the ball mill as a means of investigating the mechanical failure of dental materials original

8/2/2019 The Ball Mill as a Means of Investigating the Mechanical Failure of Dental Materials Original

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ELSEVIER

0300-5712(95)00035-6 Journal ofDentistry Vol. 24, Nos 1-2, pp. 117~124,1996Copyright 0 1996ElsevierScience td. All rights reservedPrinted in Great Britain.0300-5712/96 $15.00+ 0.00

The ball mill as a means of investigating themechanical failure of dental materialsN. I-L Abu Kasim*, D. T. Millettt and J. F. McCabe**Dental Materials Science Unit and tDepartment of Child Dental Health, Dental School, Newcastle upon Tyne, UK

ABSTRACTObjectiw: The main purpose of this paper is to present a new method of predicting clinical performanceusing mechanical loading in a ball mill.Methods: A series of four experiments (two involving a hybrid composite and one each on orthodonticbrackets and bands) is described in which the ball mill was used to subject specimens to mechanicalfatigue.Results: A reproducibility study using composite beam specimens showed no significant d ifferencebetween the Mean Survival Time (MST) in all the three experimental runs (P = 0.42). When subjected tothermal cycling, the MST of the cycled group was 155.0 min compared to 247.0 min for the control group(P < 0.01). The MST of untreated and sandblasted brackets was 7.9 h and 14 h respectively (P < 0.01).There is also a significant difference (P < 0.001) n the MST of sandblasted bands when compared to theuntreated bands.Conclusions: The ball mill proved to be a convenient and reproducib le m eans of producing mechanicalfatigue and may be useful in predicting the clinical performance of dental materials.KEY WORDS : Ball mill, Fatigue, Composites, OrthodonticsJ. Dent. 1996; 24: 117-124 (Received 24 February 1994; reviewed 18 July 1994; accepted 24 August 1994)

INTRODUCTIONThe properties of dental materials are often evaluatedusing test specimens and in environments which do notclosely approach that of the clinical situation, but inmany cases are carefully controlled. While initialstrength is an obvious requirement for clinical function,the durability of the material subjected to oral stressesover a period of time is equally important. Materialsare subjected to mechanical, thermal and chemicalprocesses in the mouth during routine drinking andeating, which by their cyclic nature invariably inducefatigue. Fatigue may lead to material or bond failuresand may be classified as follows:1. Mechanical fatigue-results from fluctuations in ex-

ternally applied stresses or strains.2. Thermomechanical fatigue-results when the tem-perature of the cyclically stressed materials alsofluctuates.3. Corrosion fatigue-results when the cyclic loads areimposed in the presence of a chemically aggressiveor embrittling environment.

Correspondence should be addressed to: Mrs N. H. Abu Kasim,Dental Materials Science Unit, Dental School, Framlington Place,Newcastle upon Tyne NE2 4BW, UK.

4. Fretting fatigue-occurs as a result of pulsatingstresses along with oscillatory relative motion andfrictional sliding between surfaces.In a fatigue test, either the fatigue limit or thefatigue life is normally assessed3a4. he fatigue limit isthe stress below which failure is unlikely to occurwithin a predeterm ined time period, while the fatiguelife is measured when a fixed fatigue stress is applied toa specimen until it fails.The majority of research reported in the dentalliterature on fatigue pertains to metallic materials , butin recent years much interest has been shown in non-metallic materials and composites. The progression offatigue damage can be generally classified into thefollowing stages5:

1. Substructural and microscopic changes which causedeformation of a permanent nature.2. Creation of microscopic cracks.3. Growth and coalescence of microscopic flaws toform dominant cracks.4. Structural instability or complete fracture. At thisstage fatigue damage can occur at either a micros-copic or macroscopic level. When damage occurs ata macroscopic level, it can lead to bulk fracture.There are essentially two means of producing fa-


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118 J. Dent. 1996; 24: Nos l-2

Tumbling

Grinding

fig. 7. Typical charge motion in a ball mill. (Reproduced withpermission from the Managing Editor of the Transactions of theSociety for Computer SimulationB)

tigue, i.e. by thermal insults (thermocycling) or by me-chanical means. This paper deals with the productionof mechanical fatigue by the use of a ball mill. Generalapplications of the ball mill w ill be described, followedby its possible dental applications.

