Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution

Wallin, Kim; Saario, Timo; Törrönen, Kari

doi:10.1007/978-94-009-6146-3_32

Cited by 8 publications

(5 citation statements)

References 5 publications

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“…The Weibull plot of the K Ic data also showed m = 3. This level of m is consistent with the m values of 2 to 10 that are generally obtained in brittle fracture as reported by Wallin et al [32,116], who theoretically predicted m = 4 for K Ic of generic brittle solids. This should make designers cautious, despite its high fracture toughness.…”

Section: Estimation Of M From Standard Deviation or From Coefficient supporting

confidence: 92%

“…Nine of 19 exceeded m = 20. These results certainly contradict the above conclusion of Wallin [116] and the results in Table 4. Salem concluded that no relationship exists between fracture toughness and CV, but it is plausible that the CV data he collected was unrepresentative of real ceramics behavior.…”

Section: Estimation Of M From Standard Deviation or From Coefficient contrasting

confidence: 55%

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A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

Ono

2019

Applied Sciences

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This study examines methods for simplifying estimation of the Weibull modulus. This parameter is an important instrument in understanding the statistical behavior of the strength of materials, especially those of brittle solids. It is shown that a modification of Robinson’s approximate expression can provide good estimates of Weibull modulus values (m) in terms of average strength (<σ>) and standard deviation (S): m = 1.10 <σ>/S. This modified Robinson relation is verified on the basis of 267 Weibull analyses accompanied by <σ> and S measurements. Estimated m values matched normally obtained m values on average within 1%, and each pair of m values was within ± 20%, except for 11 cases. Applications are discussed, indicating that the above relation can offer a quantitative tool based on the Weibull theory to engineering practice. This survey suggests a rule of thumb: ductile metal alloys have Weibull moduli of 10 to 200.

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Section: Estimation Of M From Standard Deviation or From Coefficient supporting

confidence: 92%

Section: Estimation Of M From Standard Deviation or From Coefficient contrasting

confidence: 55%

A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

Ono

2019

Applied Sciences

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“…In non-local model [27,28], damage is evaluated such that it includes the effect of damage from other volumes affecting/influencing the current volume. To model the cleavage aspect of the material Landes [29], Beremin [30], Mudry [31], Wallin et al [32]) have used the weakest link concept. The most simple and promising model is given by Beremin [30] and the model is derived from Weibull's statistical description.…”

Section: Introductionmentioning

confidence: 99%

Fracture toughness evaluation of 20MnMoNi55 pressure vessel steel in the ductile to brittle transition regime: Experiment & numerical simulations

Gopalan

Samal²,

Chakravartty

2015

Journal of Nuclear Materials

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“…The Weibull distribution function has been widely used in characterizing scatter in fracture toughness results of brittle materials due to its versatility and relative simplicity [14]. In the case of fracture toughness, the two parameter Weibull distribution function can be written in the form of…”

Section: Fracture Toughness Resultsmentioning

confidence: 99%

Fracture Toughness Testing and Prediction for Ceramic Materials Using in Large-Flow-Rate Emulsion Pumps

Li¹

2019

IJMEA

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Fracture toughness (K IC) tests have been carried out on single edge precracked beam specimens with dimensions in accordance with ISO15732 requirements for two types of zirconia and one type of alumina, i.e. ZrO 2-1, ZrO 2-2 and Al 2 O 3. Experimental determinations of K IC for the two zirconia and one alumina materials are 12.18 MPa•m 1/2 , 16.35 MPa•m 1/2 and 4.99 MPa•m 1/2 , respectively. The median rank method is used to calculate the probability of fracture, F(K IC) of the three cermaic materials for representing the experimental results. The SEM analysis on fracture surfaces of ZrO2-1 materials is carried out, which indicates the fracture in ZrO 2-1 material occurred at the interior of the grain associated with interior stress distribution with principal components of ZrO 2 and SiO 2. Th extended finite element method (XFEM), based on the linear elastic fracture mechanics in conjuciton with a bilinear traction-separation damage law, is used to simulate the progressive crack growth process in the SEPB specimens. The XFEM predicted K IC results are compared with the corresponding experimental data. The XFEM approach overpredicts the K IC values, from 10.4% to 25.6%, for the three ceramic materials. The possible reasons, in the aspect of loading conditions and contact assumptions, for the difference between the predicted and tested results are also discussed.

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Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution

Cited by 8 publications

References 5 publications

A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

A Simple Estimation Method of Weibull Modulus and Verification with Strength Data

Fracture toughness evaluation of 20MnMoNi55 pressure vessel steel in the ductile to brittle transition regime: Experiment & numerical simulations

Fracture Toughness Testing and Prediction for Ceramic Materials Using in Large-Flow-Rate Emulsion Pumps

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