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  • 1.
    Ekengren, Jens
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Enineering.
    Bergström, Jens
    Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Enineering.
    Estimating the volume distribution of large defects using Generalized Extreme Values2011In: Extremes, ISSN 1386-1999, E-ISSN 1572-915XArticle in journal (Other academic)
    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.

  • 2.
    Ekengren, Jens
    et al.
    Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Engineering.
    Bergström, Jens
    Karlstad University, Faculty of Technology and Science, Department of Mechanical and Materials Engineering.
    Extreme value distributions of inclusions in six  steels2012In: Extremes, ISSN 1386-1999, E-ISSN 1572-915X, Vol. 15, p. 257-265Article in journal (Refereed)
    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.

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