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Extreme value distributions of inclusions in six  steels
Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Engineering.
Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Engineering.
2012 (English)In: Extremes, ISSN 1386-1999, E-ISSN 1572-915X, Vol. 15, 257-265 p.Article 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, 257-265 p.
Keyword [en]
Extreme values – Non-metallic inclusions – Steel
National Category
Metallurgy and Metallic Materials
Identifiers
URN: urn:nbn:se:kau:diva-8200DOI: 10.1007/s10687-011-0139-5ISI: 000303585200006OAI: oai:DiVA.org:kau-8200DiVA: diva2:439825
Available from: 2011-09-09 Created: 2011-09-09 Last updated: 2016-08-08Bibliographically 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. 31 p.
Series
Karlstad University Studies, ISSN 1403-8099 ; 2011:47
Keyword
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:kau:diva-8226 (URN)978-91-7063-382-9 (ISBN)
Public defence
2011-10-27, Eva Eriksson, 21A 342, Karlstads universitet, Karlstad, 13:15 (Swedish)
Opponent
Supervisors
Available from: 2011-10-05 Created: 2011-09-12 Last updated: 2011-10-25Bibliographically approved
2. Estimating inclusion content in high performance steels
Open this publication in new window or tab >>Estimating inclusion content in high performance steels
2008 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

Non-metallic inclusions in steel pose a major problem for the fatigue resistance, especially regarding fatigue at very long lives corresponding to low cyclic stress levels, as well as being detrimental to material toughness and polishability.

The largest inclusions are quite rare, which makes conventional detection methods timeconsuming if reliable results are to be obtained. Based on surface scanning using light or electron microscopes, these methods provide results that have to be converted to reflect the statistical volume distribution of inclusions.

Very high cycle fatigue (in the order of 109 cycles or more) using ultrasonic fatigue at 20 kHz has been found efficient at finding the largest inclusions in volumes of about 300 mm3 per specimen. The inclusions found at the fatigue initiation site can then been used to estimate the distribution of large inclusions using extreme value statistics.

In this work, a new method for estimating the volume distribution of large inclusions is presented as well as a suggested ranking variable based on the volume distribution.

Results from fatigue fractography and area scanning methods are compared to the endurance limit at 109 cycles for a number of batches from two high performance steels.

In addition, the extreme value distributions of fatigue initiating inclusions in six high performace steels, produced by different routes, are presented. It is shown that all modes of the Generalized Extreme Values distribution can be found in different materials. This result shows that the assumption of mode I distribution, also known as Gumbel or Largest Extreme Value distribution, must be substantiated.

Place, publisher, year, edition, pages
Karlstad: Karlstad University, 2008. 18 p.
Series
Karlstad University Studies, ISSN 1403-8099 ; 2008:50
National Category
Materials Engineering
Research subject
Materials Engineering
Identifiers
urn:nbn:se:kau:diva-3520 (URN)978-91-7063-207-5 (ISBN)
Presentation
2008-12-19, Ljungbergssalen, 21A 244, Karlstads universitet, Karlstad, 13:15 (Swedish)
Opponent
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2011-11-29Bibliographically approved

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Ekengren, JensBergström, Jens

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