UNIVERSITY PRESS Nickel and cobalt-based superalloys with a - microstructure are known for their excellent creep resistance at high temperatures. Their microstructure is engineered using differentγ γ′ alloying elements, that partition either to the fcc matrix or to the ordered phase. In the present work the effect of alloying elements on their segregation behaviour in nickel-based superalloys,γ diffusion in cobalt-basedγ′ superalloys and the temperature dependent solid solution strengthening in nickel-based alloys is investigated. The effect of dendritic segregation on the local mechanical properties of individual phases in the as-cast, heat treated and creep deformed state of a nickel-based superalloy is investigated. The local chemical composition is characterized using Electron Probe Micro Analysis and then correlated with the mechanical properties of individual phases using nanoindentation. Furthermore, the temperature dependant solid solution hardening contribution of Ta, W & Re towards fcc nickel is studied. The room temperature hardening is determined by a diffusion couple approach using nanoindentation and energy dispersive X-ray analysis for relating hardness to the FAU Studien Materialwissenschaft und Werkstofftechnik 8 chemical composition. The high temperature properties are determined using compression strain rate jump tests. The results show that at lower temperatures, the solute size is prevalent and the elements with the largest size difference with nickel, induce the greatest hardening consistent with a classical solid solution strengthening theory. At Hamad ur Rehman higher temperatures, the solutes interact with the dislocations such that the slowest diffusing solute poses maximal resistance to dislocation glide and climb. Lastly, the diffusion of different technically relevant solutes in fcc cobalt is investigated using diffusion couples. The results show that the large atoms diffuse faster in cobalt-based superalloys Solid Solution Strengthening similar to their nickel-based counterparts. and Diffusion in Nickel- and Solid Solution Strengthening and Diffusion in Nickel- and Cobalt-based Superalloys and Diffusion Solid Solution Strengthening Cobalt-based Superalloys ISBN 978-3-944057-71-2 FAU UNIVERSITY PRESS 2016 FAU Hamad ur Rehman Hamad ur Rehman Solid Solution Strengthening and Diffusion in Nickel- and Cobalt-based Superalloys FAU Studien Materialwissenschaft und Werkstofftechnik Band 8 Herausgeber der Reihe: Prof. Dr. Mathias Göken Hamad ur Rehman Solid Solution Strengthening and Difusion in Nickel- and Cobalt-based Superalloys Erlangen FAU University Press 2016 Bibliografische Information der Deutschen Nationalbibliothek: Die Deutsche Nationalbibliothek verzeichnet diese Publikation in der Deutschen Nationalbibliografie; detaillierte bibliografische Daten sind im Internet über http://dnb.d-nb.de abrufbar. Das Werk, einschließlich seiner Teile, ist urheberrechtlich geschützt. Die Rechte an allen Inhalten liegen bei ihren jeweiligen Autoren. Sie sind nutzbar unter der Creative Commons Lizenz BY-NC-ND. Der vollständige Inhalt des Buchs ist als PDF über den OPUS Server der Friedrich-Alexander-Universität Erlangen-Nürnberg abrufbar: https://opus4.kobv.de/opus4-fau/home Verlag und Auslieferung: FAU University Press, Universitätsstraße 4, 91054 Erlangen Druck: docupoint GmbH ISBN: 978-3-944057-71-2 (Druckausgabe) eISBN: 978-3-944057-72-9 (Online-Ausgabe) ISSN: 2197-2575 Solid Solution Strengthening and Diffusion in Nickel- and Cobalt-based Superalloys Mischkristallh¨artungund Diffusion in Nickel- und Kobaltbasissuperlegierungen Der Technischen Fakult¨atder Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg zur Erlangung des Grades DOKTOR-INGENIEUR vorgelegt von Hamad ur Rehman aus Lahore, Pakistan Als Dissertation genehmigt von der Technischen Fakult¨atder Friedrich-Alexander-Universit¨at Erlangen-N¨urnberg Tag der m¨undlichen Pr¨ufung: 6. Mai 2016 Vorsitzender des Promotionsorgans: Prof. Dr. Peter Greil Gutachter: Prof. Dr. rer. nat. Mathias G¨oken Prof. Dr.-Ing. Uwe Glatzel I am and ever will be a white-socks, pocket-protector nerdy engineer, born under second law of thermodynamics, steeped in the steam tables, in love with the free body diagrams, transformed by Laplace and propelled by compressible flow. Neil Armstrong Table of Contents 1 Introduction and Objectives 5 2 Fundamentals and Literature Overview 9 2.1 Solid solution strengthening . 9 2.1.1 Dislocation locking . 10 2.1.2 Dislocation friction . 11 2.1.3 Quantification of solid solution strengthening . 11 2.1.4 Effect of temperature on solid solution strengthening . 12 2.2 Creep of solid solutions . 14 2.2.1 Solid solution strengthening in nickel-based alloys . 17 2.3 Creep deformation in nickel-based superalloys . 19 2.4 Diffusion . 23 2.4.1 Diffusion mechanisms . 