Experimental stress analysis of dental restorations

Experimental

stress

Part II. Two-dimensional Robert

G.

Floyd

A.

University

Craig,

photoelastic

Ph.D.,**

Peyton,

of dental

analysis

M.

Kamal

stress El-Ebrashi,

restorations* analysis D.D.S.,

of crowns MS.,***

and

D.Sc.****

of Michigan,

.Sch.ool of Dentirtry,

Ann Arbor,

Miclr.

A

crown is a restoration that reproduces the entire surface anatomy of the clinical crown and fits over a prepared tooth stump.’ The preparation of teeth for crowns having full shoulders were reported to fulfill all the requirements necessary for good periodontal health.2 The shoulderless crown constructed for shoulderless preparation< also was claimed to have an accurate marginal fit.” Strength of crowns, from the engineering point of view, does not depend upon the area covered by the crown, but upon the section modulus which is the quotient found by dividing the moment of inertia by the distance from the neutral axis to the outermost fiber.l Stresses have been measured in posterior fixed partial dentures,” and it was found that, when a posterior four unit fixed partial denture was loaded, it deflected in a typical transverse manner. The stress and direction of strain wercs found to be a function of load, site of force application, and mass and shape of tht. individual restoration. The theoretical aim in designing structures is to achieve a uniform stress at di points in the surface of the part, with the magnitude of the surface stress such that failure is just avoided in service.” The practical designing of structures involves safety factors such that the stress required for failure is rarely reached. It was the purpose of this investigation to study the general stress distribution in full crowns: using static loading conditions and a two-dimensional photoelastic Presented Chicago.

in part

This investigation DE-01817, from the Bethesda, Md. *Part

***Research ****Professor

The

American

Academy

of Crown

was supported by United States Public National Institute of Dental Research.

I, J. PROS. DENT.

**Professor

292

before

17:

277.

and Health National

1967.

of Dentistry. Associate. and Chairman.

Department

of Dental

Materials.

Bridge

Prosthodontics

Service Kesearch Institutrs of

Grant Health

iti

Stress analysis

Fig.

of dental

restorations.

Part II

293

1

A photoelastic model of a full shoulderless crown on a tipped abutment loaded on the tip of the cusp with 75 pounds. stress analysis technique, and to investigate cordance with occlusal problems. MATERIALS

AND

second mandibular

the effect of two sites of loading

molar

in ac-

METHODS

A circular transmission polariscope was the instrument used to record the isochromatic and isoclinic fringes. The instrument has been described in detail along with methods of interpretation of the fringes.’ The photoelastic material used in this study was Cataline resin.” Models were constructed following the technique described in Part I of this investigation.’ The base for the plastic model was fabricated of aluminum, and improved stone? was used to cement the fabricated plastic model to the aluminum base. The composite model was ready for loading after the stone had set and was allowed to dry. The model was then loaded in a manner similar to the prototype, and a quantitative measure was obtained for the stresses produced by measuring change in optical properties of the plastic portion of the model due to stress. A photograph was taken of the stress pattern corresponding to each load and the stress optical coefficient was computed by the method previously described.; RESULTS

AND

DISCUSSION

The tipped molar abutment (mesially or distally) was chosen because it is one of the most common problems encountered in restorative dentistry. The second mandibular molar model was used to simulate the situation when the lower first molar is lost and a fixed partial denture restoration is to be used. A load of 75 pounds was used to load the tip of the distal cusp (two-dimensional model) of a full crown, on a mesially inclined lower second molar (Fig. 1) “Cataline resin 61-893, Bakelite Company, New York, N. Y. iVelmix. Kerr Manufacturing Company. Detroit. Mich.

Sfv7i

isochrornatir

f’rinsys

arca

shown. 7

I.-sirry i.11 ~~. 211

tlw

Fkltm?tion

1 !I

where T is the shear stress? (frl - crz I 2, I’ is the str’ess optical coefficient. n is tjlc, number of fringes, and h is the thickness of the model: the shear stress T xj~as found to be 476 pounds per square inch (psi) . on thr surface of the model. \,\‘hen tl~* load was increased to 125 pounds, as shoI\-n in Fig. 2A, the number of fringes increased to ten, and the shear stress increased to 680 psi. The ratio bet\\-ecn the sheal stresses in the two instances is equal to the ratio of the number of fringes in the firs1 to those in the second. The stress distribution along line A-B, passin connected sents the magnitude of the compressive stress at th of tllc, compressive stress on the cxterio, reduced cusp surface. Of course, the maximum surface was at the point of loading. This stress clistl,ibution will be compared late1 with stresses in restorations cemented on abutments which arc> not considered to b(l tipped mesially or distally. Loads were applied to cro\vns on normally aligned teeth. and a load of 50 I)ounds was used in Fig. 3A \vhere thr rcsllltinp isochromatic frinprbs arc% recorded.

Fig. 2A ‘I‘hp photoelastic.

