NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

31 1.0 5-1 1 -31 1056 1 December 31, 1969

NBS REPORT

10 177

Progress Report

on

ULTRASONIC METHODS FOR DETERMINATION

OF MECHANICAL PROPERTIES OF DENTAL MATERIALS

by

George Dickson

Physicist, Dental Research Section, National Bureau of Standards,

Washington, D. C. 20 234.

This investigation is part of the dental research program conducted

by the National Bureau of Standards in cooperation with the Council

on Dental Research of the American Dental Association; the National

Institute for Dental Research; the Dental Research Division of the

L). S. Army Medical Research and Development Command; the Dental

Sciences Division of the School of Aerospace Medicine, USAF; and the

Veterans Adm in istration.

NATIONAL BUREAU OF S

for use within the Government

and review. For this reason, whole or in part, is not autt Bureau of Standards, Washin,

the Report has been specitica

IMPORTANT NOTICE

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 2015.

ress accounting documents intended

is subjected to additional evaluation

re listing of this Report, either in

the Office of the Director, National

, by the Government agency tor which

copies for its own use. <NBS>

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
1
ULTRASONIC METHODS FOR DETERMINATION

OF MECHANICAL PROPERTIES OF DENTAL MATERIALS

by

George Dickson

1. INTRODUCTION

The most commonly reported mechanical property of dental materials is strength, usually compressive or tensile. However, strength

is not a measure of the reaction of a material within its functional

range. To obtain some characterization of the mechanical reaction

of a material to the forces encountered in use. Young's modulus is

often determined. Generally, Young's modulus is calculated from a

stress-strain curve obtained by loading a specimen in a testing

machine and measuring the change in length with increase in load.

While the modulus determined in this way is usually considered a

measure of the elastic characteristics of the material, the data

often represent a combination of properties: elastic, retarded elastic

and viscous with varying magnitudes of time and stress dependence.

This is illustrated in the stress-strain curves for dental amalgam

shown in Figure 1.^^^

It is evident that even with low stresses, the behavior of dental

amalgam is not purely elastic. A plot of the strain of dental amalgam

vs. time when under constant stress (Figure 2) indicates that at

least three types of response to mechanical force are present, an
2

instantaneous elastic response, a retarded elastic response and a

( 2 ) VISCOUS response.

To determine the magnitude of the instantaneous elastic

response,- it is necessary to isolate this particular property of

the material.

Time dependent responses such as viscous creep and retarded

elasticity can be eliminated or reduced to a negligible level if

the stress can be applied and removed rapidly enough. One method

of accomplishing this is by introducing sonic or ultrasonic waves

into the material. Essentially this causes small volume elements

of the material to be cyclically strained as a series of stress

waves is propagated through the specimen. The velocity of the

stress wave depends upon the mass or density of the particles or

small volume elements of the material which are displaced and upon

the elastic characteristics of the material which provide the

forces tending to restore the particles to their equilibrium

positions

.

In addition to minimizing time dependent responses, ultrasonic

methods have other advantages. They are rapid and non-destructive,

and they permit repeated measurements on the same specimen as it

is aged or subjected to temperature change or other treatments. Ultrasonic methods can be applied to small and brittle specimens on which

other methods of stress application and strain measurement may be

difficult. Also, ultrasonic methods are particularly suitable for
3

measuring elastic coefficients in different directions in anisotropic

materials

For measuring the mechanical properties of materials, low

amplitude or low energy ultrasonic waves are employed and the effects

of the medium on the wave are observed. High amplitude waves which

would produce a permanent change in the specimen are avoided.

There are two types of stress waves which are particularly useful for determination of mechanical properties. These (Figure 3) are

the compressional or longitudinal wave in which particle motion in

the medium is parallel to the direction of propagation of the wave,

and the shear or transverse wave in which the particles vibrate at

right angles to the direction of propagation of the wave.