THE BALL MILLGenerally, the ball mill is used to apply a force to alarge number of particles producing predominantlyshatter fracture6. It is used mainly as a method ofparticle s ize reduction in mineral processing.

Mechanism of the ball millIn a rotary mill, the energy is consumed in keeping themill shell, the grinding media and the material chargein motion, and fractures occur as a byproduct of thepassageof the material through the mill. When rotarymills were first developed, rods were often used insteadof balls, and Haultain and Dyer7 characterized themotion of the tumbling rods in a rotating shell. Thereare three types of motion:1. Rotation of the rods around their own axis.2. Rolling of the rods down the surface of the mass(cascading).3. Parabolic free fall above the mass (cataracting).

This has been further clarified in recent studies8 andit has been suggested that there are three zones ofcomminution in the mill (Fig. 1). Each zone is charac-terized by the type of action produced by the balls,namely the crushing, grinding and tumbling zones. Thecrushing zone consists of the falling balls crashing onthe material, so that the material caught between theballs is pulverized. Grinding occurs between ball layersin the charge, where the ball layers slip past oneanother, grinding any material caught between them.

Grinding can take place by several mechanisms, nclud-ing:1.2.3.

Impact or compression, due to forces applied almostnormally to the particle surface.Chipping due to oblique forces.Attrition due to forces acting parallel to the sur-faces.Finally, tumbling is characterized by cascading ballsthat roll over one another; breakage here may becaused by impact, but an impact of a much lowerenergy leve18.When ball milling, the factors that can be variedare:

1. Total charge.2. Type, size and weight of the ball charge.3. Speed of rotaion.4. Duration of grinding.Total chargeThe charge of a ball m ill is the percentage of the millinterior filled with the grinding media, including thevoids between the media and the batch charge. It hasbeen suggested hat optimum efficiency can be achievedwhen the ball mill is 60-70% full but others havesuggested hat the optimum charge is 30-50%.Type, size and weight of the ball chargeA range of sizes of balls or particles from the samematerial can be used as the charge media in the ballmill. In order to achieve the maximum grinding power,the size of the balls should be the minimum sizecapable of performing the grinding action. The surfacearea of a given weight (or volume) of the balls variesinversely as the square of the diameter. Thus, by re-placing balls with others half their size, the effectivesurface area for grinding is increased. The weight ofballs to be used can be obtained by the sum of thevolume o f balls to be used and their specific gravity. Anequal proportion of balls of different sizes should berepresented.Speed of rotationThe grinding efficiency is greatly affected by the speedof rotation. It has been shown that as the speed of themill is increased, work input initially increases in pro-portion to the speed 2 Then, as slippage increases, thework input increases more slowly than the speed; itcontinues to increase until a critical speed is reachedbeyond which the power input decreases apidly due tothe solids being centrifuged onto the mill shell. It hasbeen suggested hat the movement of a single ball in asmooth-lined ball mill reaches its critical position when


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Abu Kasim et al. Ball mill in investigation of dental materials 119

the weight of the ball balances the centrifugal force onthe ball, i.e. at the highest point of its pathi3. This is atheoretical speed and is referred to as the criticalspeed of the ball mill. The equation quoted for thecritical speed is:

where N, is the critical speed in r.p.m., D, is theinner diameter of the ball mill and D, is the diameterof the largest ball in metresi4.In practice, ball mills are driven at 50-90% of theircritical speed, the choice being influenced by efficiencyand economic considerations14.The duration of grindingA long period of grinding will not necessarily bringabout greater size reductionlo. The aim should be togrind the material so that the desired particle size isquickly achieved throughout the batch. The time se-lected for grinding may be influenced by the tempera-ture of the charge8.The development of the ball mill for dentalapplicationsThe first use of a ball m ill in this laboratory was toinduce fatigue on orthodontically banded and bondedteeth prior to bond strength testing5,16. The sameprinciple of ball milling as used in mineral processingcan be applied to produce mechanical fatigue, therebysimulating the oral forces. However, the charge, forceand the temperature at which the ball mill operatesneed to be altered for this purpose.It was the aim of this work to determine the opti-mum conditions for using the ball mill as a means ofsubjecting dental materials to fatigue and to evaluatethe method using dental composite restoratives andorthodontic luting cements.

