Stochastic concepts in the study of size effects in the mechanical strength of highly oriented polymeric materials

Wagner, H. Daniel

doi:10.1002/polb.1989.090270108

Cited by 85 publications

(27 citation statements)

References 38 publications

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“…(Salem et al 1996;Okabe and Hirata 1995), and have also been observed for other quasibrittle materials, e.g. concrete (Weibull 1939) and fibrous materials (Wagner 1989;Schwartz 1987), though not for finegrained perfectly brittle materials at normal laboratory scale.…”

Section: Existing Strength Histograms On Ceramics and Their Fits Withmentioning

confidence: 88%

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

Pang

Bažant

2008

Int J Fract

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It is argued that, in probabilistic estimates of quasibrittle structure strength, the strength threshold should be considered to be zero and the distribution to be transitional between Gaussian and Weibullian. The strength histograms recently measured on tough ceramics and other quasibrittle materials, which have been thought to imply a Weibull distribution with nonzero threshold, are shown to be fitted equally well or better by a new weakest-link model with a zero strength threshold and with a finite, rather than infinite, number of links in the chain, each link corresponding to one representative volume element (RVE) of a non-negligible size. The new model agrees with the measured mean size effect curves. It is justified by energy release rate dependence of the activation energy barriers for random crack length jumps through the atomic lattice, which shows that the tail of the failure probability distribution should be a power law with zero threshold. The scales from nano to macro are bridged by a hierarchical model with parallel and series couplings. This scale bridging indicates that the

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Section: Existing Strength Histograms On Ceramics and Their Fits Withmentioning

confidence: 88%

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

Pang

Bažant

2008

Int J Fract

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“…The observed strength histograms for ceramics, concrete, and fiber composites (10,30,31) typically exhibit in Weibull scale a kink that separates two segments. The lower segment is a Weibull straight line and the upper one deviates from this line to the right.…”

Section: Macrocrack Growth Law As Consequence Of Subcritical Nanocrackmentioning

confidence: 99%

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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“…This phenomenon is usually called the size effect and can be understood by two distinct arguments, based either on probability or fracture mechanics. From a probabilistic viewpoint, Weibull (3,4) and Freudenthal (5) proposed a formal link between the probability of occurrence of a critical defect in a solid of (dimensionless) volume, the concentration of defects, and the size (length, area, and volume) of the solid specimen. According to Weibull's model the probability of occurrence of a critical defect (and thus of failure) increases rapidly with increasing size for a given defect concentration.…”

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confidence: 99%

On the mechanical behavior of WS ₂ nanotubes under axial tension and compression

Kaplan‐Ashiri

Cohen

Gartsman

et al. 2006

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

269

226

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The mechanical properties of materials and particularly the strength are greatly affected by the presence of defects; therefore, the theoretical strength (Ϸ10% of the Young's modulus) is not generally achievable for macroscopic objects. On the contrary, nanotubes, which are almost defect-free, should achieve the theoretical strength that would be reflected in superior mechanical properties. In this study, both tensile tests and buckling experiments of individual WS2 nanotubes were carried out in a highresolution scanning electron microscope. Tensile tests of MoS2 nanotubes were simulated by means of a density-functional tightbinding-based molecular dynamics scheme as well. The combination of these studies provides a microscopic picture of the nature of the fracture process, giving insight to the strength and flexibility of the WS2 nanotubes (tensile strength of Ϸ16 GPa). Fracture analysis with recently proposed models indicates that the strength of such nanotubes is governed by a small number of defects. A fraction of the nanotubes attained the theoretical strength indicating absence of defects.inorganic ͉ mechanical properties T he strength of macroscopic objects is determined by the intrinsic (crystalline) properties of the material as well as by such extrinsic factors as grain boundaries, dislocations, vacancies, and other defects (1, 2). These extrinsic factors are affected by the manufacturing processes used for the preparation of a specific specimen. Thus, the strength of macroscopic objects is generally much smaller than the theoretical value of 10% of Young's modulus. This apparent discrepancy highlights the fact that the strength of materials is only partially determined by their intrinsic mechanical properties (1, 2), i.e., the strength of their chemical bonds.In general, the strength of macroscopic materials increases as the scale decreases. In reinforcing fibers for example, this is true whether the scale is taken as the diameter of the fiber or its length. It is also true for the characteristic (or average) dimension of a reinforcing particle or a platelet. This phenomenon is usually called the size effect and can be understood by two distinct arguments, based either on probability or fracture mechanics. From a probabilistic viewpoint, Weibull (3, 4) and Freudenthal (5) proposed a formal link between the probability of occurrence of a critical defect in a solid of (dimensionless) volume, the concentration of defects, and the size (length, area, and volume) of the solid specimen.

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Stochastic concepts in the study of size effects in the mechanical strength of highly oriented polymeric materials

Cited by 85 publications

References 38 publications

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

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

On the mechanical behavior of WS ₂ nanotubes under axial tension and compression

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Stochastic concepts in the study of size effects in the mechanical strength of highly oriented polymeric materials

Cited by 85 publications

References 38 publications

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

Statistics of strength of ceramics: finite weakest-link model and necessity of zero threshold

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

On the mechanical behavior of WS 2 nanotubes under axial tension and compression

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On the mechanical behavior of WS ₂ nanotubes under axial tension and compression