stress fatigue principles

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    Stress Fatigue: Basic Principies and

    Prosthodontic Implications

    H.W. Anselm Wiskotl, DMD. MS. MSD- Unñeríity of Ceneva Geneva Switzerland

    lack I. Nicbolls, PhD Univeisity of Washington Seattle, Washington

    Urs C. Belser DMD' University of G e n e r a Geneva Switzerland

    Clinical evidence indicates that the majority of fractures that occur in prosthodontic structures do so after a period of many years. Such failures generally are not related to an episode of acute overload hut result from fatigue failure. This paper reviews the current kno wledge o í fatigue idilure and test methods. A n ove rview oí pu hlished studies is given, and the authors suggest guidelines for future p rosthodontie studies of this nature. Int I Prostbodont 1995:8:105-116.

    F atigue is a mode of fracture whereby a structureeventually fails after being repeatedly subjected to loads that are so small that one application appar- ently does nothing detrimental to the component.'

    The term fatigue was first proposed by Panalet in 1839, a time w hen the industrial re volution had started and rapidly moving parts beeame increasingly common. In those times, the main line of thought explained fatigue fractures by crystallization of the material which became brittle after continued use and thus more prone to fracture. Much credit should be given to researchers such as Rankine (1843), McConnell (1849], Wohler (1858), and Fairbairn (1864), who, through systematic investigation and testing, were able to reproduce fatigue failure by cyclic loading. They also developed the concept of fatigue lim it and the S -N curve (Table ).'

    Today fatigue failure Is explained by the devel- opment of microscopic cracks in areas of stress

    concentra t ion. With cont inued loadings , these cracks fuse to an ever-growing fissure that insidi- ously weakens the restoration. Catastrophic failure

    'Lecturer, Division of Fixed Proslhod ontii:;, Scho ol of Dentis ry.

    "Professor, Depsrlmenl of estorative Dentistry, School of Dentistry.

    •"Professor and Chairmm, Division of Fixed Prosthodontics School o f Dentistry.

    Reprint requests: Or H.W.A. Wiskatt, D ivision of Fixed

    Prosthodontici, School of Dentistry University of Geneva, 19,rue Bartheiémy-Menn, ¡205 Geneva, Switzerland.

    results from a final loading cycle that exceeds the mechanical capacity of the remaining sound por- tion of the material.

    When subjected to cyclic stresses of sufficient magnitude, almost any manufactured component is likely to fail by fatigue. Similar processes have also been observed in biologic structures. Military recruits and athletes are especially prone to stress fractures, as they are often referred to in the ortho - pedic literature .' Sim ilarly, spontaneous fractures have also been linked to fatigue phenomena.

    Table Abbreviations Used 1, II , til a

    ö „ tfuo T

    E

    fK

    N N, n P Rs s s S. s„ , s„„

    s . T X

    (as indices) F racture modes 1, II or III Applied stress (monotonie) (tensile: +,

    compressive. - ) Yield strength Ultimate tensile strength Applied stress (monotonie, shear) Modulus of elasticity (tensile)

    Frequency of cyclic loadingStress concentration factor Critical stress concentration in mode Number of cycles in a (atigue test Number of cycles at failure Number of specimens in tesl sample Probability of non-failure Stress ratio: S^^/S. „ Applied stress (cyclic, tensile) Sample standard deviation Stress amplitude Mean stress - p re stress Maximum level of applied cyclic stress Minimum level of applied cyclic stress Conventional endurance limit at W cycles Applied stress (cyclic, stiear) Sample m ean

    B, Number 2, 1995 105 The Intematioral louitial of Pro5tliodonrics

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    : Princifte and [mplíf.iuoii

    Neutral fiber

    Tension

    Fig 1 Elemenlary leatures of crack nucleation and progression. Under compression from above, the beam tends to dislocate on the tensile (lower) surface oí the beam. The crack appearing on the tensile side is said to open in mode / (the most frequent). Modes II and I II are shear and twist modes.

    Fig 2 Close up of an intact beam and the crack of Fig 1. Note concentration of force flow-lines around the crack tip with increasing sharpness

    Indeed, microcracks do appear in heterogeneous anisotropic iiving tissue such as hone.^ It has been hypothesized that the damage caused by these fis- sures may act as a slimulus for hone remodeling.

    The purpose of this report is to present an overview of present knowledge on fatigue failure, i t s phys ica l o r ig in , me thods o f ana lys i s , and prosthodontic implications.

