A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

Lei, Weidong

doi:10.1080/14786435.2016.1232494

Cited by 27 publications

(63 citation statements)

References 72 publications

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“…This consensus justifies the adoption of statistical approach for size scaling of concrete strength. In brief, the previous work by Lei 10,11 has emphasized the following important aspects of the weakest-link formulation for brittle fracture: 6 This is illustrated in Figure 3.…”

Section: Introductionmentioning

confidence: 99%

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

Qian

Zhai

et al. 2018

Fatigue Fract Eng Mat Struct

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A procedure for non‐proportional size scaling of the strength of concrete based on the weakest‐link statistics is proposed to synchronize strength data from specimens of different geometries and different loading modes. The procedure relies on proportional size scaling of strength to determine the parameters of the statistical model and often on finite element analysis to calculate the coefficient of the equivalent strength. The approach for non‐proportional size scaling is capable to synchronize the uniaxial strength data of concrete from uniaxial tensile specimens and 3‐point bending specimens, or the biaxial tensile strength data of circular plates in different loading mode. The non‐transference of the uniaxial strength data to the biaxial strength data is unclear in its mechanism but possibly due to the variation of statistical distribution of microcracks with stress states in different specimens.

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Section: Introductionmentioning

confidence: 99%

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

Qian

Zhai

et al. 2018

Fatigue Fract Eng Mat Struct

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“…Notwithstanding the foregoing modifications, the uniqueness of the model parameters remains unresolved, as reviewed in detail in Lei . Recent studies have identified the fundamental defects of the Beremin model, which are summarized in Table .…”

Section: Introductionmentioning

confidence: 99%

“…On the other hand, it is well known that cleavage fracture does occur at Δ σ = 0 in uniaxial tension, that is, σ th = σ 1, 0 = σ ys . Therefore, it is both conservative and reasonable to set Δ σ = 0, ie, σ th = σ 1, 0 . Detailed arguments for setting σ th = σ 1, 0 can be found in Lei …”

Section: Introductionmentioning

confidence: 99%

“…Second, it is the net amount of stress increment (Δ σ 1 = σ 1 − σ 1, 0 ) in a volume element (dV) from initial yielding state ( σ 1 = σ 1, 0 ) to the instant stress state ( σ 1 ) at a given load, rather than the amplitude of the instant stress ( σ 1 ), that contributes to the risk of cleavage fracture. Accordingly, by adopting a 3‐parameter Weibull distribution density function of microscopic cleavage fracture stress S in place of the power law distribution of microcrack size (a) (Equation 9 in Table ) as assumption (5),

g ((), S) = m \cdot ([], {(S - σ_{italicth})}^{m - 1} / σ_{0}^{m}) \cdot exp ([], - {(S - σ_{italicth})}^{m} / σ_{0}^{m})

a new local approach to cleavage fracture was proposed:

p ((),, σ, V_{0}) = \int_{σ_{th} = σ_{1, 0}}^{\infty} g ((), S) italicdS = 1 - exp {(\frac{σ_{1} - σ_{1, 0}}{σ_{0}})}^{m}

P = 1 - exp ({}, \int_{V_{p}} italicln ([], 1 - p ((),, σ, V_{0})) italicdV / V_{0}) = 1 - italicexp ([], - {(σ_{W} / σ_{0})}^{m})

σ_{W} = {[{normal\int}_{V_{p}} {((), σ_{1} - σ_{1, 0})}^{m} \cdot dV / V_{0}]}^{1 / m}

where σ W is the Weibull stress. Note that the essential difference between Equations and 3 lies in that <...>…”

Section: Introductionmentioning

confidence: 99%

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Statistical assessment of notch toughness against cleavage fracture of ferritic steels

Qian

Lei

Liu³

et al. 2017

Fatigue Fract Eng Mat Struct

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The work is an initial effort on adopting a statistical approach to correlate the fracture behavior between a notched and a fracture mechanics specimen. The random nature of cleavage fracture process determines that both the microscopic fracture stress and the macroscopic properties including fracture load, fracture toughness, and the ductile to brittle transition temperature are all stochastic parameters. This understanding leads to the proposal of statistical assessment of cleavage induced notch brittleness of ferritic steels according to a recently proposed local approach model of cleavage fracture. The temperature independence of the 2 Weibull parameters in the new model induces a master curve to correlate the fracture load at different temperatures. A normalized stress combining the 2 Weibull parameters and the yield stress is proposed as the deterministic index to measure notch toughness. This proposed index is applied to compare the notch toughness of a ferritic steel with 2 different microstructures.

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“…Both deterministic and statistical approaches have been developed to evaluate structural integrity of RPVs against brittle fracture. As reviewed in [3], the conventional transition temperature method, fracture mechanics, and fracture physics approaches are deterministic; the Master Curve (MC) method [4] and most of the Local Approach (LA) [5] are statistical. The MC method empirically describes cleavage fracture toughness distribution using a three-parameter Weibull distribution with fixed values of the modulus ( m = 4) and the threshold toughness ( = 20 √ ), with only the scale parameter (K 0 ) to be determined by fitting fracture toughness (K Ic ) data [4].…”

Section: Introductionmentioning

confidence: 99%

A new local approach model for cleavage fracture in ferritic steels and its validation

2018

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Abstract. The paper discusses and applies a statistical approach to correlate the fracture behavior of a notched and fracture mechanics specimen. The method can be used for fatigue analysis. The random nature of cleavage fracture process determines that both the microscopic fracture stress and the macroscopic properties including fracture load, fracture toughness and the ductile to brittle transition temperature are all stochastic parameters. This understanding leads to the proposal of statistical assessment of cleavage induced notch toughness of ferritic steels according to a new local approach to cleavage fracture. The temperature independence of the two Weibull parameters in the new model induces a master curve to correlate the fracture load at different temperatures. A normalized stress combining the two Weibull parameters and the yield stress is proposed as the deterministic index to measure notch toughness. This proposed index is applied to compare the notch toughness of a ferritic steel with two different microstructures.

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A framework for statistical modelling of plastic yielding initiated cleavage fracture of structural steels

Cited by 27 publications

References 72 publications

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

Non‐proportional size scaling of strength of concrete in uniaxial and biaxial loading conditions

Statistical assessment of notch toughness against cleavage fracture of ferritic steels

A new local approach model for cleavage fracture in ferritic steels and its validation

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