Two definitions of the newer HPV hardness measure as a volumetric modification of the Brinell measure

Two definitions of the newer HPV hardness measure as a volumetric modification of the Brinell measure | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Two definitions of the newer HPV hardness measure as a volumetric modification of the Brinell measure Grzegorz Marcin Koczan This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7189671/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract The Brinell ball hardness test is based on a measure of the total surface area of the indentation or a measure of the depth of the indentation. Although the Brinell hardness test is well-established, none of its basic measures has sufficient physical justification. Consequently, the Brinell hardness measure in the experiment depends on the load value, with a maximum for half-diameter indentations and a minimum for full indentations. Therefore, a slightly different hardness measure for the ball test has been proposed, which is based on the volume of the indentation and, at the same time, has an energetic justification. The newer hardness measure has been abbreviated as HPV, from the words Hardness-Pressure-Volume, which best reflects the essence of this measure. Two equivalent definitions of the HPV measure have been given. The first geometric definition relates the volume of a real indentation to the indentation volume of an ideal parabolic indenter. The second energetic definition is based on the average volume work of deformation of the material resisting hardness, in terms of pressure (stress). The preliminary experimental result showed that the HPV hardness measure is characterised by a lower correlation with the loading force than the Brinell measure on the transverse section of linden wood. This result reached a level of statistical significance of 0.03. Brinell hardness measure HPV hardness measure volumetric hardness measure energetic hardness measure ball indenter ideal parabolic indenter linden wood Fisher transformation Full Text Additional Declarations No competing interests reported. Cite Share Download PDF Status: Posted Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7189671","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":492089980,"identity":"f77ecbe1-bd39-4196-b756-75db13d5d642","order_by":0,"name":"Grzegorz Marcin Koczan","email":"data:image/png;base64,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","orcid":"","institution":"Warsaw University of Life Sciences","correspondingAuthor":true,"prefix":"","firstName":"Grzegorz","middleName":"Marcin","lastName":"Koczan","suffix":""}],"badges":[],"createdAt":"2025-07-22 18:08:06","currentVersionCode":1,"declarations":"","doi":"10.21203/rs.3.rs-7189671/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-7189671/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":88806450,"identity":"2ff556fe-29ca-4f78-b465-e0abb8788e16","added_by":"auto","created_at":"2025-08-11 15:02:03","extension":"pdf","order_by":1,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":331581,"visible":true,"origin":"","legend":"","description":"","filename":"HPVmeasure.pdf","url":"https://assets-eu.researchsquare.com/files/rs-7189671/v1_covered_accbf2db-0f14-4aef-9601-1b329e70d832.pdf"}],"financialInterests":"No competing interests reported.","formattedTitle":"Two definitions of the newer HPV hardness measure as a volumetric modification of the Brinell measure","fulltext":[],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":false,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":true,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":true,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Brinell hardness measure, HPV hardness measure, volumetric hardness measure, energetic hardness measure, ball indenter, ideal parabolic indenter, linden wood, Fisher transformation","lastPublishedDoi":"10.21203/rs.3.rs-7189671/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-7189671/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"The Brinell ball hardness test is based on a measure of the total surface area of the indentation or a measure of the depth of the indentation. 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