NATIONAL BUREAU OF STANDARDS REPORT

10 068

Progress Report

on DETERMINATION OF SHEAR MODULUS OF

DENTAL MATERIALS BY MEANS OF THE TORSION PENDULUM

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS
NATIONAL BUREAU OF STANDARDS

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NATIONAL BUREAU OF STANDARDS REPORT

NBS PROJECT

31 1.05-1 1-31 10560

31 1.05-1 1-3 11056 1

June 30, 1969

NBS REPORT

10 068

Progress Report

on DETERMINATION OF SHEAR MODULUS OF

DENTAL MATERIALS BY MEANS OF THE TORSION PENDULUM

by

J. A. Barton, Jr.,* G. Dickson+P. L. Oglesby^ and J. Kumpula + +

* Guest Worker, Dental Research Section, National Bureau of

Standards, LTC from the U. S. Air Force. + Physicists, Dental Research Section, National Bureau of

Standards, Washington, D. C. 20234.

++ Mechanical Engineering Technician, Dental Research Section,

National Bureau of Standards, Washington, D. C. 20234.

This investigation is part of the dental research program

conducted by the National Bureau of Standards, and is supported by the U. S. Air Force and the National Institute

for Dental Research Collaborative Office.

IMPORTANT NOTICE NATIONAL BUREAU OF SI

for use within the Government, and review. For this reason, tt whole or in part, is not autho Bureau of Standards, Washing!

the Report has been specifically

Approved for public release by the

Director of the National Institute of

Standards and Technology (NIST) on October 9, 201 5.

ess accounting documents intended

> subjected to additional evaluation

e listing of this Report, either in

le Office of the Director, National

by the Government agency for which

copies for its own use.

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

DETERMINATION OF SHEAR MODULUS OF

DENTAL MATERIALS BY MEANS OF THE TORSION PENDULUM

By

J. A. Barton, Jr., G. Dickson, P. L. Oglesby, and J. W. Kumpula

1. Introduction

The determination of physical and mechanical properties

of dental materials is often complicated due to the small size

specimen necessary to compare dimensionally with a dental

restoration. A method for determining the shear modulus of

such small specimens has been developed employing a torsion

pendulum apparatus.

Previous efforts have demonstrated the torsion pendulum

as being a sensitive instrument for determining the shear

‘H properties particularly on plastic and rubbery material.

Myerson investigated the structure of cross-linked methacrylate

systems by studying the changes in the mechanical energy

2 absorption and stiffness using this method. Shear modulus

and mechanical loss tangent of four denture base polymers have

3 been determined using a torsional pendulum apparatus.

If a torsion pendulum is allowed to oscillate freely after

an initial force is applied, it will oscillate at a frequency

dependent upon the characteristics of the torsion bar and the

moment of inertia of the system. The amplitude of the oscillations
will decay or damp with time as energy is dissipated. From

the frequency of the system the shear modulus of the torsion

bar material can be calculated by means of the relationship'*'

G = 2 I l (4I1

2 ~ 62

) f

2 nr

4

where G = shear modulus

I = moment of inertia

i = length of specimen

6 = logarithmic decrement (to base e)

f = frequency of the system

r = radius of the specimen.

Where 4n 2 »6 2

, the equation reduces to

G = 8 FI I ^f/

r

4

2. Methods and Materials

The torsion pendulum apparatus shown in Figure I consists

of a base which supports the pendulum; an upper collet which

supports the upper end of the specimen which may be raised

or lowered by means of a screw attached to the base; a lower

collet which rigidly attaches the lower end of the specimen

to the pendulum arm; two brass weights attached to the arm

which may be positioned to increase or decrease the moment of

inertia; and a slit aperture flag of brass which is suspended

from one end of the pendulum arm. An electromagnet attached

to the base of the instrument was used to activate the rotational

vibrations to the specimen.

2
The recording system employs a light source directed on

a photo multiplier tube through the slit aperture of the signal

flag mentioned above. The head of the photo multiplier tube

has a cover with an opening in its center in the shape of an

equilateral triangle and was positioned to produce a decreasing

signal as light travels from the base line toward the apex of

4

the opening. A Honeywell 906C Visicorder provided the tracing

of the signal from the photo tube on light sensitive paper for

frequency determinations. The end of the tube with its cover,

the light source, and the slit aperture signal flag were

covered to minimize the effects of light other than that of

the light source, on the tracing.

The total moment of inertia was calculated taking into

account each component (signal flag, steel arm, core, weights

and collet) and was verified experimentally by observing the

changes in frequency when the weights were moved and all other

conditions were held constant. Lengths of the specimens between the collets were measured using a cathetometer

.

