Method of Hardenability Bands Calculation for Low Alloy Steels

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Procedia Manufacturing 37 (2019) 486–491 Procedia Manufacturing 00 (2017) 000–000 www.elsevier.com/locate/procedia

9th International Conference on Physical and Numerical Simulation on Materials Processing (ICPNS’2019) 9th International Conference on Physical and Numerical Simulation on Materials Processing (ICPNS’2019)

Method of Hardenability Bands Calculation for Low Alloy Steels Method of Hardenability Bands Calculation for Low Alloy Steels

a a

a a MESIC 2017, 28-30 June Manufacturing Engineering Society Terentev International Conference 2017, Maksim *, Oleg Broytman a 2017, Vigo (Pontevedra), Spain Maksim Terentev *, Oleg Broytmana

All-Union Research and Development Center for Transport Technology, LLC, 2A Line 23, Vasilyevksy Island, St. Petersburg, Russia, 199106 All-Union Research and Development Center for Transport Technology, LLC, 2A Line 23, Vasilyevksy Island, St. Petersburg, Russia, 199106

Costing models for capacity optimization in Industry 4.0: Trade-off between used capacity and operational efficiency

Abstract Abstract Method of hardenability bands calculation for low-alloy steels has been proposed. The method is based on the Grossman method Method of hardenability bands has in been proposed. Thestandard. method isInbased on to thethe Grossman method a low-alloy steels a,* bcontrast for calculating hardenability from chemicalfor composition, included theZanin ASTMbA255 ASTM method, A.calculation Santana , P. Afonso , inA. , R. Wernke for calculating hardenabilityhardenability from chemical composition, included the ASTM A255 standard. In contrast to the ASTM method, which allows calculating curves for a certain chemical composition, the proposed method allows calculating a curves for which allows band calculating hardenability certain chemical composition, method allows calculating hardenability for a range of compositions ofofaaMinho, certain steel grade. For calculating hardenability band, several hundred University 4800-058 Guimarães, Portugalthe aproposed b hardenability banddifferent for a range of compositions ofare a generated. certain steel Chapecó, grade. For a hardenability band, several hundred virtual heats with chemical compositions Unochapecó, 89809-000 SC,calculating Brazil virtual heats can withbedifferent compositions are generated. The method used forchemical hardenability based selection of steels for manufacturing quenched and tempered parts, as well as for The methodquenching can be used for hardenability based steelsthere for manufacturing and data. tempered parts, as well as for developing regimes for parts made of selection steels for of which is no reference quenched hardenability developing regimesoffor madecalculation of steels forresults whichhave therebeen is nocompared reference with hardenability data. bands for different steel As a part ofquenching the verification theparts method, hardenability Abstract As a part of thein verification of products the method, calculationThe results have been compared withinhardenability bands for different steel grades present various metal specifications. proposed calculation method most cases gives acceptable accuracy grades ±20%. present in various metal products specifications. The proposed calculation method in most cases gives acceptable accuracy within Under the concept of "Industry 4.0", production processes will be pushed to be increasingly interconnected, within ±20%. information based on a real time basis and, © 2019 The Authors. Published by Elsevier B.V. necessarily, much more efficient. In this context, capacity optimization © 2019 The Authors. Published by Elsevier B.V. © 2019 The Authors. Published by of Elsevier B.V.maximization, This is an open access article under thecapacity CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) goes beyond the traditional aim contributing also for organization’s profitability and value. This is open access article under under the the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) This is an anlean open access article BY-NC-ND license of (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of continuous theCCscientific committee the 9th International Conference on Physical and Numerical Indeed, management and improvement approaches suggestConference capacity on optimization of Peer-review under responsibility of the scientific committee of the 9th International Physical andinstead Numerical Peer-reviewonunder of the scientific committee of the 9th International Conference on Physical Simulation Processing maximization. Theresponsibility study of capacity optimization and costing models is an important research topic and that Numerical deserves Simulation on Materials Materials Processing Simulation on Materials Processing

