = receiving piezotransducer coupled to panel surface

Axial fibers

S R

Receivedsignal

Transverse fibers

Receivedsignal

S R

FIGURE 23. Stress wave factor versus ultimate tensile strengthfor series of graphite fiber, epoxy matrix composite laminatesamples with various ply orientations. Stress wave factorcalculated from ringdown count.82

Nor

mal

ized

str

ess

wav

e fa

ctor

(rel

ativ

e un

it)

Ultimate tensile strength, GPa (103 lbf·in.–2)

1.0

0.10.01 0.1 1 10(1.45) (14.5) (145) (1450)

Ply angles

Legend= 1.57 rad (90 deg)= 0.18 rad (10 deg)= ±0.79 rad (±45 deg)= 0 ± 0.79 rad (0 ± 45 deg)= 0 rad

FIGURE 24. Stress wave factor versus interlaminar shearstrength for filament wound graphite epoxy composite bendtest objects. Stress wave factor is the integral of voltagesquared over a partitioned zone of the waveform.Correlation factor is 0.968.59

Stre

ss w

ave

fact

or (

rela

tive

unit)

Interlaminar shear strength, MPa (103 lbf·in.–2)

0.5

0.25

08.5 9.0 9.5 10(1.2) (1.3) (1.4) (1.45)

Poor correlations or indeterminate resultswere found in other time partition zonesor over the entire time window of thewaveform.

Adhesive Bond StrengthAn alternative approach to defining thestress wave factor was found useful inestablishing a correlation with the shearstrength of adhesively bonded steelplates.61 For the results given in Fig. 25,the stress wave factor was expressed as avoltage weighted ringdown count:

(55)

where Ci is the number of counts at theith level, Vi is the threshold voltage at theith level and Vp is the peak voltage of thewaveform.

In this case, the entire raw waveformabove a preselected minimum voltagethreshold was used to quantify the stresswave factor. However, conditions maydictate that the best correlation dependson first filtering the raw waveform anddealing only with that portion of thesignal within a preselected bandwidth orfrequency zone.195

Modulus DegradationAnother alternative for defining the stresswave factor is given with respect tomeasuring changes in modulus (stiffness)associated with cyclic fatiguing andassociated microcracking (see Fig. 26).196

In this case, the stress wave factor wasdefined as the root mean square value ofthe power spectrum of theacoustoultrasonic waveform.190

Note that the stress wave factor isabout ten times more sensitive to theeffects of fatigue damage than the secantmodulus measurement. Moreover, theslopes of the two curves in Fig. 26 differin detail because, although the secantmodulus refers to the length of the entiretest object, the stress wave factormeasurements represent only part of it.

Limitations ofAcoustoultrasonicTechniquesAcoustoultrasonic testing represents ageneralized approach for materialscharacterization and carries both thecapabilities and the limitations found in avariety of kindred techniques. Beyond thelimitations common to all discontinuitydetection methods, the ultrasoniccharacterization of subtle discontinuitiesand material properties is also subject tocircumstances that affect sensitivity andsignal reproducibility.197

Both the acoustoultrasonic and pulseecho technique are vulnerable totransducers misalignment and couplantvariations. With pulse echo ultrasonictesting, it is common to misreadattenuation by a factor of ten or more.

SWF = −( )+∑V C Ci i i

i

p

1


FIGURE 25. Stress wave factor versus shearstrength of adhesively bonded steel testobjects for range of test temperatures. Stresswave factor was calculated as voltageweighted ringdown count with correlationfactor of 0.964.61

Nor

mal

ized

str

ess

wav

e fa

ctor

(rel

ativ

e un

it)

Normalized average shear strength

1.2

1.0

0.8

0.6

0.4

0.2

00.2 0.4 0.6 0.8 1.0 1.2

Legend= 30 °C (85 °F)= 60 °C (140 °F)= 90 °C (190 °F)= 120 °C (250 °F)= 150 °C (300 °F)

FIGURE 26. Covariation of stress wave factor and secantmodulus with fatigue degradation in graphite epoxy fibercomposite laminate. Stress wave factor is the root meansquare of the power spectrum.190, 196

Nor

mal

ized

sec

ant

mod

ulus

Number of fatigue cycles (thousands)