MATERIALS AND METHODSApparatusA method of inducing and testing mechanical fatigueusing the ball mill was developed. A 0.5 1 capacitycylindrical ceramic ball mill (Rg. 2) (Pascal1Engineer-ing Company, Crawley, Sussex,UK) was used. To oper-ate the mill, a motor which is external to the ovencauses a pair of rubber rollers to rotate at a prede-termined speed. These in turn cause the rotation of themill. Steatite spheres of diameter ranging from 12.8 to26.5 mm were chosen. Before any experiment was

connecteda motor

t

t ovenball mill

roller

Fig, 2. Schematic diagram of the ball mill testing apparatus.

carried out the maximum range of potential energythat could be generated in the ball m ill was investi-gated. The internal diamater of the ball mill was 90mm. The potential energy generated by the smallestand the largest steatite spheres weighing 22.14 g and2.81 g when dropped from a 90 mm height was calcu-lated. The potential energy that can be generated by asingle impact in the ball mill was determined to be inthe range o f 0.003 J to 0.02 J.In each experiment the ball mill was charged with470 + 1 g of steatite spheres, 250 ml of distilled waterand the tes t specimens all maintained at 37C. The m illrotated at 100 r.p.m. (i.e. 60% of the critical speed). Atspecified intervals the mill was opened and the numberof failed/fractured specimens noted. Fresh distilledwater at 37C was then added and all the intact speci-mens were returned to the mill and testing resumed.Four series of laboratory experiments (two involvinga hybrid composite and one each on orthodontic brack-ets and bands) will be described to demonstrate thedental applications of the ball mill.Reproducibility study using composite beamspecimens (Experiment I)Thirty specimens of composite (P50, 3M, Minnesota,USA) of approximately 2 X 2 X 25 mm were preparedusing a polyethylene mould. Composite was packedinto the mould sandwiched between two matrix stripsand two polymethymethacrylate plates (Perspex, ICI,Welwyn, Herts, UK). Hand pressure was applied to theplates to ensure that the material was properly packedinto the mould extruding all excess material. Afterremoving the plates, the specimens were placed on amoving bed and cured on both sides using a CuringLight (Luxor, ICI, Macclesfield, Cheshire, UK) for 1min per mm of material. After curing, the mould wassectioned using a band saw to aid removal of thespecimens, thus preventing unwanted stress being ap-plied to the specimens prior to testing. Excess flash onthe specimens was removed using 800 grit carborun-dum paper. All specimens were stored in distilled waterfor 24 h at 37C before testing. Ten specimens weretested in each run of the ball mill. The ball mill chargewas as shown in Table I. At 30 min intervals, the ballmill was stopped and opened and the number of frac-


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120 J. Dent. 1996; 24: Nos l-2

Table 1 . Ball charge used in the experimentsExperiments Ball charge Total charge (%ITotal weights Ball diameters

(cl) (mm)1 and 2 470 * 1 12.8, 19.8, 26.5 a43 and 4 470 f 1 17.4, 24.5, 26.5 84

tured specimens noted. A specimen is considered tohave failed/fractured when there is evidence of bulkfracture. Bulk fracture was determined as having oc-curred when the specimen length had been reduced byat least 5 mm. A small amount of material lost bychipping at the ends of the specimens was not thoughtto contribute towards bulk failure involving any sort offatigue mechanism. Such chipping failure could pro-duce around 1-2 mm of specimen length reduction; inorder to have a clear indication of when failure occursthrough the bulk of the specimen, it was thought thata clear reduction in length by an amount significantlygreater than 2 mm was required.

