Weibull parameters obtained from dependence of fiber strength on fiber length and area

Callaway, Evan Benjamin; Zok, Frank W.

doi:10.1111/jace.15709

Cited by 13 publications

(3 citation statements)

References 30 publications

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“…At high σ A , convergence to a tow failure stress of ~1.5 GPa in air as t f → 0 that is independent of temperature is suggested for the reaction and bond‐energy laws [12,13] (Figure 15), but for the power law (11) convergence to any particular value is not obvious. The 1.5 GPa value for fast fracture tow strength ( σ tow ) in air is in excellent agreement with prediction from classic fiber bundle theory: 144,164

{bold-italicσ}_{boldtow} = {bold-italicσ}_{boldo} {(α e λ / 25.4)}^{‐ 1 / α} = 1.49 GPa

α is the Weibull modulus (6), λ is the tow gauge length of 75 cm, and σ o is the Weibull characteristic strength for a 1" gauge length. For steam, convergence to a single temperature‐independent fast fracture strength is not obvious (Figure 16), and may require calculations for t f << 1 s.…”

Section: Scg‐based Models For Strain Rates and Failure Timessupporting

confidence: 80%

Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam

et al. 2021

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Three subcritical crack growth (SCG) laws were used to model strain-rates and failure times for static fatigue of Hi-Nicalon TM -S SiC fiber tows in air and Si(OH) 4 (g)saturated steam. Models were fit to tow failure times (t f ) and steady-state strain rates (ἑ) for brittle creep measured at 700 to 1100°C under initial applied stresses (σ A ) of 260 to 1260 MPa. A power law, a reaction-rate law, and a bond-energy law were used to describe SCG that caused sequential filament failure, and ultimately tow failure.Two versions of each model were developed. One allowed access of chemisorbed species to flaws throughout the fiber (mode 1) and another only allowed access to flaws at the SiC-SiO 2 interface (mode 2). The stress increase on intact filaments as others fractured and as filaments oxidized, and the increase in stress intensity geometric factors (Y) as crack size increased were incorporated in the models. The fits to data were compared for the different models by using both simple regression analysis and orthogonal distance regression (ODR) analysis. Faster convergence and more consistent results were achieved using ODR analysis. Regression analyses found parameters for all models with similar error in data fits, so validity of a model could not be distinguished by regression analysis alone. For all models, the stress dependence of SCG rates was much stronger in steam than in air, and for most models activation energies were between 300 and 420 kJ/mol, regardless of environment. For the steam environment, the bond-length parameter (δ) for the bond-energy model was very close to the lattice parameter of β-SiC (.436 nm), but in air it was significantly lower at 0.25-0.26 nm, but still larger than the Si-C bond length of 0.189 nm. Other factors suggest that either a bond-energy based law or a modified version of a reaction-rate law are the best choices for a SCG law. Filament strength distributions initially described by Weibull distributions could not be described by such distributions after application of the models. SCG mechanisms are discussed.

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{bold-italicσ}_{boldtow} = {bold-italicσ}_{boldo} {(α e λ / 25.4)}^{‐ 1 / α} = 1.49 GPa

Section: Scg‐based Models For Strain Rates and Failure Timessupporting

confidence: 80%

Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam

et al. 2021

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“…A series of 25 fibers with a gauge length of 25 mm was tested. The Weibull statistic [14] was used to estimate the average tensile strength of fibers for a failure probability of 0.632 and the average Young’s modulus was evaluated from these strain–stress curves.…”

Section: Methodsmentioning

confidence: 99%

Microstructures and Properties of Ceramic Fibers of h-BN Containing Amorphous Si3N4

Tan

Min

et al. 2019

Materials

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Composite ceramic fibers comprising about 80 wt% boron nitride (h-BN) and 20 wt% Si3N4 were fabricated through melt-spinning, electron-beam curing, and pyrolysis up to 1600 °C in atmospheres of NH3 and N2, using a mixture of poly[tri(methylamino)borazine] (PBN) and polysilazane (PSZ). By analyzing the microstructure and composition of the pyrolyzed ceramic fibers, we found the formation of binary phases including crystalline h-BN and amorphous Si3N4. Further investigations confirmed that this heterogeneous microstructure can only be formed when the introduced ratio of Si3N4 is below 30% in mass. The mean modulus and tensile strength of the fabricated composite fibers were about 90 GPa and 1040 MPa, twice the average of the pure h-BN fiber. The dielectric constant and dielectric loss tangent of the composite fibers is 3.06 and 2.94 × 10−3.

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“…Note that we have bundled all results in one Weibull curve, because the size ranges explored in our research are limited. Recent results have shown that obtaining discernible differences in Weibull distributions requires testing a size span of 2-3 decades [30]. Our size variable is surface area, as the defects controlling failure arise from the surface (see discussion).…”

Section: Behavior Of Current Density At Failure As a Function Of Diam...mentioning

confidence: 99%

Current density at failure of twinned silver nanowires

Waliullah¹,

Bernal²

2022

Nanotechnology

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Silver nanowires have a wide range of potential applications in stretchable and transparent electronics due to their excellent electrical, mechanical, and optical properties. For a successful application in electronic devices, evaluating the electrical reliability of these nanowires is required. We have studied experimentally the behavior of current density at failure for penta-twinned silver nanowires with diameters between 53 nm and 173 nm, for 93 samples. The current densities at failure are widely scattered, have an average of 9.7 x 10^7 A/cm^2 , and a standard deviation of 2.96 x 10^7 A/cm^2. Heat- transfer modelling is employed to explain the results, and Weibull statistics are used to quantify failure probabilities, thus offering guidelines for future designs based on these nanowires. The scatter observed in the measurements is attributed to surface-roughness variations among samples, which lead to local hot-spots of high current density. These results quantify the Joule-heating electrical reliability of silver nanowires and highlight the importance of heat transfer in increasing it.

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Weibull parameters obtained from dependence of fiber strength on fiber length and area

Cited by 13 publications

References 30 publications

Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam

Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam

Microstructures and Properties of Ceramic Fibers of h-BN Containing Amorphous Si3N4

Current density at failure of twinned silver nanowires

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Weibull parameters obtained from dependence of fiber strength on fiber length and area

Cited by 13 publications

References 30 publications

Subcritical crack growth models for static fatigue of Hi‐NicalonTM‐S SiC fiber in air and steam

Subcritical crack growth models for static fatigue of Hi‐NicalonTM‐S SiC fiber in air and steam

Microstructures and Properties of Ceramic Fibers of h-BN Containing Amorphous Si3N4

Current density at failure of twinned silver nanowires

Contact Info

Product

Resources

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Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam

Subcritical crack growth models for static fatigue of Hi‐Nicalon^TM‐S SiC fiber in air and steam