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Extreme value distributions of inclusions in six steels
Department of Mechanical and Materials Engineering, Karlstad University, Karlstad, Sweden. (Maskinteknik)ORCID iD: 0000-0003-1655-0392
Department of Mechanical and Materials Engineering, Karlstad University, Karlstad, Sweden.ORCID iD: 0000-0001-6029-2613
2012 (English)In: Extremes, ISSN 1386-1999, E-ISSN 1572-915X, Vol. 15, no 2, p. 257-265Article in journal (Refereed) Published
Abstract [en]

There is a prevailing assumption that the largest inclusions in steel volumes follows mode I of the Generalized Extreme Values (GEV) distribution. In this work, the GEV distributions of non-metallic inclusions in six different high performance steels, of different grades and processing routes, were investigated by means of fractography of inclusions causing failure in ultrasonic fatigue testing to one billion cycles and all three modes of the GEV were found for the different steel grades. Values of the shape parameter ξ of the GEV distribution as high as 0.51 (standard deviation 0.11) were found in one steel grade. Thus, the present results show that the assumption of GEV-I (Gumbel, LEVD) distribution has to be substantiated before being used to estimate the size of the largest inclusions.

Place, publisher, year, edition, pages
2012. Vol. 15, no 2, p. 257-265
Keywords [en]
Extreme values; Non-metallic inclusions; Steel
National Category
Metallurgy and Metallic Materials
Research subject
Mechanical Engineering
Identifiers
URN: urn:nbn:se:oru:diva-39899DOI: 10.1007/s10687-011-0139-5ISI: 000303585200006Scopus ID: 2-s2.0-84860624529OAI: oai:DiVA.org:oru-39899DiVA, id: diva2:773463
Available from: 2011-09-09 Created: 2014-12-19 Last updated: 2019-10-11Bibliographically approved
In thesis
1. Large and rare: An extreme values approach to estimating the distribution of large defects in high-performance steels
Open this publication in new window or tab >>Large and rare: An extreme values approach to estimating the distribution of large defects in high-performance steels
2011 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

The presence of different types of defects is an important reality for manufacturers and users of engineering materials. Generally, the defects are either considered to be the unwanted products of impurities in the raw materials or to have been introduced during the manufacturing process. In high-quality steel materials, such as tool steel, the defects are usually non-metallic inclusions such as oxides or sulfides.

Traditional methods for purity control during standard manufacturing practice are usually based on the light optical microscopy scanning of polished surfaces and some statistical evaluation of the results. Yet, as the steel manufacturing process has improved, large defects have become increasingly rare. A major disadvantage of the traditional quality control methods is that the accuracy decreases proportionally to the increased rarity of the largest defects unless large areas are examined.

However, the use of very high cycle fatigue to 109 cycles has been shown to be a powerful method to locate the largest defects in steel samples. The distribution of the located defects may then be modelled using extreme value statistics.

This work presents new methods for determining the volume distribution of large defects in high-quality steels, based on ultrasonic fatigue and the Generalized Extreme Value (GEV) distribution. The methods have been developed and verified by extensive experimental testing, including over 400 fatigue test specimens. Further, a method for reducing the distributions into one single ranking variable has been proposed, as well as a way to estimate an ideal endurance strength at different life lengths using the observed defects and endurance limits. The methods can not only be used to discriminate between different materials made by different process routes, but also to differentiate between different batches of the same material.

It is also shown that all modes of the GEV are to be found in different steel materials, thereby challenging a common assumption that the Gumbel distribution, a special case of the GEV, is the appropriate distribution choice when determining the distribution of defects.

The new methods have been compared to traditional quality control methods used in common practice (surface scanning using LOM/SEM and ultrasound C-scan), and suggest a greater number of large defects present in the steel than could otherwise be detected.

Place, publisher, year, edition, pages
Karlstad: Karlstad University, 2011. p. 31
Series
Karlstad University Studies, ISSN 1403-8099 ; 2011:47
Keywords
Non-metallic inclusions, Tool steel, Extreme value statistics, Distribution of defects, Generalized extreme values
National Category
Metallurgy and Metallic Materials
Research subject
Materials Engineering
Identifiers
urn:nbn:se:oru:diva-39894 (URN)978-91-7063-382-9 (ISBN)
Public defence
2011-10-27, Eva Eriksson, 21A 342, Karlstads universitet, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2015-03-09 Created: 2014-12-19 Last updated: 2018-05-06Bibliographically approved

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Ekengren, JensBergström, Jens

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