2. VELOCITY AND MODULUS DETERMINATIONS

(3) In plane waves in an elastic homogeneous medium , the velocities of the transverse and longitudinal waves can be shown to be:

V

L

E(l-y)

p (1+y) (1-2y)

where

p = density

G = shear modulus

E = Young's modulus

Y = Poisson's ratio
- 4 -

When the wave length is large compared to specimen dimensions

the equations for propagation in an infinite elastic medium do not

apply. For example, for wave propagation parallel to the sides of

a thin plate

V, =

p (1-y )

For propagation in a rod with radius small compared to wave-

(4) length , the longitudinal wave velocity is

Where frequencies high enough so that the wavelength is small

(3) compared to specimen dimensions are used , shear modulus, Young's

modulus, the bulk modulus and Poisson’s ratio can be determined from

the velocities of the longitudinal and transverse waves, and the

density of the material as follows:

Shear modulus G = pV

Young's modulus E =

Bulk modulus K = p

^ 3V ^ -

. 2 L

XT 2 \

-

f 2 2 3V^ - 4V^

L T

\ 3

Y

=

2 2 V - 2V

L T Poisson's ratio
5

From these equations, it is evident that determination of

elastic constants is essentially a problem of determination of the

velocity of sound in the material. Various methods can be employed

for determining the velocity of stress waves. One of the most widely

used is the pulse-echo technique, which has been described in numerous

papers and books^^’^ In this method (Figure 4), a quartz crystal,

or other transducer driven by a pulsed oscillator, is used to introduce

the wave at one of two parallel faces of the specimen. The same transducer, or a similar one at the opposite face of the specimen, is used to

receive the mechanical vibration and produce an electrical signal

which, after amplification, can be observed on an oscilloscope. Unless

the attenuation of the specimen material is very high, the stress wave

will echo back and forth through the specimen a number of times, and

signals representing each double transit will be observed.

If a piezoelectric quartz transducer is used, the crystal may

be cut with axes oriented so as to produce either longitudinal vibrations (x cut) or transverse vibrations (Y or AC cut) in the specimen.

The crystal can be driven at its natural frequency or at an odd harmonic

by a pulsed oscillator tuned to the required frequency. The time

interval from one pulse to the next is made long enough to allow the

echoes to die out between pulses. The transducers can be coupled to

the specimen with a thin film of oil or a viscous resin.

A waveform generator (Figure 4) can be used to control the pulse

repetition rate and supply a trigger signal to initiate both the pulse

and the oscilloscope sweep. The rectified echo signals, after passage
6

through a broadband amplifier, may be displayed on an oscilloscope

(Figure 5) with a calibrated time scale and the time between echoes

determined. The frequency, pulse length and pulse repetition rate

may vary over a wide range.

Accuracy of the velocity determination will depend on the quality

and quantity of echoes which can be observed, which, in turn, depend

upon the attenuation of the signal by the specimen material, the

presence of spurious signals which may result from reflection from

sides of the specimen with the probability of mode conversion from

longitudinal to transverse waves or vice versa and to unsatisfactory

4 specimen preparation. Specimen parallelism to 2 parts in 10 or

better is recommended, although less accurate parallelism may produce

usable results for some purposes. Under favorable conditions,

velocity determinations with a sensitivity of 0.1% and an accuracy of

1% can be obtained

In another pulse method, the sing-around technique (Figure 6),

the signal received when the stress wave has passed through the

specimen is used to trigger the next pulse from the oscillator, and

the pulse repetition frequency is measured. Since time delays other

than that required for the stress wave to pass through the specimen

are ordinarily comparatively small, the period of the system is essentially the transit time. For accurate determinations, these other

delays must be taken into account. With this simple system, velocity

changes of less than one part in 10^ can be detected

Refinements of the sing-around method have been made to provide
7

sensitivity to velocity changes of a few parts in 10^ These

refinements consist of using the signal after a specific number of

echoes rather than after the first transit to refire the transmitter

and also, using a specific cycle within the pulse. This method is

particularly useful when the interest is in measurements of small

changes in velocity rather than in an absolute value.