contributions from both the practical and theoretical perspectives. This paper presents and discusses a mathematical Keywords: hardenability bands, quenching, low alloy steels model for capacity management based on different costing models (ABC and TDABC). A generic model has been Keywords: hardenability bands, quenching, low alloy steels developed and it was used to analyze idle capacity and to design strategies towards the maximization of organization’s value. The trade-off capacity maximization vs operational efficiency is highlighted and it is shown that capacity 1. Introduction optimization might hide operational inefficiency. 1. Introduction © 2017 The Authors. Published by Elsevier B.V. Designing of new cast steel parts for the needs of machine building includes the choosing of a suitable steel grade Peer-review under responsibility ofparts the scientific committee of the Manufacturing Engineering Society International Designing of new cast steel for the needs machine building includes choosing of a suitableConference steel according to GOST 977-88, GOST 21357-87 andof various industry standards asthe well as the development of thegrade heat 2017. according regime to GOST 977-88, the GOST 21357-87 and various industry standards as well as the development of the heat treatment to provide required mechanical properties. treatment regime to provide the required mechanical properties. Keywords: Cost Models; ABC; TDABC; Capacity Management; Idle Capacity; Operational Efficiency 1. Introduction * Corresponding author. Tel.: +7 812 655-5910

address:author. [email protected] * E-mail Corresponding Tel.: +7 812 655-5910 E-mail address: [email protected] The cost of idle capacity is a fundamental information for companies and their management of extreme importance 2351-9789 2019 The Authors. Published by Elsevier in modern©production systems. In general, it isB.V. defined as unused capacity or production potential and can be measured This is an open access the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) 2351-9789 2019 Thearticle Authors. Published by Elsevier B.V. in several©ways: tons ofunder production, available hours of manufacturing, etc. The management of the idle capacity Peer-review under responsibility of the scientific committee of the 9th International Conference on Physical and Numerical Simulation on This is an open access article under CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/) * Paulo Afonso. Tel.: +351 253 510 761; fax: +351 253 604 Materials Processing Peer-review under responsibility of the scientific committee of741 the 9th International Conference on Physical and Numerical Simulation on E-mailProcessing address: [email protected] Materials 2351-9789 Published by Elsevier B.V. B.V. 2351-9789 ©©2017 2019The TheAuthors. Authors. Published by Elsevier Peer-review underaccess responsibility of the scientific committee oflicense the Manufacturing Engineering Society International Conference 2017. This is an open article under the CC BY-NC-ND (http://creativecommons.org/licenses/by-nc-nd/4.0/) Peer-review under responsibility of the scientific committee of the 9th International Conference on Physical and Numerical Simulation on Materials Processing 10.1016/j.promfg.2019.12.078

