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

Kim Wallin, Timo Saario, Kari Törrönen

Research output: Chapter in Book/Report/Conference proceedingChapter or book articleScientificpeer-review

2 Citations (Scopus)

Abstract

The Weibull distribution is often applied in describing the scatter of the brittle fracture toughness KIC. Experimentally determined values for the Weibull slope factor have been found to vary between 2 and 10.

Two different approaches, one based on the original form of the Weibull distribution and the other based on the assumption of an effective volume characterizing the fracture process volume at the crack tip, have been applied in theoretical evaluation of the scatter. With both the methods, it is shown that the theoretical value for the slope factor should be equal to 4.

This result is also shown to be consistent with a newly developed statistical model describing carbide induced cleavage fracture in ferritic and bainitic steels.

The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental KIC-measurements.

Limits of the use of the Wei bull statistics in describing scatter in fracture toughness results is discussed.
Original languageEnglish
Title of host publicationApplication of Fracture Mechanics to Materials and Structures
Subtitle of host publicationProceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983
EditorsG.C. Sih, E. Sommer, W. Dahl
Place of PublicationThe Hague
PublisherMartinus Nijhoff Publishers
Pages511-518
ISBN (Electronic)978-94-009-6146-3
ISBN (Print)978-94-009-6148-7
DOIs
Publication statusPublished - 1984
MoE publication typeA3 Part of a book or another research book

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fracture strength
slopes
bainitic steel
crack tips
carbides
cleavage
statistics
steels
evaluation

Cite this

Wallin, K., Saario, T., & Törrönen, K. (1984). Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution. In G. C. Sih, E. Sommer, & W. Dahl (Eds.), Application of Fracture Mechanics to Materials and Structures: Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983 (pp. 511-518). The Hague: Martinus Nijhoff Publishers. https://doi.org/10.1007/978-94-009-6146-3_32
Wallin, Kim ; Saario, Timo ; Törrönen, Kari. / Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution. Application of Fracture Mechanics to Materials and Structures: Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983. editor / G.C. Sih ; E. Sommer ; W. Dahl. The Hague : Martinus Nijhoff Publishers, 1984. pp. 511-518
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abstract = "The Weibull distribution is often applied in describing the scatter of the brittle fracture toughness KIC. Experimentally determined values for the Weibull slope factor have been found to vary between 2 and 10.Two different approaches, one based on the original form of the Weibull distribution and the other based on the assumption of an effective volume characterizing the fracture process volume at the crack tip, have been applied in theoretical evaluation of the scatter. With both the methods, it is shown that the theoretical value for the slope factor should be equal to 4.This result is also shown to be consistent with a newly developed statistical model describing carbide induced cleavage fracture in ferritic and bainitic steels.The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental KIC-measurements.Limits of the use of the Wei bull statistics in describing scatter in fracture toughness results is discussed.",
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Wallin, K, Saario, T & Törrönen, K 1984, Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution. in GC Sih, E Sommer & W Dahl (eds), Application of Fracture Mechanics to Materials and Structures: Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983. Martinus Nijhoff Publishers, The Hague, pp. 511-518. https://doi.org/10.1007/978-94-009-6146-3_32

Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution. / Wallin, Kim; Saario, Timo; Törrönen, Kari.

Application of Fracture Mechanics to Materials and Structures: Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983. ed. / G.C. Sih; E. Sommer; W. Dahl. The Hague : Martinus Nijhoff Publishers, 1984. p. 511-518.

Research output: Chapter in Book/Report/Conference proceedingChapter or book articleScientificpeer-review

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T1 - Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution

AU - Wallin, Kim

AU - Saario, Timo

AU - Törrönen, Kari

PY - 1984

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N2 - The Weibull distribution is often applied in describing the scatter of the brittle fracture toughness KIC. Experimentally determined values for the Weibull slope factor have been found to vary between 2 and 10.Two different approaches, one based on the original form of the Weibull distribution and the other based on the assumption of an effective volume characterizing the fracture process volume at the crack tip, have been applied in theoretical evaluation of the scatter. With both the methods, it is shown that the theoretical value for the slope factor should be equal to 4.This result is also shown to be consistent with a newly developed statistical model describing carbide induced cleavage fracture in ferritic and bainitic steels.The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental KIC-measurements.Limits of the use of the Wei bull statistics in describing scatter in fracture toughness results is discussed.

AB - The Weibull distribution is often applied in describing the scatter of the brittle fracture toughness KIC. Experimentally determined values for the Weibull slope factor have been found to vary between 2 and 10.Two different approaches, one based on the original form of the Weibull distribution and the other based on the assumption of an effective volume characterizing the fracture process volume at the crack tip, have been applied in theoretical evaluation of the scatter. With both the methods, it is shown that the theoretical value for the slope factor should be equal to 4.This result is also shown to be consistent with a newly developed statistical model describing carbide induced cleavage fracture in ferritic and bainitic steels.The reason for the discrepancy between the theoretical value and the experimentally determined values of the slope factor is shown to be caused by inadequate number of experimental KIC-measurements.Limits of the use of the Wei bull statistics in describing scatter in fracture toughness results is discussed.

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BT - Application of Fracture Mechanics to Materials and Structures

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Wallin K, Saario T, Törrönen K. Theoretical Scatter in Brittle Fracture Toughness Results Described by the Weibull Distribution. In Sih GC, Sommer E, Dahl W, editors, Application of Fracture Mechanics to Materials and Structures: Proceedings of the International Conference on Application of Fracture Mechanics to Materials and Structures, held at the Hotel Kolpinghaus, Freiburg, F.R.G., June 20–24, 1983. The Hague: Martinus Nijhoff Publishers. 1984. p. 511-518 https://doi.org/10.1007/978-94-009-6146-3_32