the ball mill that contained a charge as indicated inTable I. Testing continued for a maximum of 20 h andafter each hour the mill was opened and all bondedspecimens that had failed were removed. A fresh sam-ple of distilled water at 37C was then added to the milland testing recommenced.Surviva l of cemented orthodontic bandssubjected to ball milling (Experimenf 4)

The intact specimens and a fresh sample of distilledwater at 37C were placed in the mill and testingresumed. Testing continued up to a maximum o f 5 h.Effect of thermal cycling on survival of compositebeam specimens subjected to ball milling(Experiment 2)

Twenty first molar bands (Johnson and Johnson) werecemented to extracted human third molars with Ketac-cem mixed according to the manufacturers instruc-tions. Half of the samples had their fitting surfacessandblasted with 60 pm alumina prior to cementation.The sandblasted and untreated specimens were colourcoded and placed in the ball mill containing the sameweight and volume of water as used for the bondedspecimens. Testing was carried out as in experiment 3but ended at 7 h, as all banded specimens had failed(defined as loosening of the band) by that time.

Sixty specimens of P.50 were prepared as describedabove. The specimens were divided into two groups,each of 30 specimens. One group was sorted in distilledwater fo r 24 h at 37C (control group) and the otherwas subjected to 2000 thermal cycles. Each thermalcycle consisted of 60 s immersion in a waterbath at60C 60 s immersion in a waterbath at 24C and 60 simmersion in a waterbath at 4C with a change-overtime of 55 s. All specimens were then tested as inexperiment 1.

Statistical analysisMean survival times (MST) were determined usingsurvival analysis (BMDPlL, University of California,USA), while a Generalized Wilcoxon (Breslow) test wasused to compare the mean survival times.

RESULTS

Surviva l of bonded orthodontic brackets Reproducibility study using composite beamsubjected to ball milling (Experiment 3) specimensThirty stainless steel brackets (Johnson and Johnson,Slough, Berks., UK) were bonded to extracted humanpremolar teeth-one bracket was bonded to each tooth.Ten brackets were bonded with Right-On (T.P., LaPorte, Indiana, USA), a no-mix adhesive, following acidetching of the enamel with 37% phosphoric acid for 1min. The remaining 20 brackets were bonded withKetac-cem (Espe, Seefeld, Oberbay, Germany), mixedaccording to the manufacturers instructions; ten hadtheir bases sandblasted with 60 pm alumina prior tocementation-no enamel etching was carried out priorto bonding. The three sets of specimens were colourcoded with an indelible pen and were then p laced in

Figure 3 shows hat the test method is reproducible andthe scatter between the three runs is small. Table IIshows the mean survival times for all three runs whichwere not significantly different from each other.Effect of thermal cycling on survival of beamcomposite specimens subjected to ballmillingIt is evident from Fig. 4 that the control specimenssurvived the earlier stages of the ball milling process,whereas the specimens that have undergone 2000 ther-mal cycles failed rather quickly, even in the early


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100 I,-I. ; ___ Run 1--- Run 2L-i ,... . . . Run 3

0 50 100 150 200 250 300Time (minutes)

Fig. 3. Reproducibility study using P50

stages. At least 40% of the control specimens survivedthe test period o f 5 h whereas only 20-30% of thethermocycled specimens survived. The MST for theTable II. Survival times for composite specimens

Survival time (min)Mean S.E.

Run 1 207 31Run 2 240 29Run 3 264 22P =0.42 (Wilcoxon).

-0 thermal cycle

60 -I--

--- 2000 thermali,

t-

cycles

0 60 120 180 240 300Time [minutes)

Fig. 4. Effect of thermal cycling for P50. Percentage survivalagainst time.