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Hardenability is one of the most important properties of steels subjected to quenching and tempering. Based on the hardenability data, the distribution of hardness over the cross section of a part after quenching can be predicted; with the subsequent use of special relationships [1] and models [2, 3], mechanical properties after tempering of the part can be estimated. Thus, the initial stage of solving the problem of selecting the appropriate steel may consist in the selection of grades that meet the hardenability requirements. Information on hardenability can be found only for a limited number of steel grades. In GOST 4543-2016, for example, there are no hardenability bands for many wrought steels: 20KhM, 20KhGNM, 19KhGN, 25KhGSA, 30KhN2MA. GOST 977-88 and GOST 21357-87 standards for cast steels do not contain information about hardenability despite the fact that many cast parts are subjected to quenching and tempering. In this paper it is proposed to use the calculation method for obtaining the hardenability bands. 2. Method of hardenability bands calculation The modification of Grossman method described in ASTM A 255 [4] was adopted as the basis for the method of calculating the hardenability bands. Unlike other known methods [5-9], it has a wider range of permissible values for the alloying elements contents, which is very convenient – there is no need to look for a formula suitable for a specific range of chemical compositions. The ASTM method is calibrated on thousands of heats of various steel grades [4], while other statistical models are obtained on 200-350 heats [7, 8]. Moreover, the method has previously been successfully used for calculation of hardenability curves for Russian steel grades [10]. Besides that, the Grossman method has another feature, which can rather be considered as an aesthetic one: compared to regression models it looks more reasonable from the point of view of metal physics. For example, the regression models in SEP 1664 [7] can have a negative coefficient before the nickel content (table 3b of the standard) – this fact tells us about the negative effect of nickel on the hardenability, which is not true from the metal physics point of view. In the Grossman method, an increase in any alloying element content always yields to an increase in the hardenability of steel. The simplest and most obvious way to obtain a hardenability band for any given range of chemical compositions may seem to be the calculation of two hardenability curves corresponding to the extreme contents of the elements in steel – the minimum and maximum contents. Such a simplified approach may be acceptable when making quick estimations. However, this can lead to errors – getting hardenability bands too wide. In metallurgical practice, heats of steel with simultaneous minimum or maximum contents of all of the alloying elements are very unlikely to occur. The essence of the proposed method of calculating the hardenability bands is to generate several hundreds of virtual heats and calculate the hardenability curves for each heat according to the Grossman method described in the current edition of ASTM A 255. The limits of the hardenability band for a given range of chemical compositions will be the maximum and minimum hardness values on each standard distance from the quenched end of Jominy sample: 1.5, 3, 5, 7, 9, 11, 13, 15, 20, 25, 30 mm. The method requires a computer implementation, for example, based on an MS Excel spreadsheet. 2.1. Input data for calculation A table of normally distributed random numbers is prepared, containing n columns and m rows (for example, n = 8, m = 500). Each column corresponds to one of 8 alloying elements: C, Si, Mn, Cr, Ni, Cu, Mo, V. The numbers in each column of the table are distributed according to the standard normal distribution with a mean of 0, a standard deviation of 1 and vary from -3 to 3, that is, the sample span is 6 standard deviations. Each row of the table will be used further to generate the chemical composition of one specific virtual heat. At this stage, the chemical composition range of the steel of interest is specified: the maximum and minimum contents of alloying elements and impurities are inputted. 2.2. Calculation of hardenability curves A set of m virtual heats of steel is generated using the tables of random numbers. The content of each chemical element in each of the m virtual heats is calculated by the following formula:

Maksim Terentev et al. / Procedia Manufacturing 37 (2019) 486–491 Author name / Procedia Manufacturing 00 (2019) 000–000

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𝑋𝑋𝑖𝑖𝑖𝑖 =

𝑅𝑅𝑖𝑖𝑖𝑖 (𝑋𝑋𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 −𝑋𝑋𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 ) 6

+

𝑋𝑋𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 +𝑋𝑋𝑖𝑖𝑚𝑚𝑚𝑚𝑚𝑚 2

3

(1)

where Xij – the content of the i-th element in the j-th virtual heat (i = C, Si, Mn, Cr, Ni, Cu, Mo, V), expressed as a mass percentage; Rij – a random number (j = 1 ... m) in the range from -3 to 3; Xi max - the specified maximum content of the i-th element in steel; Xi min – the specified minimum content of the i-th element in steel. For each of these m heats, an automatic calculation of a hardenability curve is performed according to the standard method, described in ASTM A 255. 2.3. Determining the boundaries of the hardenability band For each standard distance (1.5, 3, 5, 7, 9, 11, 13, 15, 20, 25, 30 mm), the maximum and minimum hardness values are searched. The maximum hardness value for each standard distance will be the upper limit of the hardenability band, and the minimum - the lower limit. 3. Results and discussion For verification of the proposed method the calculation results had been compared with the known hardenability bands for various Russian and European steel grades present in different specifications. Some of the calculated hardenability bands in comparison with the known hardenability data are presented in Fig. 1. Comparison of hardness values for the whole set of steels used for the verification is presented in Fig. 2. As can be seen, the proposed calculation method gives acceptable accuracy, which in most cases (89%) is within ±20%. As can be seen from Fig. 2, the spread of points decreases with the increase of hardness values, which indicates an increase in the forecast accuracy. High accuracy in the range of 40-65 HRC is connected with the fact that most of the points correspond to the martensite hardness, which depends only on one parameter – the carbon content in steel [3]. Smaller hardness values reflect the mixed ferrite-cementite structures; therefore, the prediction accuracy in this range decreases.