Radii of the specimens were measured with a micrometer.

Frequency determinations were made by using the tracings

from the recorder chart with time intervals provided from the

3
Visicorder

A standard one second interval signal from the

National Bureau of Standards connected to the Visicorder was

also used for time determinations .

Briefly, the operation of the instrument was as follows:

the specimen in the form of a cylinder, whose diameter had

been measured to the nearest 0.01 mm, was clamped between the

two collets as shown in Figure II. The length of the specimen

between the collets was measured with the cathetometer . The

electromagnet, positioned in the plane of rotation of the

pendulum arm was activated and released, producing typical

oscillation curves as shown in Figure III.

The effect of temperature on shear properties of dental

amalgam was determined over the temperature range of 23-51°C

by placing the entire assembly in a controlled temperature

chamber. Frequencies were measured at 4-5 intermediate

temperatures between 23-51°C.

Since the maximum length to radius ratio that can be

obtained with a specimen comparable to the size of a dental

restoration is small, specimen end effects have a relatively

large influence on the frequency of the system. This was

initially observed using rods of steel brass, and aluminum,

at different specimen lengths with the factors G, I, and r

remaining constant. When using the equation G = Sni^f/l4

4
and assuming l to be the measured length of the specimen

between the grips, the calculated value for G decreased as the

specimen length between the collets was decreased. This error

was corrected by determining an effective value for l equal

to L, the measured length, plus a correction C. Frequency

determinations were made at 4 to 5 lengths ranging from 6 to

12 mm on each specimen and G and C were determined using the

least squares method by fitting the data to the equation

L = 15.37 (j^T) G + c

where L = measured length of specimen between grips (in.)

15.37 = a constant ( - -•— ^

r = radius of specimen (in.)

I = moment of inertia (i,b/in 2

) f = frequency of the system (H

a

) G = shear modulus (j£b/in°)

C = specimen length correction (in.)

The effective length (L + C) was found to be larger than

the measured length by approximately one to one and one half

times the radius of the specimen.

Amalgam specimens were prepared from five different

alloys certified to comply with American Dental Association

for

Specification no. l/a lloy for dental amalgam. The amalgam,

with a 9 to 6 Hg-alloy ratio was mechanically triturated for

thirty seconds and condensed into a split steel die. The cylindrical specimens were about 2.5 mm in diameter by 20 mm in

length and had Hg contents of about 46%.

5
Cylinders of an experimental composite material of the

same dimensions as the amalgam samples were also prepared in

three different powder liquid ratios. These composites are

based on a monomer formulation of a ternary eutectic system

(isomeric pthalate esters of 2-hydroxyethyl methacrylates) and

a resin filler consisting of vitreous silica and an x-ray

opaque glass.

3. Experimental Results

Shear modulus values with their respective standard

deviations were obtained for each of the five amalgam alloys

and three mixing consistencies of the experimental composite

material. They are shown in Tables I and II with the values

for dental amalgam in reasonably good agreement with those

obtained by ultrasonic methods.^ The shear modulus value of

the experimental composite material using the torsion pendulum

were about 10-30% lower than those obtained by ultrasonic

methods

Shear moduli of dental amalgam obtained over the

temperature range of 23-51°C are shown in Figure IV. A

decrease of shear modulus is observed as temperature is

increased

6
4. Discussion

By using the value for Poisson's ratio from reference 5

and experimental values for shear modulus G, Young's modulus

E can be calculated from the equation

E = 2G ( 1 + y)

where E = Young ' s modulus

G = shear modulus

y = Poisson's ratio

These values are shown in Tables I and II.

The decrease in shear modulus of dental amalgam between

23 and 51°C is consistent with the results obtained for

other mechanical properties. For example, Caul, Longton,

Sweeney and Paffenbarger show an average decrease of approximately 30% in compressive strength of five amalgams between

23 and 50°C.

One objection to the system is the fact that dynamic

values may be affected to some extent by tensile or compressive

loads on the specimen. However, it was observed that slight

compression of the specimen by engaging the fine steel point

attached to the lower collet into the lucite plate, produced no

detectable effect upon the frequency during vibration.

Since the value of the radius is raised to the fourth

power in the calculations, an error in measurement due to

7
irregularities on the surface of the specimen or nonuniformities in diameter, result in relatively large errors

in the value for shear modulus. Other possible sources

of error in the apparatus used in this investigation arise

from the inability to read the frequency of the system on

the recorder chart to better than one or two percent. Nonuniformities present in any inhomogeneous material also may

contribute to a source of variation in results.