100100 7 - Sandblasted bracketsandblasted bracketsI- ---, ---Untreated brackets--Untreated bracketsI t--i Ia0 -0 I-

! i--20 I-1 II- t01 , , , , , ,I, / ( ,0 2 4 6 8 10 12 14 16 16 20

Time [hours)Fig. 5. Percentage survival against time after ball milling for 10sandblasted and 10 untreated first molar brackets cemented withKetac-cem. (This figure was previously prublished in the BritishJournal of Orthodontics, reproduced with permissioni6)

control group was 247.0 min compared to 155.0 min forthe thermocycled group. Statistical analysis withWilcoxon revealed that the different MST fpr controland cycled groups was highly s ignificant (P < 0.01).

Surviva l of bonded orthodontic bracketssubjected to ball milling (Fig. 5)Only one of the brackets bonded with Right-on failed(after 2 h of ball milling)-all others survived the testperiod of 20 h. Of the brackets bonded with Ketac-cem,five sandblasted brackets failed, whereas all untreatedbrackets failed over the 20 h test period. The MST forthe untreated brackets bonded with Ketac-cem was(7.9) h, while the MST was 14 h for the sandblastedbrackets bonded with Ketac-cem (P < 0.01).

Surviva l of cemented orthodontic bandssubjected to ball milling (Fig. 6)All the banded specimens had failed by 7 h o f ballmilling. The MST for bands with untreated and sand-blasted fitting surfaces was calculated. This was 2.3 hand 5.9 h respectively; this difference was highly sig-nificant (P < 0.001).

DISCUSSIONThis paper has described the ball mill and has indi-cated that it can be used as a means of simulatingmechanical loading in dental materials testing. Before


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122 J. Dent. 1996; 24: Nos l-2

100

80

60

40

20

0

-Sandblasted bands---Untreated bandsIIIIL--,

L-----,IIh_----

III I I 10 1.5 3.0 4.5 6.0 7.5

Time (hours)Fig. 6. Percentage survival against t ime after ball milling for 10sandblasted and 10 untreated first molar bands cemented withKetac-cem. (This figure was previously published in the BritishJournal of Orthodontics, reproduced with permiss ioni7)

discussing the results of our experiments, it is impor-tant to consider first the development and evolution ofthis method along with an analysis of the mechanismsof material failure.The ball m ill has been used previously in mineralprocessing but its adaptation for use in dental materialstesting required alteration to both the charge and thetesting temperature. The conditions were different fororthodontic brackets and bands for two reasons. First,there is a need to adopt specific test conditions fordifferent types of material under test and, secondly,changes were made as our understanding of the ballmill improved.A pilot study was carried out using the ball chargerecommended by the manufacturer for a ball mill of 0.51 capacity (i.e. 9.5 mm, 12.8 m and 19.8 mm diamterballs) to ascertain its suitability for our study. Thirtyspecimens were tested in the ball mill, 10 specimens ata time as in experiment 1. All the specimens surviveddespite 52 h of ball milling. As this was considered tobe unreasonable as a basis for a future standard test,the smallest diameter balls were replaced by 26.5 mmdiameter balls. The new ball charge produced resultswithin a reasonable period of time (e.g. 24 h), and thiswas later used in experiments 1 and 2. However, thesame range of ball charge diameter was not used inexperiments 3 and 4 as the specimens nvolved in theseexperiments were larger, and as results could not beobtained in a reasonable period of time the 12.8 mmdiameter steatite spheres were replaced by balls of alarger diameter. It seems hat different ball charges willbe appropriate for different materials. The most ap-