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Maksim Terentev et al.Manufacturing / Procedia Manufacturing 37 (2019) 486–491 Author name / Procedia 00 (2019) 000–000

Fig. 1. Hardenability bands of steel grades with different alloying concepts: solid lines – data from specifications, dotted lines – calculated hardenability bands

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Fig. 2. Comparison of calculated and known values of hardness for 22 different low-alloyed steels

The proposed hardenability bands calculation method was used in the development of chemical compositions of steels for cast components of freight cars coupling devices and their heat treatment regimes. Fig. 3 shows the calculated hardenability bands for some of the steels being used in the freight car industry: solid lines show the hardenability bands for the standard chemical composition, dotted lines reflect the bands for the compositions that have been modified to meet the hardenability requirements. The requirements for hardenability were as follows: for 20GL steel grade, hardness at a distance of 11 mm from the quenched end of a Jominy sample should be at least 20HRC, for 30KhL grade - within 25-40 HRC. The desired increase in hardenability was achieved by increasing the lower limits of the main alloying elements and impurities contents within the ranges allowed by the metal products specifications. In the case of 30KhL steel grade, this was done by increasing the lower limits of carbon and manganese, and in the case of 20GL grade – by increasing the lower limits of carbon, manganese, chromium and nickel.

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Fig. 3. Calculated hardenability bands for cast steels: solid lines stand for the standard chemical compositions, dotted lines reflect the modified compositions meeting the hardenability requirements.

4. Conclusion The method of calculating the hardenability bands proposed in the paper can be used in the absence of reference hardenability data when selecting cast and wrought steels for parts subjected to quenching and tempering, as well as for the development of quenching regimes. References [1] DIN 17021-1: 1976 Wärmebehandlung von Eisenwerkstoffen; Werkstoffauswahl, Stahlauswahl aufgrund der Härtbarkeit [2] B.Smoljan , D.Iljkić, G.E. Totten, Mathematical Modeling and Simulation of Hardness of Quenched and Tempered Steel // Metallurgical and Materials Transactions B, 2015, Vol. 46, Iss. 6, pp. 2666-2673 [3] G.E. Totten (Editor) Steel Heat Treatment: Metallurgy and Technologies, 2nd edition, CRC Press, 2006, 820 p [4] ASTM A 255-10 (2018) Standard Test Methods for Determining Hardenability of Steel [5] R. Caspari, H. Gulden, K. Krieger, D. Lepper,A. Lübben, H. Rohloff, P. Schüler, V. Schüler, and H.J. Wieland, Härterei Tech. Mitt. 47 (3):183–188, 1992. [6] E. Just, New Formulas for Calcultaing Hardenability. Metal Progress, 96, November, 1969, 87-88 [7] SEP 1664 Ermittlung von Formeln durch multiple Regression zur Berechnung der Härtbarkeit im Stirnabschreckversuch aus der chemischen Zusammensetzung von Stählen [8] Schüler P. Calculation of hardenability in the Jominy end quench test on the basis of the Chemical composition of steels // La Revue de Metallurgie, Rev. Met. Paris, Vol. 89, No 1, pp. 93–103, 1992 [9] Brooks, C. R. Hardenability. In Principles of the Heat Treatment of Plain Carbon and Low-Alloy Steels; ASM International: Materials Park, OH, 1996; pp 43–86. [10] Nosov V.B., Yurasov S.A. Calculation of Hardenability of Structural From their Chemical Composition // Metal Science and Heat Treatment, Vol. 37, Nos. 1-2, 1995