Size Effect on Flexural Strength of Fiber-Composite Laminates

Bažant, Zdeněk P.; Zhou, Yong; Novák, Drahomı́r; Daniel, I. M.

doi:10.1115/1.1631031

Cited by 47 publications

(29 citation statements)

References 33 publications

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“…1) on the size effect on flexural strength (modulus of rupture) of plain concrete [39]. This equation was further shown to agree with the data from flexural strength tests of laminates of various lay-ups [40,42] (Fig. 1) conducted at NASA Langley Research Center by Jacksom et al [43] (see also Refs.…”

Section: Matching the Large-size And Intermediate Asymptotics Of Sizesupporting

confidence: 71%

“…Likewise for sea ice , assuming the same ratio of the inhomogeneity size. On the other hand, for fine grained ceramics, kl would be of the order of millimeters, and for the flexural strength of fiber reinforced polymer composites of the order of decimeters [42] (for a jointed rock mass, with joints about 10 m apart, k) would be about 1 km; for the ice cover of the Arctic Ocean as a whole, consisting of weakly connected thick mile-size floes, kl would probably be about 100 miles).…”

Section: Intermediate Asymptoticsmentioning

confidence: 99%

“…1) for concrete [39] and laminates [42] showed that the transition from energetic (nonlocal) size effect to statistical size effect is centered at a beam depth of about 2 m (i.e. the size effect in flexural strength, or modulus of rupture, of laboratory beams is mainly energetic, or nonlocal, while the size effect on flexural strength of an arch dam is mainly statistical).…”

Section: Intermediate Asymptoticsmentioning

confidence: 99%

See 2 more Smart Citations

Probability distribution of energetic-statistical size effect in quasibrittle fracture

Bažant

2004

Probabilistic Engineering Mechanics

109

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The physical sources of randomness in quasibrittle fracture described by the cohesive crack model are discussed and theoretical arguments for the basic form of the probability distribution are presented. The probability distribution of the size effect on the nominal strength of structures made of heterogeneous quasibrittle materials is derived, under certain simplifying assumptions, from the nonlocal generalization of Weibull theory. Attention is limited to structures of positive geometry failing at the initiation of macroscopic crack growth from a zone of distributed cracking. It is shown that, for small structures, which do not dwarf the fracture process zone (FPZ), the mean size effect is deterministic, agreeing with the energetic size effect theory, which describes the size effect due to stress redistribution and the associated energy release caused by finite size of the FPZ formed before failure. Material randomness governs the statistical distribution of the nominal strength of structure and, for very large structure sizes, also the mean. The large-size and small-size asymptotic properties of size effect are determined, and the reasons for the existence of intermediate asymptotics are pointed out. Asymptotic matching is then used to obtain an approximate closed-form analytical expression for the probability distribution of failure load for any structure size. For large sizes, the probability distribution converges to the Weibull distribution for the weakest link model, and for small sizes, it converges to the Gaussian distribution justified by Daniels' fiber bundle model. Comparisons with experimental data on the size-dependence of the modulus of rupture of concrete and laminates are shown. Monte Carlo simulations with finite elements are the subject of ongoing studies by Pang at Northwestern University to be reported later. q

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Section: Matching the Large-size And Intermediate Asymptotics Of Sizesupporting

confidence: 71%

Section: Intermediate Asymptoticsmentioning

confidence: 99%

Section: Intermediate Asymptoticsmentioning

confidence: 99%

See 1 more Smart Citation

Probability distribution of energetic-statistical size effect in quasibrittle fracture

Bažant

2004

Probabilistic Engineering Mechanics

109

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“…Size effects are well known to affect the failure load and behavior of composite materials [22][23][24], as well as the energy density in drilled cylindrical concrete specimens [25]. Unlike other metallic materials, the relative scale that exists between the representative volume element of the EMWM (i.e., the finite helix wires) and the EMWM solid is not negligible.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent mechanical behavior and boundary layer effects in entangled metallic wire material systems

Zhang

et al. 2016

J Mater Sci

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This paper describes the influence on the compressive and dissipative behavior of entangled metallic wire material (EMWM) samples provided by their size and mutual connectivity. The mechanical properties of EMWM specimens with different thicknesses are obtained from quasi-static compressive and cyclic loading. The behavior of the stress-strain curves, tangent modulus, and loss factor are strongly dependent on the thickness of the samples. The analysis from samples connected in different layouts shows that apart from the global thickness, size scale effects and contact interface also play important roles in controlling the behavior of EMWM systems. The importance of the sample size and its connectivity with adjacent different layers are defined by the unique microstructure and contact properties of the wires near the specimen boundary layer. The boundary layer produces different mechanical behaviors and a distinct structural configuration compared to the EMWM bulk solid. These peculiar characteristics are confirmed by microstructural and qualitative observations obtained from computed tomography scanning. The results and analysis presented in this work are relevant to designing EMWM material systems with adaptive performance under different loading and geometric constraints.

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“…23 for concrete and figure 2b in ref. 35 for laminates. As for ceramics, unfortunately, no size effect tests accompanied the histogram testing, although it would have been the easiest way to detect the inadequacy of Weibull distribution.…”

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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Size Effect on Flexural Strength of Fiber-Composite Laminates

Cited by 47 publications

References 33 publications

Probability distribution of energetic-statistical size effect in quasibrittle fracture

Probability distribution of energetic-statistical size effect in quasibrittle fracture

Size-dependent mechanical behavior and boundary layer effects in entangled metallic wire material systems

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

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