11

Volume

h-umber

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1;

:1

analysis

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Part II

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The stress distribution along two lines of interest (A-B and C-D) was investigated and the values are shown in Fig. 3B. The stresses along line A-B changed from compressive near the preparation to tensile near the surface of the restoration. The stress along line C-D, however, remained the same in nature, and the compressive stresses decreased from the point of load application (0) to the reduced cusp on the preparation (C). Fig. 3C shows the fringe orders and lines A-B and C-D, and also shows the surface stresses present in the restoration. Tensile stresses at the surface

l@

246

3%

406

546

646

706

S(16

9fi6

IO&6

I1116

IN.

STRESS (p 175 200 225

COMPRESSION

(4

TENSION

I+1

250 275 300 325 350 375 400

Fig. 26 A plot of the stress distribution

along line A-B

LOAO

P = 125 Ibs

COMPRESSION

(-1

TENSION

I+)

Fig. 2C Stress distribution

pattern

along the border.

model

(Right)

The

are

drawn.

shown in Fig. 2A.

magnitude

(Left) The of the surface

isochromatic fringe orders in the stresses on the model is shown.

296

Craig, El-Ebrashi,

and Peytolc

Fig. 3A Isochromatic fringes in the photoelastic model are shown with two-point contact at a 10x1 of 50 pounds. (A-R) and [C-D’: are the lines along which strrss was analyzed.

0 IS0 125 100 75 STRESS

DISTRIBUTION

50 +

25

ALONO

/ii

A-0

strus

COMPRESsiDN

f-1

50 TEN0lON 75

(41

125 I50 175

22s 250 275

Fig. 36 The stress distribution along lines A-B and C-D, shown in Fig. 3A, is plotted. The stres\ along line A-B changed from compression (-) to tension i+) at 7/G inch from the interiol surface of the preparation.

v$lml~* 2 ”

‘j

Stress analysis

LOhD

Fig. 3C (Left) Isochromatic in the model.

P=

of dental

Part II

297

SOIbs

COMPRESSION

(-)

TENSION

(+)

fringes in the model.

restorations.

(Right)

The magnitude

of the surface stresses

are shown by perpendicular projections from the surface of the restoration toward the interior surface of the restoration and these projections again were connected to give a curve representing the tension at the surface of the restoration. The center of the restoration near the central fossa, and the exterior mesial and distal surface near the cusps were in tension (+) while compressive stresses (-) were present on much of the interior surface and on the exterior surfaces of the restoration near the points of loading. It should be emphasized that no tensile stresses were demonstrated near the proximal margins. When the load was increased from 50 to 133 pounds, the fringes increased in number, as shown in Fig. 4A. Crowding of the isochromatic fringes around the reduced cusps on the preparation was evidence of stress concentration. A detailed tracing of the isochromatic fringes was made, and numbers signifying the fringe orders were assigned as shown in Fig. 4B, following the general rules of photoelasticity. The zero fringes are of special interest, since they represent regions of inflection of the stress from tension to compression. Also worthy of noting is the higher the fringe order, the higher the stress. The stress distribution along two lines of interest was made line A-B, which is the axis of symmetry of the restoration in two dimensions, and line C-D passing through the reduced cusp, as shown in Fig. 48. The stress distribution along line A-B is shown in Fig. 4C. Compressive stresses changed to tensile stresses near the preparation ( loA inch), and the maximum tensile stress was found to be in the order of 450 psi near the surface of the restoration compared to 150 psi along line A-B in Fig. 3B, when the load was 50 pounds. The stresses along line C-D shown in Fig. 40 remained compressive in nature, although a minimum stress of 220 psi was observed at F/
L,NE

THRCJUGH

AXIS

OF

THE

REDUCED

CUSP

SYMMETRY

Fig. 48 .4 detailed

tracing

of the

fringe

orders

in

the

nlodcl

of the

cwvvu

Stress analysis

of

dental restorations.

Part II

299

400

350

300

250

200

I50

compresrion

I-)

Tension

(+)

100

+50

Fig. 4C The stress distribution along line A-B shown in Fig. 4A, where the stress changed from compression to tension at a point less than half the distance from the interior to the exterior surface of the crown.

+

20

STRESS

-

P

2/m

4(l6

M6

q6

M6

1246

l4As

l6&

m/l6

eO(l6

INCH-

220

240

260

260

300

320

340

360

360

400

420

440

Fig. 40 Stress distribution observed.

along line C-D shown in Fig. 4A and only compression

stresses were

300

Craig,

El-Ebrashi,

Fig. 4E Stress distribution

and Peyton

along the interior

and exterior surfaces of the model.

faces of the crown under a load of 133 pounds is shown in Fig. 4E. On the external occlusal surface, compressive stresses were found to be high at the site of load application, and they decreased to zero between the site of application and axis of symmetry. The change from tensile to compressive stresses in the central fossa area was approximately midway between the internal and external surfaces. The tensile stresses previously demonstrated on the external proximal side of the restoration (tl ) in Fig. 3C, changed to compressive stresses (-1) when the load was increased to 133 pounds as seen in Fig. 4E. Tensile stresses were rather high along the axis of symmetry, demonstrating the presence of tension in the center of the restoration. The fringes increased from +4 to +lO in the area of the central fossa when the load was increased from 50 to 133 pounds. On the internal surface of the restoration, compressive stresses remained the same along the reduced cusps, as can be seen by comparing Figs. 3C and 4E. Two zero fringes were found midway between the proximal margins of the crowns, and the points of maximum compression on the interior of the restoration were in the area of the reduced cusps (-5). The zero fringes are considered to be points of inflection, where the stresses will change from compressive to tensile in nature. Tensile stresses near the proximal margins of the crowns (t-1) could interfere with the requirements necessary for good periodontal health if the tensile stress was sufficient to fracture the cement film. ENGINEERING

