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Estimating the volume distribution of large defects using Generalized Extreme Values
Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Enineering.
Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Enineering.
2011 (English)In: Extremes, ISSN 1386-1999, E-ISSN 1572-915XArticle in journal (Other academic) Submitted
Abstract [en]

The presence of defects, such as oxides and other non-metallic inclusions, is an important factor in determining the properties of steels. Due to improvements in the manufacturing of high-quality steels, the amount of large defects has decreased and therefore it has become increasingly difficult to accurately determine their distribution using conventional methods. Previously, a method for estimating the distribution of large defects using a conversion from the Gumbel distribution has been presented. However, it has been shown that the Gumbel distribution is not always appropriate for modelling the sizes of the largest defects and that the Generalized Extreme Values (GEV) distribution should be used instead. In this work a more general method for the estimation of the total volume distribution of large defects isproposed, showing how the volume distribution may be calculated from the estimated parameters for the GEV distribution. The new method is applied to the results of a series of specimens made from high-quality tool steel tested in ultrasonic resonance fatigue. Possible methods for obtaining the confidence limits of thevolume distribution are also discussed.

Place, publisher, year, edition, pages
2011.
National Category
Materials Engineering Metallurgy and Metallic Materials
Identifiers
URN: urn:nbn:se:kau:diva-8222OAI: oai:DiVA.org:kau-8222DiVA: diva2:440888
Available from: 2011-09-14 Created: 2011-09-12 Last updated: 2011-10-26Bibliographically 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

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Ekengren, JensBergström, Jens

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