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Large and rare: An extreme values approach to estimating the distribution of large defects in high-performance steels
Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Enineering.
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 [en]
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: urn:nbn:se:kau:diva-8226ISBN: 978-91-7063-382-9 (print)OAI: oai:DiVA.org:kau-8226DiVA: diva2:440913
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
List of papers
1. Relating gigacycle fatigue to other methods in evaluating the inclusion distribution of a H13 tool steel
Open this publication in new window or tab >>Relating gigacycle fatigue to other methods in evaluating the inclusion distribution of a H13 tool steel
2007 (English)In: Fourth International Conference on Very High Cycle Fatigue (VHCF-4) / [ed] John E. Allison, J. Wayne Jones, James M. Larsen & Robert O. Ritchie, TMS (The Minerals, Metals & Materials Society) , 2007, 45-50 p.Conference paper, Published paper (Refereed)
Abstract [en]

Inclusions play a crucial role for the fatigue properties of high strength steel, but to find the largest inclusions by microscopy measurements large areas have to be examined.In this study ultrasonic gigacycle staircase fatigue testing has been used to find large inclusions in an H13 tool steel. The inclusions have been examined in SEM and their size distribution modeled using methods from extreme value statistics. The inclusion distribution obtained from the fatigue crack surfaces is compared to distributions acquired by microscopy study of cross sections as well as ultrasound immersion tank measurements and to the corresponding staircase fatigue data via the Murakami √Area model.It is shown that the fatigue method more effectively finds large inclusions than the other methods. It is also shown that the correlation between predictions of inclusion sizes by the √Area model from stress levels and fatigue initiating inclusions is weak forthis material.

Place, publisher, year, edition, pages
TMS (The Minerals, Metals & Materials Society), 2007
Keyword
non-metallic inclusion, steel, gigacycle fatigue
National Category
Materials Engineering
Research subject
Materials Engineering
Identifiers
urn:nbn:se:kau:diva-3516 (URN)978-0-87339-704-9 (ISBN)
Conference
Fourth International Conference on Very High Cycle Fatigue (VHCF-4)
Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-06Bibliographically approved
2. Detecting large inclusions in steels: evaluating methods
Open this publication in new window or tab >>Detecting large inclusions in steels: evaluating methods
2009 (English)In: Steel Research International, ISSN 1611-3683, E-ISSN 1869-344X, Vol. 80, no 11, 854-858 p.Article in journal (Refereed) Published
Abstract [en]

The distributions of large non-metallic inclusions in two steel grades have been investigated using light optical microscopy, scanning electron microscopy and ultrasonic fatigue testing in the gigacycle range. The different methods have inherently different capabilities for finding inclusions in different size ranges. A measure of the distribution of large inclusions is proposed as the size S at which half of the fatigue specimens are expected to contain at least one inclusion of size S or larger, corresponding to 50% failure probability. Values of S are obtained using the volume distribution estimated by the three methods. Extrapolation from microscopy measurements on surfaces agree with fatigue fractography results regarding density of large inclusions, as measured by the proposed ranking variable S

Place, publisher, year, edition, pages
Wiley-VCH Verlagsgesellschaft, 2009
National Category
Materials Engineering
Research subject
Materials Engineering
Identifiers
urn:nbn:se:kau:diva-3517 (URN)10.2374/SRI09SP079 (DOI)
Note

Vid tidpunkten för författarens licentiatseminarium, förelåg detta delarbete som manuskript. This paper was first published as a manuscript at time for the author's licentiate seminar.