1.0

0.96

0.92

0.88

0.84

0.8 Nor

mal

ized

str

ess

wav

e fa

ctor

1.0

0.8

0.6

0.4

0.2

00 10 20 30 40 50 60 70

Loading ratio R = 0.1[0, 90, ±45]S laminate

Stiffness(left scale)

Stresswavefactor

This magnitude of error can occur if thetransducer is not literally ground onto thetest object surface.28 This error isparticularly common at high frequencies(over 20 MHz) where couplant thicknessvariations, bubbles, surface porosity andreflection coefficient anomalies can haveserious effects.29,33

Factors Affecting Test ResultsAcoustoultrasonic measurements areaffected by several factors associated withthe attachment of the transducer to thetest object: (1) applied pressure, (2) typeand amount of couplant, (3) objectsurface roughness, (4) transduceralignment, (5) spacing betweentransducers and (6) exact location oftransducers on the object.

Even if these are optimized, a furtherproblem remains. In practice,acoustoultrasonic measurements must berepeatable over the test object surface.This may require lifting and recouplingthe transducers or inventing transducersthat can scan while remaining in contactwith the surface.

The coupling problems associated withscanning may be avoided by usingnoncontact laser ultrasonics. However,laser ultrasonics introduces otherproblems that can limit signal control andreadout. Such problems arise from surfaceroughness, reflectivity and other factors.

The selection of sending and receivingtransducers, their bandwidth, theirresonance frequencies and their internaldamping all have an effect on test results,primarily because ringdown in anundamped transducer can be confusedwith reverberations. In testing compositepanels, it is useful to select transducerfrequencies that introduce wavelengthsless than the panel thickness. Or, in thecase of continuous fiber reinforcedcomposites, it is helpful to cover thefrequency range likely to be transmittedby both the composite and fibers acting aswaveguides.

These two considerations dictatetransducer spacing, which must be smallenough to avoid losing the reception ofhigh frequency signal components.However, general guidelines for selectingtransducer frequency, bandwidth andinstrumentation parameters cannot beprescribed for all cases. The best approachis to use the successful examples citedhere and to experimentally seek theoptimum conditions for particularapplications. This approach can befacilitated by waveform (or spectrum)partitioning and by regression analysis toidentify the portion of the signal that bestcorrelates with the material property ofinterest.

ClosingUltrasonic nondestructive materialproperty characterization can be dividedinto several categories.

1. Elastic moduli are determined throughmeasurements of ultrasonic speed ordynamic vibration.

2. Some methods depend on speed andattenuation measurements tocharacterize residual stress, grain size,porosity, texture and othermicrostructural factors of materialbehavior. Sometimes thesemicrostructural factors can be used topredict values or variations ofmechanical properties such as strengthor toughness.

3. Ultrasonic measurements can becorrelated with mechanical properties:speed with hardness or attenuationwith toughness. This categorygenerally includes empiricalcorrelations that have been found toapply only to specific materials,usually in the form of laboratoryspecimens.

Precise ultrasonic measurements mustbe made on test objects with specific size,shape, thickness and surface condition.Or, for the measurements to have at leastrelative significance, geometric propertiesof the test objects must be held constant,as in damping measurements to obtainrelative modulus changes. This leads to analternative approach to materialscharacterization in which greateremphasis is placed on signal analysis toextract information on relative changes inmaterial properties. In this approach,ultrasonic wave propagation, energytransfer and signal modulation propertiesof a material are used to assess relativevariations in mechanical properties:ultimate strength or bond strength.

Empirical correlations betweenultrasonic measurements and mechanicalproperties have important roles inindustry. There are likely to beambiguities concerning the exact natureand influence of underlyingmicrostructural factors being measured.This is true in the case of complex,heterogeneous, anisotropic, textured andcomposite materials where severalvariables can simultaneously affect wavepropagation. These factors introducecomplex relations among microstructure,mechanical properties and load response(deformation and fracture modes).

The inferring of material propertiesoften depends on the use of two or morecorroborative and complementary testmethods, some of which are neitherwidely applied nor widely accepted inindustry. The biggest challenge in


ultrasonic materials characterization hasbeen to apply the techniques to practicalfield work.

Wider use of ultrasonic methods hasexpanded through significantimprovements in computers,instrumentation and materialsthemselves, particularly with respect toelectronic materials and nanotechnology.The literature describing theseadvancements has continued togrow.198-207


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