Tensile strength and its variation of PAN‐based carbon fibers. I. Statistical distribution and volume dependence

Yu, Weidong; Jiangwei, Yao

doi:10.1002/app.23399

Cited by 17 publications

(22 citation statements)

References 12 publications

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“…For example, for Nextel™ fibers, measured values of m A / m WP ranged from 0.20 to 0.56 . Similar studies on carbon fibers yielded comparable results: m A / m WP ≈ 0.2 . For the test parameters used in those studies ( N = 50 and Z A = 0.1), the present analysis suggests that the median Weibull modulus would be m A ,med /m t ≈ 0.4 and that the uncertainty in m would exceed m itself.…”

Section: Discussionsupporting

confidence: 80%

“…Discrepancies in Weibull moduli obtained from the various methods have been previously interpreted as a breakdown of the Weibull function in describing strength distributions, without due consideration of the statistical significance of differences in measured values and systematic errors introduced by inadequate sample size . These interpretations have not only fueled misconceptions about the utility of the Weibull distribution but have also led to a number of proposed alternative distribution functions that violate the underlying weakest‐link scaling principles .…”

Section: Discussionmentioning

confidence: 99%

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

Callaway

Zok

2018

J Am Ceram Soc

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Weibull strength parameters of ceramic fibers can be inferred from variations in strength with fiber diameter or gauge length. The goal of this article is to provide a critical assessment of the efficacy of these methods. The issues are addressed using theorems in regression analysis and uncertainty propagation as well as Monte Carlo simulations. The results show that, when Weibull moduli are obtained from strength variations with fiber area, inordinately large sample sizes (>1000) are required to achieve reliable results. In contrast, Weibull moduli can be accurately estimated from the dependence of average fiber strength on gauge length for a modest sample size at each of two gauge lengths, provided the gauge length range is sufficiently large. The dependence of strengths of bundles containing many (ca. 500) fibers on gauge length yields yet more reliable results. The results are used to assess the fidelity of Weibull moduli obtained from these methods and provide guidance for preferred test methods.

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Section: Discussionsupporting

confidence: 80%

Section: Discussionmentioning

confidence: 99%

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

Callaway

Zok

2018

J Am Ceram Soc

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“…Although fibre tensile strength is most commonly determined using processes such as the single fibre tensile tests [20], as mentioned in the Introduction, other methods can also be used with varying levels of accuracy. These are, for example, the methods of fibre fragmentation tests [21] and fibre bundle tests [22].…”

Section: Fibre Tensile Strengthmentioning

confidence: 99%

Evaluation of Critical Parameters in Tensile Strength Measurement of Single Fibres

2019

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Mechanical properties of fibre reinforced composites are primarily dependent on those of fibres. Fibre properties are used for estimating the damage and strength behaviour of composite materials and structures. Tensile strength of fibres is commonly determined by single fibre tensile tests, which is challenging and is prone to measurement errors. In this study, different possible sources of errors due to experimental limitations in the fibre testing process were identified. Their effect on fibre tensile strength was analytically modelled. This model was used to evaluate the uncertainty in experimentally determined fibre strength. A sensitivity analysis was conducted to rank the relative significance of input quantities on the calculated fibre strength. Since composite models require fibre properties determined at very small gauge lengths, the results of the sensitivity analysis were extrapolated to determine critical parameters for tests done at those small gauge lengths of a few millimetres. It was shown that, for sufficiently long fibres, their strength depends mainly on the diameter and failure force; however, for shorter gauge lengths, the effects of misalignment become very significant. The knowledge of uncertainty would be useful in estimating the reliability of the predictions made by composite strength models on the damage and failure behaviour of composite materials and structures. Minimising the influence of critical parameters on fibre strength would help in designing improved single fibre testing systems capable of determining fibre strength more accurately.

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“…An accurate characterization of the strength of a single fibre is thus critically important and attracts constant attention. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] Because of the presence of surface and internal flaws along the length of a fibre formed during the manufacturing and handling processes, the strength of a single fibre exhibits a large dispersion and remarkable size effect. The two-parameter Weibull statistics is commonly used to describe the strength distribution of a single fibre:…”

Section: Introductionmentioning

confidence: 99%

Statistics of single‐fibre tensile strength incorporating spatial distribution of microcracks

Lei¹

2016

Fatigue Fract Eng Mat Struct

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A B S T R A C T The random distribution of single-fibre tensile strength has been commonly characterized by the two-parameter Weibull statistics. However, the calibrated Weibull model from one set of strength data at a given gauge length cannot accurately predicts the strength variation of the fibre at different gauge lengths. Instead of presuming the twoparameter Weibull distribution or any other specific statistical distribution for the single-fibre strength to begin with, this work proposes an approach to incorporating the appropriate spatial flaw distribution within a fibre and synchronizing multiple sets of tensile strength data to evaluate the single-fibre strength distribution. The approach is examined and validated by published single-fibre strength data sets of glass, ceramic and synthetic and natural carbon fibres. It is shown that the single-fibre strength statistics does not necessarily always follow the two-parameter Weibull distribution.Keywords fibre; fibre-reinforced composite; flaw distribution; size effect; tensile strength; weakest link model. N O M E N C L A T U R Ea = microcrack size a max = maximum microcrack size a min = minimum microcrack size c, α, β = constants f(a) = probability density function of microcrack with respect to size a g(S) = probability density function of microcrack with respect to strength S k = resistance to fracture l = length l 0 = reference length m = shape parameter M = 1/V 0 , average number of flaws in unit volume p = pressure p (σ, V 0 ) = fracture probability of an elemental volume V 0 under stress σ P = cumulative probability of failure R 2 = coefficient of determination S = strength of an elemental volume V 0 containing a microcrack of size a, S ¼ k = ffiffi a p RMSE = root-mean-square error V = volume of fracture process zone dV, δV = differential volume element ρ = average density of flaws in unit length μ = location parameter σ = strength or stress σ 1 = maximum principal stress σ 0 = scale parameter σ th = threshold strength ξ = a stress value in the range σ th ≤ ξ ≤ σ

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Tensile strength and its variation of PAN‐based carbon fibers. I. Statistical distribution and volume dependence

Cited by 17 publications

References 12 publications

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

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

Evaluation of Critical Parameters in Tensile Strength Measurement of Single Fibres

Statistics of single‐fibre tensile strength incorporating spatial distribution of microcracks

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