Interference methods can be used for measuring velocities. In

optical interferometers, such as the type used in measuring the

setting expansion of amalgam and in ultrasonic interferometers in a

liquid medium, the number of wave lengths between two reflecting

surfaces is changed by a continuous variation of path length. Such

a system is not feasible for ultrasonic measurement of the properties

of solids since path length cannot be readily varied. A similar effect can be obtained, however, by a continuous variation of frequency

and consequent change in wave length. For example, sets of two gated,

phase coherent pulses from a continuous wave oscillator may be spaced

in time so that the second pulse which has passed once through the

specimen arrives at the receiving transducer at the same time as the

first pulse which has echoed and passed three times through the

( 3 ) specimen . If the oscillator frequency is then adjusted, the phase

relationship of the pulses will vary and when the signals are added a

series of nulls will be produced. The velocity can be determined from

the frequency difference necessary to pass from one null to the next.

If the phase change on reflection from the ends of the specimen can

be neglected

V = - f^) .
8

where I is the length of the specimen and and represent the

frequencies at successive null positions. If the specimen material

causes relatively high attenuation of the ultrasonic wave, a continuous

(3)

wave interferometric method can be used . Here, the signal from

the receiving transducer is compared with the signal being fed into

the transmitting transducer and again phase change is observed as

frequency is varied.

Resonance methods can also be used for velocity determinations.

Such methods generally are used with frequencies in the lower ultrasonic range. At the natural frequency of a half-wave length specimen

bar, the longitudinal velocity is

V = 2£f

J_i

and Young’s modulus is

E = p (2£f)^ .

/"S') One experimental arrangement'" which has been used for such resonance

determination involves the use of a three-component system, shown in

Figure 7, consisting of a quartz crystal driver with the specimen of

closely matched resonance frequency cemented to one end and a second

quartz bar, also closely matched in frequency, cemented to the other

end of the driver to act as a piezoelectric gauge.

Another method of velocity measurement analogous to optical index

of refraction measurement is based on the determination of the angle

of refraction of a stress wave as it passes from a liquid medium into

a solid specimen or on the determination of the focal length of an

(3) ultrasonic lens made from the specimen material
9

(3) Velocity measurements can also be made by reflection methods

If ultrasonic pulses are reflected from the surface of a solid immersed in a liquid medium, the reflection coefficient can be defined

as follows

a

r

P

r

P.

1

P2^2 Pj^l

^ 2^2 ^ 1^1

where

P^ and P^ represent the pressure amplitudes of the reflected

and incident pulses, respectively;

and represent longitudinal wave velocities in the incident

(liquid) and reflecting (solid) media;

and represent densities of the liquid and solid media.

Instead of making absolute measurements of the reflection coefficient,

the amplitude of the pulse reflected from the test specimen may be

compared with the amplitude of the pulse reflected from a specimen for

which the reflection coefficient is known. In this case

a a

r

where and represent the amplitudes of the pulses reflected from

the known and unknown materials, respectively. From the reflection

coefficient and the density of the test material, the velocity of the

longitudinal wave and the accoustic Impedance, pV, can be calculated.

This method can be used with materials which have a high attenuation.

It has the advantage also that only one flat surface is required on

the specimen. The accuracy is reported to be of the order of 5 percent
10

3. ATTENUATION OF ULTRASONIC WAVES

The attenuation of ultrasonic stress waves in materials and

loss interactions are discussed in detail by Truell, Elbaum and Chick

in a recent book. Ultrasonic Methods in Solid State Physics In

brief, energy losses may be divided into two categories, those that

are dependent on the physical characteristics of the specimen material and those that are characteristic of the method of measurement.

In the latter group are such as coupling losses, losses due to nonparallelism of specimen faces, phase effects in the transducers and

diffraction and mode conversion effects in the specimen. The losses

that are of interest, those that are characteristic of the material,

are of two main types, scattering effects and absorption effects.

