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The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy
Mark Evans
Materials at High Temperatures, Pages: 1 - 20
Swansea University Author: Mark Evans
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DOI (Published version): 10.1080/09603409.2025.2556580
Abstract
It is important to be able to predict the life of materials at high temperatures and an analysis of minimum creep rates vs. time to failure is one way of approaching this problem. However, recent studies on 9Cr steels, for example, have shown that this Monkman-Grant plot exhibits a low overall value...
| Published in: | Materials at High Temperatures |
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| ISSN: | 0960-3409 1878-6413 |
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Informa UK Limited
2025
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| URI: | https://cronfa.swan.ac.uk/Record/cronfa70329 |
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<?xml version="1.0"?><rfc1807><datestamp>2025-10-30T11:52:26.0743217</datestamp><bib-version>v2</bib-version><id>70329</id><entry>2025-09-11</entry><title>The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy</title><swanseaauthors><author><sid>7720f04c308cf7a1c32312058780d20c</sid><firstname>Mark</firstname><surname>Evans</surname><name>Mark Evans</name><active>true</active><ethesisStudent>false</ethesisStudent></author></swanseaauthors><date>2025-09-11</date><abstract>It is important to be able to predict the life of materials at high temperatures and an analysis of minimum creep rates vs. time to failure is one way of approaching this problem. However, recent studies on 9Cr steels, for example, have shown that this Monkman-Grant plot exhibits a low overall value for the exponent on the minimum creep rate (ρ = –0.85), together with a substantial scatter of data points around the relation. Both these phenomena, together with it being a mainly empirical relation, have restricted its use for life prediction purposes and so this paper aims to identify the causes of these two phenomena and to provide an explanation of this relation based on creep mechanisms. This is done within the 4-θ methodology so that the roles played by hardening, softening and damage mechanisms in causing this large scatter and low ρ value can be explicitly quantified. By manipulating the 4-θ equations, it was found that the role played by hardening and softening in identifying the form of the Monkman-Grant relation is restricted to the determination of a theoretical secondary creep rate measured as θ3θ4 - the exponent on which is predicted to equal −1 in this methodology. However, the data obtained on Waspaloy revealed ρ to equal −0.778 over all test conditions. This paper demonstrated that this was caused by the Monkman-Grant proportionality constant falling into three well defined groupings depending on values for both the amount of accumulated damage and the rate at which this damage occurred in a test specimen. It then turned out that within each such grouping, the exponent on the secondary creep rate equalled −1 as suggested by the 4-θ methodology. Then, by considering the damage at failure and the rate of its accumulation in the determination of the Monkman-Grant proportionality constant, together with the replacement of the minimum creep rate with θ3θ4, resulted in a Monkman-Grant exponent of −1 with minimal scatter around this relation.</abstract><type>Journal Article</type><journal>Materials at High Temperatures</journal><volume>0</volume><journalNumber/><paginationStart>1</paginationStart><paginationEnd>20</paginationEnd><publisher>Informa UK Limited</publisher><placeOfPublication/><isbnPrint/><isbnElectronic/><issnPrint>0960-3409</issnPrint><issnElectronic>1878-6413</issnElectronic><keywords>Waspaloy; Monkman-Grant relation; 4-θ methodology; damage; rates of damage accumulation; recovery; hardening</keywords><publishedDay>5</publishedDay><publishedMonth>10</publishedMonth><publishedYear>2025</publishedYear><publishedDate>2025-10-05</publishedDate><doi>10.1080/09603409.2025.2556580</doi><url/><notes/><college>COLLEGE NANME</college><CollegeCode>COLLEGE CODE</CollegeCode><institution>Swansea University</institution><apcterm>SU Library paid the OA fee (TA Institutional Deal)</apcterm><funders>Swansea University</funders><projectreference/><lastEdited>2025-10-30T11:52:26.0743217</lastEdited><Created>2025-09-11T10:55:17.0084748</Created><path><level id="1">Faculty of Science and Engineering</level><level id="2">School of Engineering and Applied Sciences - Materials Science and Engineering</level></path><authors><author><firstname>Mark</firstname><surname>Evans</surname><order>1</order></author></authors><documents><document><filename>70329__35436__0985f27547eb43c9af6d26322b7c5af5.pdf</filename><originalFilename>70329.VOR.pdf</originalFilename><uploaded>2025-10-22T10:33:23.9793933</uploaded><type>Output</type><contentLength>2452239</contentLength><contentType>application/pdf</contentType><version>Version of Record</version><cronfaStatus>true</cronfaStatus><documentNotes>© 2025 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY).</documentNotes><copyrightCorrect>true</copyrightCorrect><language>eng</language><licence>http://creativecommons.org/licenses/by/4.0/</licence></document></documents><OutputDurs/></rfc1807> |