5. Conclusion

A method for determining the shear modulus characteristics

of dental amalgam and an experimental composite material

using the torsion pendulum has been demonstrated.

Shear modulus values of approximately 3 x 10 c psi have

been obtained which are in relative agreement with those

obtained by other methods for dental amalgams. A decrease

of shear modulus for dental amalgam was observed as temperature

was raised to 51°C.

Shear modulus of an experimental composite material was

determined by this method using three different mixing consistencies, with values of 0.7 to 0.8 x 10 6 psi being

obtained compared to 0.9 to 1.0 x 10 R psi by ultrasonic methods.

8
References

1. Nielsen, L. E. A Recording Pendulum for Measurement of

the Dynamic Mechanical Properties of Plastics and Rubbers,

The Review of Scientific Instruments, 22:9, Sept. 1951.

2. Myerson, Richard L., Effects of Cross-Linking on Mechanical

Damping and Stiffness of Methacrylates. IADR Abstract

1962.

3. Braden, M. and Stafford, G. D. , Viscoelastic Properties of

Some Denture Base Materials, J. Dent. Res. Vol. 47, No. 4,

August 1968.

4. Gardner, T. V., Jr., Dickson, George and Kumpula, J. W.

,

Application of Diffraction Gratings to Measurement of

Strain of Dental Materials, Journal of Dental Research,

Vol. 47, No. 6, Part 2, November-December , 1968.

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

,

Characterization of a Composite Resin Material Developed

for Temporary Posterior Restorations, IADR Abstract, 1969.

6. Dickson, George and Oglesby, P. L., Elastic Constants of

Dental Amalgam, Journal of Dental Research, Vol. 47, No. 6,

Part 2, November-December, 1968.

9
7. Caul, H. J., Longton. R., Sweeney, W. T. and Paf f enberager

,

George C., Effect of Rate of Loading, Time of Triturations

and Test Temperature on Compressive Strength Values of

Dental Amalgam, J.A.D.A. 67:670, November, 1963.

10
Torsion

Pendulum

Apparatus

and

Recording

System
View

of

Specimen

Attached

to
'1

Figure 3

Typical Oscillation Curve Recorded

on Measuring Shear Modulus of Dental

Amalgam by the Torsion Pendulum

Method

.
ain 

itj CO

l4 44

CO 0

S40 CO Eh 3i—I QJ 3

,3 13

4-> 0S C0 S4 a, 3 3 0) -3

CO CO

4->a

n

a; 0

4-1 S4 • 44 3 6 W CO 3 3 tn

CD a)

H

S-l S rti 3 E

4-1 E < 3 3 1 1 i—i 3 a 3

Q.

V 4-J E c c

(L) CD 3

E-c &<

Q

—L_

*0X

IO

10 1 1 O to

CL

fO

ro

ro

CM

rrf

TEMPERATURE
Table 1

Elastic Moduli of Dental Amalgam

G E

_L lUy

N/m 2 S. D. PSI S . D 0 "An* PSI

A

0) O

i •

00 X 1— CN CN 0.76 x 109 3.3 x 10 6 0.11 x 106 60.7 x 109 * 8.8 x 10 6 *

B 22.1 0.21 3.2 0.03 58.6 * 8.5 *

C 20.7 1.52 3.0 0.22 55.2 * 8.0 *

D 20.7 0.83 3.0 0.12 55.2 * 8.0 *

E 20.0 2.14 2.9 0.31 53.1 * 7.7 *

F

4 20. 7 + 3. Of 55.2 8.0

G

6 23.4 3.4 62.7 9.1

* Young's Modulus —Calculated using values for G and Assuming

P isson's ratio to be 0.3346

.

t Shear Modulus —Calculated using values for E

grating4

) and Assuming P isson's ratio to be

(diffraction

0.334 6

.
Table II

Elastic Moduli of Experimental Composite Material

' : L

Modulus 1 . 10 1 . 35 1 . 4 5

N/m2 PSI N/m2 PSI N/m2 PSI

Shear

1. Torsion 4.8 x 109 0.7 x 10 e 5.5 x 109 0.8 x 10s 5.5 x 1CP 0.8 x_lC

Pendulum

* 2. Ultrasonic 6 o 9 1.0 6.9 1.0 6.2 0.9

Young ' s 1. Optical

Strain Gages 8.3 x 109 1.2 x 10 6 9.0 x 109 1.3 x 10 s 9.6 x 109 1.4 x 1(

(between 2000 - 5000 psi)

Torsion Pendulum* 12.4 1.8 13.8 2.0 13.8 2.0

2. Ultrasonic* 17.2 2.5 17.9 2.6 16.5 P.4

I

'I

t'c

\

I