Scattering losses are caused by lattice defects or other discontinuities

in the medium. The relative size of wavelength and defect and the

defect density will determine whether or not the scattering can be

measured. Adsorption losses include dislocation damping losses, thermoelastic losses, conduction electron damping losses, phonon-phonon

interactions, ferromagnetic resonance effects, paramagnetic resonance

effect and nuclear spin energy Interactions.

The attenuation of ultrasonic waves may be used to determine the

internal friction of a material. Internal friction may be defined as

the energy loss per cycle in an element of volume divided by 2tt times

the maximum energy stored in the element per cycle or as the tangent

of the angle by which the strain lags behind the stress. When energy

1 1 u ( 6 ) losses per cycle are not high
11

Q

= tan a AE

2ttE TTA TT TT

where E = energy

A = amplitude

6 = logarithmic decrement

The attenuation of ultrasonic waves in materials can be determined by a number of methods. With the pulse-echo technique, attenuation is measured by comparison of the amplitude of successive echoes.

Losses which occur at each reflection also must be taken into consideration. Effects of coupling losses may be determined by making

measurements with a transducer at only one end of the specimen and

comparing with results obtained when an identical dummy transducer

is coupled to the opposite end of the specimen^^^ . By making

measurements on specimens of different lengths, effects other than

the increased path length can be kept constant and the attenuation

calculated from measurements on the different specimens. Reflection

of the wave from the sides of the specimen may result in mode conversion from transverse to longitudinal waves or vice versa, and

result in energy loss and apparent attenuation. Such effects will

depend on wavelength and specimen size.

When the attenuation is small, it can be determined from the

decay curve of free vibrations in the speclmen^^\ The resonance apparatus described for determination of velocity has as a primary use

(g) the determination of internal friction. It can be shown^ that the

logarithmic decrement of the specimen in such a system is proportional
12

to the ratio of the driver crystal voltage to the gage crystal voltage

« =

where the constant K is a characteristic of the system. After K has

been determined from the free decay of the system, the logarithmic

decrement can be determined under different strain amplitudes or other

specimen conditions by measurements of the two voltages.

The Internal friction can also be determined from the amplitude

frequency curve in the region of resonance from the relation

where Af is the total spread from one side of resonance to the other

^ ( 6

)

where the amplitude has dropped to times the resonance amplitude

4. APPLICATIONS OF ULTRASONIC METHODS TO DENTAL MATERIALS

Ultrasonic methods have been used to measure the mechanical

(9) properties of a number of dental materials. Dickson and Oglesby

reported the elastic constants of dental amalgams in which the mercury

content was varied by varying the condensation pressure. Specimens

8mm in diameter by 6 to 15mm in length were prepared as shown in

Table 1. Measurements were made by a pulse-echo technic with a frequency of 5.5 MHz, a pulse length of 0.5 to 1.0 y sec. and a pulse

repetition rate of 6 KHz. Elastic constants obtained for an amalgam

containing about 48% mercury are shown in Table 2. As the plot in

Figure 8 shows, the relationship between Young's modulus and mercury

content was essentially linear over the range Investigated.
13

Using a resonance method with the three component system of

specimen, driver crystal and gage crystal, Larson^^*^^ investigated

the Young's modulus and internal friction of amalgam. The frequency

was in the 50 KHz range. Young's modulus values of 8.5 X 10^ to

10.6 X 10 psi were found with mercury contents varying from 30 to

60%. A peak in both modulus and internal friction was reported in

the 45 to 50% mercury ranges.

As would be expected, the Young's modulus values obtained for

amalgam by the rapid strain rates inherent in ultrasonic methods are

considerably higher than those reported from conventional stress-strain

curve procedures. However, using a diffraction grating strain gage

which permitted stress-strain curve data to be obtained in 3 to 4

seconds, Gardner, Dickson and Kumpula^^^^ obtained a modulus value

of 8 X 10 psi which does not differ greatly from those obtained by

ultrasonic methods.

