The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint

Kozák, Vladislav; Vlček, Libor

doi:10.1016/j.nucengdes.2005.05.006

Cited by 8 publications

(5 citation statements)

References 4 publications

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“…A central feature emerging from the probabilistic treatment of brittle fracture based upon the weakest link model is that, under small scale yielding conditions, the scatter of cleavage fracture toughness data is characterised by b J = 2 for J C ‐distributions or b K = 4 for ‐distributions. Similarly, Kozák and Vlèek 18 expressed in 2005 that: the 3P‐W model is used to fit the relationship between and the cumulative probability of failure, where b K is a shape parameter, which is assumed at given temperature to be close to 4, and later they also commented that: from the weakest link statistic for J ‐integral, , a central feature emerging from this model is that, under small scale yielding condition, the scatter in the cleavage fracture toughness data is characterized by b J = 2 for J C values.…”

Section: Discussionmentioning

confidence: 92%

“…It can also be observed that the approximation with a 3P-W(K) for the transformed K JC values is Table 1 Comparative examples of parameters obtained by means of Options 1a, 1b and 2 excellent in the range of 1.8% up to 99.5% for the cumulative probability. According to Eqs (18) and (19), the approximate slope, b KAp , depends not only on b J , but on the three parameters. This is evidenced in Fig.…”

Section: Options 1a and 1bmentioning

confidence: 99%

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Comparison of 3P-Weibull parameters based on JC and KJC values

Larrainzar

Berejnoi

Ipiña

2010

Fatigue &Amp; Fracture of Engineering Materials &Amp; Structures

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A B S T R A C T The characterization of fracture toughness of ferritic steels in the ductile-to-brittle transition is problematic due to the scatter of test results. Several proposals using Weibull statistics have been made, some of them in terms of J and others in terms of K; some authors employ a two parameters Weibull function (2P-W), while others use a three parameters function (3P-W), although ASTM E1921 uses 3P-W in terms of K with two fixed parameters to determine the Reference Temperature To. An analysis about the relationship between Weibull distributions expressed in terms of J and K is presented in this paper. It is shown that if the J C results follow a 3P-W, their equivalent K JC values do not exactly fit a 3P-W function obtained by means of a simple transformation of the three parameters. Nevertheless, an approximated 3P-W function in K terms is proposed in this work. It fits very well with the transformed values and their parameters are related to the ones expressed in J terms. In case the experimental results follow a 3P-W in K JC , a similar analysis can be performed. For the particular situation of a 2P-W, there is an exact equivalence between the distributions in terms of J and K, being the Weibull slope in terms of K twice the slope in terms of J.Keywords ductile-brittle transition; J C to K JC transformation; Weibull function. N O M E N C L A T U R E b = shape parameter or Weibull slope. b J = shape parameter or Weibull slope in J values. b JAp = approximated shape parameter or Weibull slope in J values. b K = shape parameter or Weibull slope in K values. b KAp = approximated shape parameter or Weibull slope in K values. B = specimen thickness B 0 = reference specimen thickness J = J-integral value. J C = J-integral at the point of onset of cleavage fracture. J i = an individual value of a set of J values. J min = threshold parameter or lowest value of J in the population.J 0 = scale parameter of the Weibull distribution in J values (J 0 = J for P = 0.632). K = linear elastic stress intensity factor. K J = an elastic-plastic equivalent stress intensity factor derived from a J value. K JC = an elastic-plastic equivalent stress intensity factor derived from J C value. K min = threshold parameter or lowest value of K in the population. K 0 = scale parameter of the Weibull distribution in K values (K 0 = K for P = 0.632). K 1 = an individual value of stress intensity factor. LRM = linear regression method.

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Section: Discussionmentioning

confidence: 92%

Section: Options 1a and 1bmentioning

confidence: 99%

Comparison of 3P-Weibull parameters based on JC and KJC values

Larrainzar

Berejnoi

Ipiña

2010

Fatigue &Amp; Fracture of Engineering Materials &Amp; Structures

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“…1 show lower or higher effect of the epistemic uncertainty, namely for the last four quantities in Table 1 above all where there is not any possibility to find the histograms obtained by measurements. The results are dependent, too, on the definition and mathematical description of the structure limit states, and they can differ, e.g., when taking into consideration time dependent effects [13][14][15], when modeling macro and microscale behaviour of materials [16][17][18], when solving stability problems [19][20][21], and when describing system imperfections for nonlinear solutions [22]. The results are dependent, too, on the definition and mathematical description of the structure limit states, and they can differ, e.g., when taking into consideration time dependent effects [13][14][15], when modeling macro and microscale behaviour of materials [16][17][18], when solving stability problems [19][20][21], and when describing system imperfections for nonlinear solutions [22].…”

Section: Failure Probability Analysismentioning

confidence: 99%

Reliability of Steel Members Designed in Accordance with the Code Design Concepts

Kala¹

2010

AIP Conference Proceedings

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In the present paper, reliability of an axial tensile steel member is studied. The influence of partial safety factors of standard EUROCODE 3 and EN 1990 on the reliability of design is examined. The reliability is determined, applying probability procedures based on Monte Carlo method. The measure of reliability is the probability of the structure failure. The failure probability of designed steel members is a function of input random material and geometrical characteristics obtained by experimental research. The failure probability carried out is compared with target probability given in standard EN1990. A simplified problem of a member loaded by permanent load action combined with a longtime leading single variable load action is considered for the elaboration of the parametric study.

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“…Most authors have assumed Weibull exponent (m) as a constant value that does not depend on geometry or temperature. Wallin [1], Jason, Petti and Dodds [4], Kozak et al [5] and some others assumed the fixed value of four for this exponent. But Weibull exponent is dependant on geometry [6], temperature and maybe other factors.…”

Section: K 0 and M Global Equationsmentioning

confidence: 99%

Temperature and Geometry Dependence of Fracture Toughness in "Euro Fracture Dataset"

Akbarzadeh

Hadidi-Moud

2010

KEM

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Reliable prediction of fracture conditions is a major concern in the integrity assessment of structural components. This is specifically critical within the transition regime where there is a significant scatter in fracture test data. In recent years local stress based approaches that use a "Weibull distribution function" have been examined to predict probability of cleavage fracture at lower shelf temperature. Furthermore the role of constraint in toughness prediction has been noted. An extensive experimental programme known as "Euro fracture dataset" aimed at characterisation of the "Ductile-to-Brittle" transition (DBT) behaviour of ferritic steels. Recently this data set was used by authors to propose a set of "Global" equations for determination of temperature and thickness dependence of Weibull distribution parameters. In this paper finite element simulations of fracture tests are carried out firstly to verify the experimental findings and secondly to examine and validate the proposed "Global" equations. This objective has been achieved through the comparison between the experimental data, predictions of "Global" curves and the results of performed finite element simulations.

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The Weibull stress parameters calibration upon the toughness scaling model between cracks having different constraint

Cited by 8 publications

References 4 publications

Comparison of 3P-Weibull parameters based on JC and KJC values

Comparison of 3P-Weibull parameters based on JC and KJC values

Reliability of Steel Members Designed in Accordance with the Code Design Concepts

Temperature and Geometry Dependence of Fracture Toughness in "Euro Fracture Dataset"

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