propriate total charge determined for each of the ex-periments performed is given in Table I.Experiments 3 and 4 were performed by using dis-tilled water initially at 37C and testing was carried outat room temperature in contrast to experiments 1 and 2where testing was carried out at a maintained tempera-ture of 37 + 1C in an oven. This was not possible forthe earlier experiments (presented here as experiments3 and 4), as a means of placing the ball mill in the ovenhad not been developed at that time. However, thetemperature of the water was noted after each testinterval in experiments 3 and 4 and the temperaturehad dropped by only 2C following each hour of testing,probably due to the energy generated in the mill.Central to the efficacy of the ball mill for materialstesting is the mechanism of failure. The precise mecha-nism of failure has not been adequately described inthe engineering literature; however, three processesbywhich a mineral may be gradually broken down in theball mill during processing have been proposed17.First,the balls fall onto the material fracturing it by impact,compressive and tensile forces. Secondly, the largerparticles of the materials being milled act on the smallerparticles in much the same way as the balls bringingabout autogenous grinding. Lastly, all the contents ofthe ball mill may slide over themselves and over theball-mill wall causing compressive or shear forces lead-ing to further breakdown by attrition or shear failure14.The mechanism described above implies that frac-ture of a material is by a single load application orimpact. However, if loading is insufficient to causefailure through a single application it is likely thatfracture may occur through repeated loading, i.e. afatigue mechanism. It can therefore be inferred thatthese same processes may have occurred in the ballmill when used for testing dental materials.Fracture o f dental materials during ball milling isthought to occur by one of several possible mecha-nisms. First, by the force of impact on a perfect speci-men as in the situation of a three-point bend test. Thisis unlikely to be a significant factor in the current test,as the potential energy generated by a single impact bythe largest steatite sphere was approximately 0.02 J,whilst the energy required to fracture equivalent speci-mens of P50 is 0.73 J (k 0.20) as determined in ourlaboratory using a three-point bend test. It has beenpreviously suggested hat breakage in the ball mill maybe caused by impact in the tumbling zone of the mill,which is characterized by cascading balls that roll overone another, and this involves a much lower energylevel than the maximum used in our calculation8. Theenergy required for fracture to occur is reduced by thepresence of wa ter. Failure caused by impact forcescould also be ruled out, as nearly all control specimensin experiments 1 and 2 survived at least the first 30 minof ball milling. This is further supported by the speci-men failure rate observed with thermocycling. If f rac-


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ture had been caused by a single impact, the failuretrend would have been random or erratic and wouldnot have followed any set pattern.A second possible mechanism of failure may involveimpact forces acting on chipped specimens. This is akinto that of a single edge-notched fracture-toughnesstest. The energy required to fracture a single edge-notched specimen of P50 is 0.02 J (-t 0.004), where thedepth of the notch is half the depth of the specimen.Although this potential energy is quite similar to themaximum possible potential energy generated by thelargest steatite sphere in the ball mill, fracture is un-likely to occur by this mechanism as the chip on thespecimen is unlikely to be deep enough.A third mechanism involves slow crack propagationthrough a prechipped specimen as in a normal fa tigueprocess. Finally, mechanical action by the balls maycause gradual weakening of specimens leading to ulti-mate failure.Specimen failure in the ball mill does not appear tobe a random fracture process. The reproducible natureof the test results indicates a dependence on materialproperties which change under the influence of rela-tively small loads during contacts with the mill ballcharge (Fig 3). This is further supported by the effectof thermocycling (Fig. 4), where the specimens seem tohave a shorter survival time when compared to thecontrol group even though there was no significantdifference in the flexural strength of the material (165MPa and 162 MPa). The low stresses mparted by thesteatite spheres are most likely to induce fatigue in thespecimens, and failure probably occurs when the fa-tigue limit is reached.It is normal to characterize fracture processes bymicroscopic imaging of the fracture surfaces. It has notbeen possible to characterize the fracture mechanismsof specimens broken in the ball mill, probably becausefragments continue to be impacted by the balls afterfracture has occurred. This masked the structural fea-tures of the fracture surfaces which would otherwiseproduce useful evidence as to the mode of failure.In relation to bonded and banded orthodontic at-tachments, bond strength tests give an incomplete indi-cation of the clinical performance, and a more accuratemethod of testing bond reliability may be achieved byusing simulated mechanical loading in a ball mill. Themean survival time was almost twice as long (14 h) forsandblasted brackets relative to untreated brackets (7.9h), and 2.5 times longer for sandblasted bands (5.9 h)relative to untreated bands (2.3 h). One would expect,therefore, better clinical performance from bracketsand bands with sandblasted fitting surfaces. This hasbeen shown to be the case when the effect of sandblast-ing was investigated as part o f a clinical trial. Theshapes of the survival curves from the ball m ill and theclinical studies were very similar, except, of course, forthe fact that the ball-mill study was performed over amuch shorter time-scale. It would not have been possi-

ble to propose this from the results of bond strengthtesting alone.The test environment and mechanical loading in themill are similar to that occurring in the mouth. It wouldappear, therefore, that the ball mill may be useful as ameans of predicting the durability of restorative andorthodontics materials.All techniques have their advantages and disadvan-tages, and to conclude this discussion it seems ap-propriate to mention those related to the ball mill. Theadvantages of this method compared to methods usedby other workers in fatigue studies of dentalmaterials34:19,20re:1.2.