In our laboratory, the pulse-echo method has been employed to

measure the elastic characteristics of experimental composite quartz

or glass-filled resins. The attenuation of the ultrasonic wave in

these materials is high and often no suitable echoes are obtained so

that the procedure is reduced to measurement of a single transit

time. Effects of time delays other than transit time are eliminated

by measurements on specimens of various lengths. Data on Young's

( 12 ) modulus for an experimental restorative material are given in Table 3

The elastic properties of apatites were investigated by Gilmore

(13) and Katz using an ultrasonic interference technic. Powdered
14

specimens of hydroxyapatite, f luorapatite, chlorapatite and sodium

chloride-hydroxyapatite composites were studied when subjected to

pressures of up to 50 K bar. Transducers were mounted on the back

faces of tungsten carbide pistons, as shown in Figure 9, and interference was obtained between reflections from the near and far

specimen-piston interfaces. Values obtained for some of the apatites,

as well as values for bovine dentin and enamel, are given in Table 4.

Moduli of the apatites were found to increase linearly with pressure

in the higher pressure ranges.

(14) Lees reported values for the specific accoustic Impedance

of bovine enamel and dentin obtained by the reflection coefficient

method using specimens mounted in acrylic resin. A pulse of 60 nanoseconds length was reflected from the specimens in water. The signal

amplitude was compared with that of a pulse reflected from stainless

steel under similar conditions. Values obtained for accoustic

impedance (product of density and sonic velocity) were in general

agreement with values obtained by other ultrasonic methods.

The elastic coefficients of animal bone have been investigated

by Lang^^^^ using an ultrasonic pulse method for measurement of

velocities. Analysis of the crystallographic structure of components

of bone and the piezoelectric and pyroelectric characteristics of

bone suggested that bone should behave elastically as a hexagonal

single crystal, and the elastic stiffness coefficients were determined

on this basis. Young's and shear moduli found for axial and transverse bone directions, in dried bovine femur and phalanx and fresh
15

phalanx, are given in Table 5.

5. SUMMARY

A variety of ultrasonic methods are available for determining

the elastic characteristics of materials. These methods are precise, rapid, non-destructive, applicable to small specimen, and

they measure a specific property of the material. As a number of

recent reports in the dental literature indicate, they offer particular advantages to the study of dental materials and mineralized

tissues

USCOMM-NBS-DC
16

REFERENCES

1. Rodriguez, M. S. and Dickson, G. Some Tensile Properties of

Amalgam. J. D. Res. 41:840, July-August 1962.

2. Oglesby, P. L., Dickson, G., Rodriguez, M. S., Davenport, R. M.,

and Sweeney, W. T. Viscoelastic Behavior of Dental Amalgam.

J. Res. NBS 72C:203, July-Sept. 1968.

3. Fllipczynski , L. , Pawlowski, Z., and Wehr, J. Ultrasonic Methods

of Testing Materials. Butterworths , London, 1966.

4. Hueter, T. F. and Bolt, R. H. Sonics. John Wiley & Sons, Inc.,

New York, 1955.

5. Truell, R., Elbaum, C. and Chick, B. B. Ultrasonic Methods in

Solid State Physics. Academic Press, New York, 1969.

6. Mason, W. P. Physical Acoustics - Principles and Methods.

Academic Press, New York, 1966.

7. Forgacs, R. L. Improvements in the Sing-around Technique for

Ultrasonic Velocity Measurements. J. Acoust. Soc. Am. 32:1697,

December I960.

8. Marx, J. Use of the Piezoelectric Gauge for Internal Friction

Measurements. Rev. Scl. Inst. 22:503, July 1951.

9. Dickson, G. and Oglesby, P. L. Elastic Gonstants of Dental

Amalgam. J. Dent. Res. 46:1475, Nov. -Dec. 1967.

10. Larson, R. V. Ingernal Friction Damping in Dental Amalgam.

Thesis, Dept, of Mechanical Engineering, University of Utah,

August 1967.

