Lifetime prediction of CAD/CAM dental ceramics

Lohbauer, Ulrich; Petschelt, Anselm; Greil, Peter

doi:10.1002/jbm.10468

Cited by 93 publications

(70 citation statements)

References 26 publications

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“…Fig. 1 H-K documents further close fits of histograms of flexural strength of various industrial and dental ceramics (32)(33)(34). Previous investigators fitted them closely by the 3-parameter Weibull distribution with a nonzero threshold, though with unreasonably small Weibull moduli m. It is now clear that close fits were possible because only a few hundred tests were made.…”

Section: Macrocrack Growth Law As Consequence Of Subcritical Nanocracksupporting

confidence: 66%

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Bažant

Bazant

2009

Proc. Natl. Acad. Sci. U.S.A.

105

110

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The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10 −6 . The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activationenergy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size-and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.cohesive fracture | crack growth rate | extreme value statistics | size effect | multiscale transition A comprehensive theory of the statistical strength distribution exists only for perfectly brittle structures failing at macrocrack initiation from a negligibly small representative volume element (RVE) of material. The objective of the present article is to extend recent studies (1-3) by developing a comprehensive and atomistically based theory for strength and lifetime distributions of structures consisting of quasibrittle materials. These materials, which include fiber composites, concretes, rocks, stiff soils, foams, sea ice, consolidated snow, bone, tough industrial and dental ceramics, and many other materials on approach to nanoscale, are characterized by a RVE that is not negligible compared with structure size D. The space does not allow commenting on previous valuable contributions made by Coleman (4), Zhurkov (5, 6), Freudenthal (7), Phoenix (8, 9) and others (10, 11) (for such comments, see, e.g., refs. 2, 3, 12, and 13).

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Section: Macrocrack Growth Law As Consequence Of Subcritical Nanocracksupporting

confidence: 66%

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Bažant

Bazant

2009

Proc. Natl. Acad. Sci. U.S.A.

105

110

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“…SEM images of fracture surfaces of (a) VM7 feldspathic porcelain (reproduced with permission from [57]) and (b) IPS Empress (reproduced with permission from [34]) with wake hackles (WH). Table 1 Strength data sets of ten dental ceramics, where 4PBT indicates the 4-point bending test and B3BT represents the ball-on-three-balls test [18][19][20][21][22]. A c c e p t e d M a n u s c r i p t 30 Table 2 The fitted parameters by using the Weibull, normal and log-normal distributions, respectively.…”

Section: Discussionmentioning

confidence: 99%

“…The strength data sets of ten dental ceramics were collected (see Table 1), including their specific names, the category, test methods and the source of data [18][19][20][21][22]. The details of categories of these dental ceramics are as follows:…”

Section: Strength Data Of Dental Ceramicsmentioning

confidence: 99%

“…Moreover, the kink of a Weibull line due to multimodal flaw size can be realized if the specimen has an appropriate effective volume (V eff ≈ 7.5 mm 3 ) [13]. The investigated Vitablocs Mark II (data set 1) specimens have dimensions of 3445 mm 3 and the strength measurements were carried out by four-point bending tests M a n u s c r i p t 19 according to European Standard EN 843 [18]. The effective volume of Vitablocs Mark II (data set 1) specimens is equal to V eff = 11 mm 3 [61].…”

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confidence: 99%

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Fracture statistics of dental ceramics: Discrimination of strength distributions

Nohut

2012

Ceramics International

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The Weibull distribution is the most widely used function in the reliability analysis and structural design of dental ceramics; however, it is still unclear whether Weibull distribution is always the most suitable one. With wide applications of dental ceramics, a special attention has been paid in discriminating their strength distributions. In this paper, three versatile functions, involving normal, log-normal and Weibull distributions, are applied to the analysis of ten strength data sets of dental ceramics with different compositions and the results are compared in terms of the Akaike information criterion and the Anderson-Darling test. It reveals that various microstructures and compositions in the investigated dental ceramics cause their strength distributions deviated from the Weibull distribution. The influence of microstructure induced fracture properties (multiple-modal flaw size distribution, R-curve behavior and subcritical crack growth) on strength distributions is discussed.

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“…Extensive experimental data showed that the strength histograms of various quasibrittle materials, such as concrete, industrial and dental ceramics (Salem et al 1996;Munz & Fett 1999;Tinschert et al 2000;Lohbauer et al 2002;dos Santos et al 2003), and fiber composites (Wagner et al 1986;Wagner 1989), consistently deviate from the two-parameter Weibull distribution. Recently, the three-parameter Weibull distribution with a non-zero threshold has been adopted as a remedy (Stanley & Inanc 1985;Duffy et al 1993;Gross 1996).…”

Section: Introductionmentioning

confidence: 99%

Size effect on strength and lifetime probability distributions of quasibrittle structures

Bažant

2012

Sadhana

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Abstract. Engineering structures such as aircraft, bridges, dams, nuclear containments and ships, as well as computer circuits, chips and MEMS, should be designed for failure probability < 10 −6 -10 −7 per lifetime. The safety factors required to ensure it are still determined empirically, even though they represent much larger and much more uncertain corrections to deterministic calculations than do the typical errors of modern computer analysis of structures. The empirical approach is sufficient for perfectly brittle and perfectly ductile structures since the cumulative distribution function (cdf) of random strength is known, making it possible to extrapolate to the tail from the mean and variance. However, the empirical approach does not apply to structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared to structure size. This paper presents a refined theory on the strength distribution of quasibrittle structures, which is based on the fracture mechanics of nanocracks propagating by activation energy controlled small jumps through the atomic lattice and an analytical model for the multi-scale transition of strength statistics. Based on the power law for creep crack growth rate and the cdf of material strength, the lifetime distribution of quasibrittle structures under constant load is derived. Both the strength and lifetime cdfs are shown to be sizeand geometry-dependent. The theory predicts intricate size effects on both the mean structural strength and lifetime, the latter being much stronger. The theory is shown to match the experimentally observed systematic deviations of strength and lifetime histograms of industrial ceramics from the Weibull distribution.

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Lifetime prediction of CAD/CAM dental ceramics

Cited by 93 publications

References 26 publications

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Fracture statistics of dental ceramics: Discrimination of strength distributions

Size effect on strength and lifetime probability distributions of quasibrittle structures

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