23 2.4.2 Fick's laws for diffusion . 25 2.4.3 Diffusion in nickel-based alloys . 29 2.4.4 Diffusion in cobalt-based alloys . 31 3 Materials and Experimental Methods 33 3.1 Materials and heat treatments . 33 3.1.1 Single crystalline nickel and binary nickel-based alloys 33 3.1.2 Cobalt-based alloys . 34 3.1.3 Nickel-based superalloy (ERBO-1) . 35 3.2 Compression tests . 35 3.2.1 Compression under constant strain rate . 35 3.2.2 Compression under constant stress . 36 3.3 Nanoindentation . 38 3.3.1 Nanoindenting AFM . 39 3.4 Diffusion couples . 40 3.5 Microstructural analysis . 42 i 4 Mechanical Properties of the γ/γ0 & µ-phase in Dependence of the Dendritic Microstructure 45 4.1 Chemical segregations . 46 4.2 Microstructure . 48 4.2.1 As-cast state . 48 4.2.2 Heat treated state . 49 4.2.3 Creep deformed state . 49 4.3 Large scale indentation . 52 4.4 Small scale indentation . 54 4.4.1 As-Cast ERBO-1 . 54 4.4.2 Creep deformed state . 60 5 Temperature Dependent Solid Solution Strengthening of Ni 67 5.1 Solid solution hardening at room temperature . 67 5.1.1 Diffusion couple approach . 67 5.1.2 Ni-NiW diffusion couple . 69 5.1.3 NiTa, NiRe, NiIr & NiPt diffusion couples . 71 5.2 Effect of temperature on solid solution strengthening . 72 5.2.1 Strain rate jump tests . 73 5.2.2 Creep tests . 75 5.2.3 Effect of temperature on plastic flow . 78 5.2.4 Physical modelling of glide and climb forces . 80 5.3 Strengthening mechanisms . 84 5.3.1 Room temperature . 84 5.3.2 Effect of temperature on solid solution strengthening . 87 6 Diffusion in Cobalt-based Alloys 91 6.1 Determination of interdiffusion coefficients . 92 6.2 Interdiffusion coefficients . 95 6.2.1 Period-3 (Al) . 95 6.2.2 Period-4 (Ti, V, Cr, Mn, Fe) . 97 6.2.3 Period-5 (Nb, Mo & Ru) . 100 6.2.4 Period-6 (Ta, W, & Re) . 102 6.3 Mean interdiffusion coefficients . 105 7 Summary 109 8 Zusammenfassung 113 ii References 117 Appendix 128 A List of Symbols and Abbreviations 129 B Experimental Data 133 C Matlab Codes for Evaluation of Interdiffusion Coefficients 135 iii Abstract Nickel and cobalt-based superalloys with a γ-γ0 microstructure are known for their excellent creep resistance at high temperatures. Their microstruc- ture is engineered using different alloying elements, that partition either to the fcc γ matrix or to the ordered γ0 phase. In the present work the effect of alloying elements on their segregation behaviour in nickel-based superalloys, diffusion in cobalt-based superalloys and the temperature dependent solid solution strengthening in nickel-based alloys is investigated. The effect of dendritic segregation on the local mechanical properties of individual phases in the as-cast, heat treated and creep deformed state of a nickel-based su- peralloy is investigated. The local chemical composition is characterized using Electron Probe Micro Analysis and then correlated with the mechani- cal properties of individual phases using nanoindentation. Furthermore, the temperature dependant solid solution hardening contribution of Ta, W & Re towards fcc nickel is studied. The room temperature hardening is determined by a diffusion couple approach using nanoindentation and energy dispersive X-ray analysis for relating hardness to the chemical composition. The high temperature properties are determined using compression strain rate jump tests. The results show that at lower temperatures, the solute size is preva- lent and the elements with the largest size difference with nickel, induce the greatest hardening consistent with a classical solid solution strengthening theory. At higher temperatures, the solutes interact with the dislocations such that the slowest diffusing solute poses maximal resistance to dislocation glide and climb. Lastly, the diffusion of different technically relevant solutes in fcc cobalt is investigated using diffusion couples. The results show that the large atoms diffuse faster in cobalt-based superalloys similar to their nickel-based counterparts. 1 Kurzfassung Nickel- und Cobaltbasissuperlegierungen mit γ-γ0 mikrostruktur sind fur¨ ihre exzellent Kriechbest¨andigkeit bei hohen Temperaturen bekannt. Ihre Mikrostruktur wird uber¨ verschiedene Legierungselemente eingestellt, wel- che sich entweder in der fcc γ Matrix oder der geordneten γ0 Phase an- reichern. In der vorliegenden Arbeit wurde das Segregationsverhalten ver- schiedener Legierungselemente in Nickelbasissuperlegierungen, deren Diffu- sivit¨at in Kobaltbasislegierungen und die temperaturabh¨angige Mischkris- tallh¨artung von Nickelbasislegierungen untersucht. Der Einfluss chemischer Segregationen auf die mechanischen Eigenschaften einzelner Phasen wurde mittels einer Kombination aus Nanoindentierung und Elektron Probe Mi- kroanalyse untersucht. Zus¨atzlich wurde der H¨artungsbeitrag unterschied-