11. Gardner, T. V., Dickson, G. and Kumpula, J. W. Application of

Diffraction Gratings to Measurement of Strain of Dental Materials.

J. Dent. Res. 47:1104, Nov-Dec. 1968.

12. Burns, C. L. , Barton, J. A., Jr. and Chandler, H. H. Development

of a Composite Resin Material for Temporary Posterior Restoratives. lADR Abstracts, 47th General Meeting, March 1969.

13. Gilmore, R. S. and Katz, J. L. Elastic Properties of Apatites.

Proceedings of International Symposium on Structural Properties

of Hydroxyapatite and Related Compounds, National Bureau of

Standards, Sept. 1968. To be published.
17

14. Lees, S. Specific Acoustic Impedance of Enamel and Dentin.

Private Communication, 1968.

15. Lang, S. B. Elastic Coefficients of Animal Bone.

165:287, July 18, 1969.

Science
. i
TABLE 1

(9) AMALGAM SPECIMEN PREPARATION^ ’

11 to 8 Hg/Alloy ratio

20 sec. trituration, Wig-L-Bug

3 to 6 mixes of two pellets

Condensed in steel die

8 mm diameter by 6 to 15 mm length

5000 to 25000 psi

35 to 49% Hg content
TABLE 2

(9) ELASTIC CONSTANTS OF AMALGAM^ ^

•k Property Value Range

Hg Content 48 .6% 0,.7

Young’s Modulus 9. 09 X o

1

—

1

psi 0.. 06 X 10

Shear Modulus 3. 41 X o

1

—

i

psi 0.,03 X 10

Bulk Modulus 9. 12 X 10^ psi 0.,22 X lo'

Poisson’s Ratio 0. 334 0.,005

* Range of three values
TABLE 3

ELASTIC MODULI OF EXPERIMENTAL

COMPOSITE RESIN RESTORATIVE MATERIAL

(In 10^ psi)

Modulus Method

Powder-Liquid

(grams powder to 0

Ratio

4 ml liquid)

1.10 1.35 1.45

E Stress-strain curve 1.2 1.3

11—

E Ultrasonic 2.5 2.6 2.4

G Torsion pendulum 0.7 0.8 0.8

G Ultrasonic 1.0 1.0 0.9
TABLE 4

ELASTIC MODULI OF APATITES

(In 10^ psi)

(13)

E G K

Hydroxyapatite 15.7 7.7 12.5

Fluorapatite — 7.5 13.8

Chlorapatite — 6.3 10.0

Dentin 3.0 1.2 2.6

Enamel 10.7 4.4 6.7
TABLE 5

ELASTIC MODULI OF BOVINE BONE

(In 10^ psi)

(15)

Phalanx Femur

Fresh Dried Dried

E (axial) 3.19 4.42 3.77

E (transverse) 1.6A 2.31 2.60

G (axial) 0.78 1.09 1.18

G (transverse) 0.65 0.94 1.07

STRAIN

IN.

/IN.

Fig.

1.

Typical

stress-strain

curves

of

various

amalgams

in

tension,

using

0.003

in.

/min.

head

speed

and

7

day

old

specimens
X NlVdlS

rirppn

pnH

T'pnrv^7PT*-\r
Direction

of

Wave

Propagation

Fig.

3.

Two

types

of

ultrasonic

stress

waves

used

for

determination

of

mechanical

properties

of

materials
Fig.

A.

Typical

pulse

echo

system
IIeIiIIIIIIIIIIIII

Fig.

5.

Pulse

echo

pattern, ainput

pulse, bpulses

after

passage

through

specimen.
Fig. 6. Simplified diagram of

sing-around system.
Fig. 7. Three component resonance

system (8)
90l^'s^l 3

Fig.

8.

Effect

of

mercury

content

on

Young's

modulus

of

dental

amalgam
X-cut quartz

transducer

Piston

Specimen

Y-cut quartz

transducer

Fig. 9. Diagram of transducer, piston and

specimen arrangement for determination

of moduli under high pressure (^3)
i

^11 I V