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2025-10-30T11:52:26.0743217 v2 70329 2025-09-11 The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy 7720f04c308cf7a1c32312058780d20c Mark Evans Mark Evans true false 2025-09-11 It is important to be able to predict the life of materials at high temperatures and an analysis of minimum creep rates vs. time to failure is one way of approaching this problem. However, recent studies on 9Cr steels, for example, have shown that this Monkman-Grant plot exhibits a low overall value for the exponent on the minimum creep rate (ρ = –0.85), together with a substantial scatter of data points around the relation. Both these phenomena, together with it being a mainly empirical relation, have restricted its use for life prediction purposes and so this paper aims to identify the causes of these two phenomena and to provide an explanation of this relation based on creep mechanisms. This is done within the 4-θ methodology so that the roles played by hardening, softening and damage mechanisms in causing this large scatter and low ρ value can be explicitly quantified. By manipulating the 4-θ equations, it was found that the role played by hardening and softening in identifying the form of the Monkman-Grant relation is restricted to the determination of a theoretical secondary creep rate measured as θ3θ4 - the exponent on which is predicted to equal −1 in this methodology. However, the data obtained on Waspaloy revealed ρ to equal −0.778 over all test conditions. This paper demonstrated that this was caused by the Monkman-Grant proportionality constant falling into three well defined groupings depending on values for both the amount of accumulated damage and the rate at which this damage occurred in a test specimen. It then turned out that within each such grouping, the exponent on the secondary creep rate equalled −1 as suggested by the 4-θ methodology. Then, by considering the damage at failure and the rate of its accumulation in the determination of the Monkman-Grant proportionality constant, together with the replacement of the minimum creep rate with θ3θ4, resulted in a Monkman-Grant exponent of −1 with minimal scatter around this relation. Journal Article Materials at High Temperatures 0 1 20 Informa UK Limited 0960-3409 1878-6413 Waspaloy; Monkman-Grant relation; 4-θ methodology; damage; rates of damage accumulation; recovery; hardening 5 10 2025 2025-10-05 10.1080/09603409.2025.2556580 COLLEGE NANME COLLEGE CODE Swansea University SU Library paid the OA fee (TA Institutional Deal) Swansea University 2025-10-30T11:52:26.0743217 2025-09-11T10:55:17.0084748 Faculty of Science and Engineering School of Engineering and Applied Sciences - Materials Science and Engineering Mark Evans 1 70329__35436__0985f27547eb43c9af6d26322b7c5af5.pdf 70329.VOR.pdf 2025-10-22T10:33:23.9793933 Output 2452239 application/pdf Version of Record true © 2025 The Author(s). This is an Open Access article distributed under the terms of the Creative Commons Attribution License (CC BY). true eng http://creativecommons.org/licenses/by/4.0/ |
| title |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
| spellingShingle |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy Mark Evans |
| title_short |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
| title_full |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
| title_fullStr |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
| title_full_unstemmed |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
| title_sort |
The role of primary and tertiary creep in defining the form of the Monkman-Grant relation using the 4-θ methodology: an application to Waspaloy |
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7720f04c308cf7a1c32312058780d20c_***_Mark Evans |
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Mark Evans |
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It is important to be able to predict the life of materials at high temperatures and an analysis of minimum creep rates vs. time to failure is one way of approaching this problem. However, recent studies on 9Cr steels, for example, have shown that this Monkman-Grant plot exhibits a low overall value for the exponent on the minimum creep rate (ρ = –0.85), together with a substantial scatter of data points around the relation. Both these phenomena, together with it being a mainly empirical relation, have restricted its use for life prediction purposes and so this paper aims to identify the causes of these two phenomena and to provide an explanation of this relation based on creep mechanisms. This is done within the 4-θ methodology so that the roles played by hardening, softening and damage mechanisms in causing this large scatter and low ρ value can be explicitly quantified. By manipulating the 4-θ equations, it was found that the role played by hardening and softening in identifying the form of the Monkman-Grant relation is restricted to the determination of a theoretical secondary creep rate measured as θ3θ4 - the exponent on which is predicted to equal −1 in this methodology. However, the data obtained on Waspaloy revealed ρ to equal −0.778 over all test conditions. This paper demonstrated that this was caused by the Monkman-Grant proportionality constant falling into three well defined groupings depending on values for both the amount of accumulated damage and the rate at which this damage occurred in a test specimen. It then turned out that within each such grouping, the exponent on the secondary creep rate equalled −1 as suggested by the 4-θ methodology. Then, by considering the damage at failure and the rate of its accumulation in the determination of the Monkman-Grant proportionality constant, together with the replacement of the minimum creep rate with θ3θ4, resulted in a Monkman-Grant exponent of −1 with minimal scatter around this relation. |
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2025-10-05T05:25:51Z |
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