    Physical Mechanism

    Inasmuch as fatigue is a peculiar mode of mate-rial ruptijre, a brief overview of elementary fracture

    mechanics is ind icated . For explanatory purposes, a simplified beam model of fracture is presented in Fig 1. Since Hooke (1676) it has been known that for small loads, such a bar deforms elastically in a mode that is proportional to the stress applied. Bending the beam, as in Fig 1 causes two zones to develop: in the superior layers, the material is placed under compression, whereas tensile stresses develop in the inferior zones. Because of the general shape of the beam, the transition between zones of tension and compression is smooth and gradual. If, however, notches or grooves are machined into the

    surface under tension, they act as local stress raisersand, depending on their location and shape, can increase the stresses that develop inside the material by several orders of magnitude (Fig 2)- Similarly, if flaw develops, its tip acts as a stress concentrator, thereby accelerating crack propagation until even- tual failure.

    Thus, the resistance of the material to crack pro- gression (ie, its fracture toughness) is an important parameter. This property is characterized by the stress intensity factor A', which can be loosely described as the ma thema tical equ ivalen t of the stress fringes in pola rized light tests. Und er load, (he beam of Fig I develops internal stresses that locally may he high enough to initiate a crack and cause it (o progress. In other words, K h s reached its critical ievel and is therefore equated to the fracture toughness of the material. In general terms fracture toughness is given by

    K = \

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    5tr«5 Fatigue: Principles and Implications

    Table Typical K^ of Some Dental Restorative Materials

    Material Composition

    Modulus of Rupture

    [ M P a | [MPa] [MPam'^l H Igh-a Hoy steels Fe+ 0.1Gr0.5Mn

    18Cr8Ni Superalloys

    Titanium

    Aluminum Dental ceramics Zirconia Silicons Concrete

    Poly(methyl methacrylate]

    Epoxy

    Composites

    Ni + 10Co 10W9Cr 5AI 2Ti TI 6AI 4V Al 3Mg 0.5 Mn

    ZrO, + 5wt%MgO SijAION, C aO SiOj AI20ä

    [n ] 1- H COOCH J „

    75-200 300-500 500-830

    7

    OH

    170-1600

    800

    800-900 40-300

    460-1700

    1300

    900-1000 120-430

    50 170

    100

    50 80 3 0 ^ 0

    3-5

    4 12 5

    0.2

    O - C,H,-C - C,M, - o - CH,-CH - CH, -

    5 8 % uniaxial C in epo>;y

    80-90 1.6[20 C)

    0.6 1

    1050 32-45 Data from engineered stnjclures are given lor comparison. Note extremely lew material constants o( concrete.

    Opening crack

    Fig 3 Irwin's plastic zone correction. The metal distends ahead ct the crack tip. Therefore, the effective crack length is a„ = a + ir„isthe limiting stress factor inside the material.

    refers to the fracture m ode (Fig 1). Y is a correction parameter that is required because of the finiteness of the specimen whose boundaries also alter the force flo w lines of Fig 2. It is a dimensionless geometry factor on the order of 1. Table 2 lists K,,, T„,

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    Fíitigue: Principies and Implicali

    where er is the overall applied stress, a, the crack length, and p, the radius of the crack tip, IT„,.„ is the stress inlensity that develops at the crack t ip. Laboratory production and handling of ceramics make Griffith flaws inevitable, and since the crack

    tip radius can be as small as an interatomic spac-ing, stress intensification can be extreme. As stated, fatigue failure is initiated by micro-

    scopic cracks that develop in areas of stress con- centration at or near the surface. The most com- mon iocal stress raisers are grain boundaries, inclusions, local intrusions and extrusions, and sudden changes in the geometric configuration of the surface. This initial step is termed nucleation and represents a mandatory stage of fatigue failure. It has been show n that per io dic al ly ha l t ing a fatigue test and polishing a layer off the material

    under investigation could extend tbe fatigue life ofthe specimen indefinitely,

    When a fissure has reached its critical size, it will definitely progress at each loading cycle. This pro- cess is referred to as propagation and amounts to about 90% of fatigue life. It is commonly divided into three stages. During stage 1, the fissures propa- gate in crystallographic shear mode, intragranularly along the slip-bands of the crystal. At this stage, the rate of crack progression is of the order of a few nanometers/cycle. In stage II propagation, the direc- tion of flaw progression has been altered and is nor- mal to the tensile stress (plane strain c

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