Available from: 2009-02-05 Created: 2009-02-05 Last updated: 2017-12-14Bibliographically approved
3. Assessment of strength and inclusions of Tool Steels in Very High Cycle Fatigue
Open this publication in new window or tab >>Assessment of strength and inclusions of Tool Steels in Very High Cycle Fatigue
2009 (English)In: Proceedings of the 8th International Tooling Conference, Vol 1 / [ed] P. Beiss, C. Broeckmann, S. Franke, B. Keysselitz, Verlag Mainz, Wissenschaftsverlag , 2009Conference paper, Published paper (Refereed)
Abstract [en]

Fatigue strength is an important material property for many tooling applications, particularly in high performance applications. The research in Very High Cycle Fatigue (VHCF) has demonstrated that the traditional fatigue limit may not be valid for many materials subjected to 107 or more load cycles. Presently, both materials data and mechanism knowledge is missing on VHCF applications, even though many components are run at these life lengths. The fatigue strength is commonly controlled by different defects initiating failure, as in well controlled laboratory experiments may be internal inclusions. In this paper VHCF experimental testing was accomplished by the use of ultrasonic fatigue testing run at 20 kHz allowing long life evaluation within reasonably short test time. Fatigue strength, failure mechanisms and inclusion content were accordingly assessed. Fatigue strength data on H13 tool steel are presented, as well as a statistical approach considering available defect distribution and load distribution in the critically stressed volume, important to both steel supplier and end-user.

Place, publisher, year, edition, pages
Verlag Mainz, Wissenschaftsverlag, 2009
Keyword
very high cycle fatigue, tool steel, inclusion distribution
National Category
Metallurgy and Metallic Materials
Identifiers
urn:nbn:se:kau:diva-8225 (URN)9783810793058 (ISBN)
Available from: 2011-09-12 Created: 2011-09-12 Last updated: 2017-12-06Bibliographically approved
4. Extreme value distributions of inclusions in six  steels
Open this publication in new window or tab >>Extreme value distributions of inclusions in six  steels
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.

Keyword
Extreme values – Non-metallic inclusions – Steel
National Category
Metallurgy and Metallic Materials
Identifiers
urn:nbn:se:kau:diva-8200 (URN)10.1007/s10687-011-0139-5 (DOI)000303585200006 ()
Available from: 2011-09-09 Created: 2011-09-09 Last updated: 2017-12-08Bibliographically approved
5. Influence of life length on estimated defect  distribution in a low defect steel material
Open this publication in new window or tab >>Influence of life length on estimated defect  distribution in a low defect steel material
2011 (English)In: Proceedings of the Fifth International Conference on Very High Cycle Fatigue / [ed] C. Berger and H.-J. Christ, 2011, 177-182 p.Conference paper, Published paper (Refereed)
Abstract [en]

This paper reports on results of very high cycle fatigue tests on a steel with a relatively low number of defects per unit volume. Two series of newly designed dog-bone specimens, with low stress gradients, were tested at two constant stress levels, aiming at providing fatigue life lengths of 106–108 cycles and 107–109 cycles, respectively. Fatigue-initiating defects on the fracture surfaces were measured and the corresponding size distributions were analysed to investigate the influence of the elevated stress level needed to achieve shorter life lengths.The presented results indicate a difference between the distribution of initiating defects in the long and shorter life length test series. The main conclusion is that fixed stress level fatigue testing to life lengths around 107 cycles may be a suitable method to estimate the content of large defects in low defect steel materials, provided a suitable test specimen geometry with low stress gradients is used.

Keyword
Defect volume distribution, Extreme value statistics, Tool steel
National Category
Metallurgy and Metallic Materials
Identifiers
urn:nbn:se:kau:diva-8201 (URN)978-3-9814516-0-3 (ISBN)
Conference
Fifth International Conference on Very High Cycle Fatigue
Available from: 2011-09-09 Created: 2011-09-09 Last updated: 2017-12-06Bibliographically approved
6. Estimating the volume distribution of large defects using Generalized Extreme Values
Open this publication in new window or tab >>Estimating the volume distribution of large defects using Generalized Extreme Values
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.

National Category
Materials Engineering Metallurgy and Metallic Materials
Identifiers
urn:nbn:se:kau:diva-8222 (URN)
Available from: 2011-09-14 Created: 2011-09-12 Last updated: 2017-12-08Bibliographically approved

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