3.

1.2.

It is inexpensive in terms of equipment and time,and uses readily available equipment.Tests are reproducible and results are produced witha relatively small number of specimens within ashort period of time.It produces results which can be related to clinicalsurvival data.The disadvantages of the ball m ill are:The exact forces in the mill cannot be preciselydetermined.It is possible that some of the fractures may occurby mechanisms other than fatigue.The experimental method described in this paperforms a basis from which a standard testing regimencould be established. From our results the following

conclusions may be drawn:1. The ball mill offers a convenient and reproduciblemeans of producing mechanical fatigue.2. It may be useful as a potential method of predictingthe clinical performance of new restorative materi-als and luting agents for orthodontic brackets andbands.

References

8.

Phillips RW . Skinners Scienceof Dental Materials, 8th edn.London, Sanders, 973.Smith DC. Dental cements-Current status and futureproperties.Dent Clin North Am 1983; 83: 763-792.Draughn RA. Compressive atigue limits of compositerestorativematerials.J Dent R es 1979; 58: 1093-1096.McCabe JF, Carrick TE, Chadwick RG, Walls AWG .Alternative approacheso evaluating he fatigue charac-teristics of materials.Dent Mater 1990; 6: 24-28.Suresh S. Fatigue and Materials, 2nd end. CambridgeSolid State ScienceSeries,1991.Spink K. Comminutionmethodsof machinery.Min MinerErg 1972; 8: 5-21.Haultain HET, Dyer FC. Ball paths in tube mills androck crushing in rolls. Tram Am Inst Mining Met Engr1923; 69: 198-207.TarasiewiczS, Radziszewski . Ballmill simulation: PartIII-Energy and the breakageevent. Trans Sot ComputSimul 1990; 6: 291-306.


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9. Kelly EG, Spottiswood DJ. Introduction to Mineral Pro-cessing.New York: John Wiley, 1982.10. Channel DR. The operation of ball mills. Zndust Chem1951; 27: 69 -73.11. Bond FC. Crushing and grinding calculations. Part I. BrChem Eng 1961; 6: 378-385.12. Horne HF. A grinding mill with micarta bearings. EngMiningJ 1937; 138: 43-44.13. Fahrenwald AW, Lee HE. Ball mill studies. Am ZnstMining Met Erg Tech Pub1 1931; 375-379.14. Willis BA. Mineral Processing Technology, 5th edn. Ox-ford: Pergamon Press, 1992.15. Durning P. A Clinical and Laboratory Investigation intoCements Used to Retain Orthodontic Bands. MDS The-sis, University of Newcastle upon Tyne, 1989.

16. Millett D, McCabe JF, Gordon PH. The role of sand-blasting on the retention of metallic brackets appliedwith glass onomer cement. BrJ Orthod 1993;20: 117-12217. Jones M. Mineral Processing.Milton Keynes: The OpenUniversity Press, 1979.18. Millet DT, McCabe JF, Bennett TG, Carter NE, GordonPH. The effect of sandblasting on the retention of firstmolar orthodontic bands cemented with glass ionomercement. Br J Orthod (in press).19. Drummond JL, Miescke KJ. Weibull models for thestatistical analysis of dental composite data: aged in phys-iologic media and cyclic-fatigued. Dent Mater 1991; 7:25-29.20. Asmussen E, Jorgensen KD. Fatigue strength of someresinous materials. Stand J Dent Res 1982; 90: 76-79.

the ball mill as a means of investigating the mechanical failure of dental materials original

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