DESIGN

The improvement of engineering the cross-sectional area of low-stressed

designs is accomplished by two methods: ( 1) regions may be reduced, and (2) the cross-

Volume Number

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Stress analysis of dental restorations. Part II

301

sectional area in the region of maximum stress may be increased, allowing the concentration of stress to be distributed over a greater area. In the design of restorations in dentistry, the saving of material by reducing the size of the sections having low stresses is of minimal importance unless the bulk of the restoration or appliance interferes with the tongue or other soft tissues. Of major importance is the design of restorations having uniform stress distribution. The stress distribution in the crown considered in this article could be made more uniform by the following modifications. The stress could be distributed by increasing the area of contact of the load rather than having one- or two-point contact. If compatible with the anatomy of the tooth, the occlusal section could be made thicker and the reduced cusps on the tooth could be prepared with less curvature. Also, the margin could be thickened by using a beveled box preparation which would reduce the tensile stresses at the higher loads. Of course, alloys having higher values for the elastic modulus than those of the usual gold alloys would improve the situation, although the laboratory procedures in the use of these alloys present considerable difficulty. Simple sections having no concentration of stress present little difficulty in design, but their attachment to sections of different size, for example, a pontic soldered to a MOD inlay can introduce stress concentrations during soldering or nonuniform stress distribution may occur when loads are applied. Nonuniform stress distribution also may result from the restored tooth when it is loaded, since it consists of materials of different elastic mod&. Since the values of stress in this article represent the stress in the photoelastic model, a method for relating these stresses to the prototype, in this instance the clinical crown, is important. The stress in the model may be converted to stress in the prototype by the use of Equation (2))

where o is the stress in the prototype, F is the force applied to the prototype, L is a linear dimension in the prototype, and m is a subscript denoting corresponding values for the model. Future studies in three-dimensional photoelastic will use this dimensional analysis equation. SUMMARY The general stress distribution in full crown restorations was investigated using a two-dimensional photoelastic stress analysis method. Crowns on tipped molar abutments as well as on normally aligned molars were analyzed. The maximum compressive stresses on the interior of crowns were generally found to be on the reduced cusp surface of the restorations. Maximum tensile stresses were observed in the central fossa and along the axis of symmetry of the crown, when the crowns were loaded bilaterally to simulate oral conditions. Stresses were also investigated at the free boundaries of the crown, and tensile stresses were observed at the cervical margins of the restoration with compressive loads of 133 pounds and at a cusp angle of 39 degrees.

302

Craig,

El-Ebrashi,

and Peyton

J. Pros. Dent. March, 1967

CONCLUSIONS 1. It is desirable to have multiple point contact when an antagonistic tooth occludes with the abutment crown, to reduce stress concentrations near the central fossa of the restored tooth. 2. Full shoulders (or their equivalent) on complete crowns are recommended, and, in instances of proximal caries, proximal boxes and bevels are suggested in order to increase the bulk in the critical cervical margin, thus redistributing the tensile stresses developed. 3. Reduced cusps should be rounded on the preparation, to avoid the development of high compressive stresses on the interior surface of the crown, which may induce postoperative pain. 4. Deep developmental grooves carved near the center of the tooth should be avoided, as they will tend to produce deleterious stress concentrations. This consideration is also important if cusps of teeth are reduced and then protected in occlusal rehabilitation. References 1. Boucher, C. O., Editor: Current Clinical Dental Terminology, St. Louis, 1963, The C. V. Mosby Company, p. 87. 2. Miller, I. F., and Belsky, M. W.: The Full Shoulder Preparation for Periodontal Health, D. Clin. North America, March, 1965, p. 83-102. 3. Smith, G. P.: The Marginal Fit of the Full Cast Shoulderless Crown, J. PROS. DENT. 7: 231-243, 1957. 4. Brumfield, R. C.: Dental Gold Structures, Analysis and Practicalities, New York, 1953, The J. F. Jelenko Co., p. 49-52. of Stresses in Fixed-Bridge Restorations 5. Craig, R. G., and Peyton, F. A.: Measurement Using a Brittle Coating Technique, J. D. Res. 44: 756-762, 1965. 6. Heywood, R. B.: Designing by Photoelasticity, London, 1952, Chapman and Hall, Ltd.. pp. 314-365. 7. Craig, R. G., El-Ebrashi, M. K., LePeak, P. J., and Peyton, F. A.: Experimental Stress Analysis of Dental Restorations. Part I. Two-Dimensional Photoelastic Analysis of Inlays, J. PROS. DENT. 17: 277, 1967. UNIVERSITY

OF MICHIGAN

SCHOOL OF DENTISTRY ANN ARBOR, MICH. 48104