{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,12]],"date-time":"2026-09-12T03:53:42Z","timestamp":1789185222940,"version":"build-2803163510"},"reference-count":60,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T00:00:00Z","timestamp":1653350400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Kongju National Universit"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Governing void growth, stress triaxiality (\u03b7) is a crucial parameter in ductile damage prediction. \u03b7 is defined as the ratio of mean stress to equivalent stress and represents loading conditions. Attempts at introducing material anisotropy in ductile damage models have started only recently, rendering necessary in-depth investigation into the role of \u03b7 here. \u03b7 is commonly derived via finite elemnt (FE) simulation. An alternative is presented here: based on analytical expressions, \u03b7 is obtained directly from the strains in the critical zone. For anisotropic materials, \u03b7 associated with a specimen varies with yield criterion and material (anisotropy). To investigate the meaning of triaxiality for anisotropic materials, metal sheets made of dual phase steel DP780, and zirconium alloy Zirlo are chosen. Analytical expressions for \u03b7 are derived for three popular yield criteria: von Mises, Hill48 and Barlat89. Tensile tests are performed with uniaxial tension, notch, and shear specimens, and the local principal strains, measured via digital image correlation (DIC), are converted to h. The uniaxial tension case reveals that only the anisotropic yield criteria can predict the expected \u03b7 = 1\/3. The ramifications associated with anisotropy become apparent for notched specimens, where \u03b7 differences are highest; for shear specimens, the yield criterion and material-dependence is relatively moderate. This necessitates \u03b7 and, consequently, the triaxiality failure diagram (TFD) being accompanied by the underlying yield criterion and anisotropy parameters. As the TFD becomes difficult to interpret, it seems more advantageous to provide pairs of principal strain ratio \u03b2 and failure strain. Suggestions for deriving representative \u03b2 and \u03b7 are made.<\/jats:p>","DOI":"10.3390\/ma15113738","type":"journal-article","created":{"date-parts":[[2022,5,24]],"date-time":"2022-05-24T03:16:55Z","timestamp":1653362215000},"page":"3738","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":27,"title":["Stress Triaxiality in Anisotropic Metal Sheets\u2014Definition and Experimental Acquisition for Numerical Damage Prediction"],"prefix":"10.3390","volume":"15","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-1722-7343","authenticated-orcid":false,"given":"Felix","family":"Rickhey","sequence":"first","affiliation":[{"name":"Department of Automotive and Mechanical Engineering, Kongju National University, Cheonan 31080, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5569-6285","authenticated-orcid":false,"given":"Seokmoo","family":"Hong","sequence":"additional","affiliation":[{"name":"Department of Automotive and Mechanical Engineering, Kongju National University, Cheonan 31080, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,24]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"614","DOI":"10.1007\/BF00184558","article-title":"Ductile fracture by hole growth in shear bands","volume":"2","author":"McClintock","year":"1966","journal-title":"Int. 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