{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,8]],"date-time":"2026-09-08T16:48:00Z","timestamp":1788886080826,"version":"build-2803163510"},"reference-count":37,"publisher":"MDPI AG","issue":"7","license":[{"start":{"date-parts":[[2022,3,22]],"date-time":"2022-03-22T00:00:00Z","timestamp":1647907200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Materials"],"abstract":"<jats:p>Traditional fatigue fracture theory and practice focus principally on structural design. It is thus too conservative and inappropriate when used to predict the high-cycle fatigue life of dies used for metal forming, especially cold forging. We propose a novel mean stress correction model and diagram to predict the high-cycle fatigue lives of cold forging dies, which focuses on the upper part of the equivalent fatigue strength curve. Considering the features of die materials characterized by high yield strength and low ductility, a straight line is assumed for the tensile yield line. To the contrary, a general curve is used to represent the fatigue strength. They are interpolated, based on the distance ratio, when finding an appropriate equivalent fatigue strength curve at the mean stress and stress amplitude between the line and curve. The approach is applied to a well-defined literature example to verify its validity and shed light on the characteristics of die fatigue life. The approach is also applied to practical forging and useful qualitative results are obtained.<\/jats:p>","DOI":"10.3390\/ma15072351","type":"journal-article","created":{"date-parts":[[2022,3,22]],"date-time":"2022-03-22T23:30:23Z","timestamp":1647991823000},"page":"2351","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":17,"title":["A New General Fatigue Limit Diagram and Its Application of Predicting Die Fatigue Life during Cold Forging"],"prefix":"10.3390","volume":"15","author":[{"given":"Man-Soo","family":"Joun","sequence":"first","affiliation":[{"name":"Engineering Research Institute, School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju 52828, Gyeongsangnam-do, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7209-6561","authenticated-orcid":false,"given":"Su-Min","family":"Ji","sequence":"additional","affiliation":[{"name":"Graduate School of Mechanical and Aerospace Engineering, Gyeongsang National University, Jinju 52828, Gyeongsangnam-do, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6264-3592","authenticated-orcid":false,"given":"Wan-Jin","family":"Chung","sequence":"additional","affiliation":[{"name":"Department of Mechanical System Design Engineering, Seoul National University of Science and Technology, Seoul 01811, Gyeonggi-do, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Gue-Serb","family":"Cho","sequence":"additional","affiliation":[{"name":"Advanced Process and Materials Group, Korea Institute of Industrial Technology, Incheon 21999, Gyeonggi-do, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kwang-Hee","family":"Lee","sequence":"additional","affiliation":[{"name":"Pungkang Co., Ltd., Hwaseong 18572, Gyeonggi-do, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2022,3,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"104545","DOI":"10.1016\/j.engfailanal.2020.104545","article-title":"Predicting damage and failure under thermomechanical fatigue in hot forging tools","volume":"113","author":"Ghalehbandi","year":"2020","journal-title":"Eng. Fail. Anal."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"104910","DOI":"10.1016\/j.engfailanal.2020.104910","article-title":"Fatigue life prediction model of WC-Co cold forging dies based on experimental and numerical studies","volume":"118","author":"Karakuzu","year":"2020","journal-title":"Eng. Fail. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"e20190697","DOI":"10.1590\/1980-5373-mr-2019-0697","article-title":"Thermal fatigue analysis of hot forging closed dies","volume":"23","author":"Vianello","year":"2020","journal-title":"Mater. Res."},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Byun, J.B., Razali, M.K., Lee, C.J., Seo, I.D., Chung, W.J., and Joun, M.S. (2020). Automatic multi-stage cold forging of an SUS304 ball-stud with a hexagonal hole at one end. Materials, 13.","DOI":"10.3390\/ma13225300"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1113","DOI":"10.1007\/s12239-020-0105-9","article-title":"FEM analysis and experiment validation on multi-pass forging of torx round flange bolt","volume":"21","author":"Lin","year":"2020","journal-title":"Int. J. Automot. Technol."},{"key":"ref_6","unstructured":"Stephens, R.I., Fatemi, A., Stephens, R.R., and Fuchs, H.O. (2000). Metal Fatigue in Engineering, John Wiley & Sons. [2nd ed.]."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Forrest, P.G. (1962). Fatigue Testing. Fatigue of Metals, Pergamon Press Ltd.. [1st ed.].","DOI":"10.1016\/B978-0-08-009729-9.50005-1"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1213","DOI":"10.1016\/S0890-6955(02)00079-2","article-title":"Finite element analysis of prestressed die set in cold forging","volume":"42","author":"Joun","year":"2002","journal-title":"Int. J. Mach. Tools Manuf."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"2381","DOI":"10.1016\/S1359-6454(02)00071-X","article-title":"On the fatigue crack growth behavior of WC-Co cemented carbides: Kinectics description, microstructural effects and fatigue sensitivity","volume":"50","author":"Llanes","year":"2002","journal-title":"Acta. Mater."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1016\/0921-5093(95)10106-3","article-title":"Fatigue of hard metals and cermets","volume":"209","author":"Schleinkofer","year":"1996","journal-title":"Mater. Sci. Eng. A"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"2001","DOI":"10.1016\/j.proeng.2010.03.215","article-title":"Effect of microstructure on fatigue properties of WC-Co hard metals","volume":"2","author":"Marsoner","year":"2010","journal-title":"Procedia Eng."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"281","DOI":"10.1016\/j.matchar.2005.06.001","article-title":"Mechanical properties of WC\/Co cemented carbide with larger WC grain size","volume":"55","author":"Okamoto","year":"2005","journal-title":"Mater. Charact."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1016\/0924-0136(94)90102-3","article-title":"Fatigue life of cold forging tooling: Causes and possible solutions through fatigue analysis","volume":"46","author":"Knoerr","year":"1994","journal-title":"J. Mater. Processing Technol."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"527","DOI":"10.1016\/0020-7403(95)00064-X","article-title":"Service life estimation of extrusion dies by numerical simulation of fatigue-crack growth","volume":"38","author":"Tekkaya","year":"1996","journal-title":"Int. J. Mech. Sci."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"799","DOI":"10.1016\/S0020-7403(99)00019-3","article-title":"Numerical modelling of cyclic plasticity and fatigue damage in cold-forging tools","volume":"42","author":"Pedersen","year":"2000","journal-title":"Int. J. Mech. Sci."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/S0924-0136(01)00934-7","article-title":"Fundamental aspects for the evaluation of the fatigue behaviour of cold forging tools","volume":"119","author":"Falk","year":"2001","journal-title":"J. Mater. Processing Technol."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"479","DOI":"10.5228\/KSPP.2007.16.6.479","article-title":"A study on life estimation of a forging die","volume":"16","author":"Choi","year":"2007","journal-title":"Trans. Mater. Processing"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"843","DOI":"10.1007\/s00170-006-0762-5","article-title":"Die fatigue life design and assessment via CAE simulation","volume":"35","author":"Fu","year":"2008","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"3766","DOI":"10.1016\/j.jmatprotec.2008.08.032","article-title":"The effect of shrink fitting ratios on tool life in bolt forming processes","volume":"209","author":"Lee","year":"2009","journal-title":"J. Mater. Processing Technol."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"271","DOI":"10.1016\/j.matdes.2012.08.075","article-title":"Three-point bending fatigue behavior of WC\u2013Co cemented carbides","volume":"45","author":"Li","year":"2013","journal-title":"Mater. Des."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"2215","DOI":"10.1016\/j.proeng.2017.10.984","article-title":"Determination of optimal shrink fitting ratio for 2-layer compound forging die by improving fatigue life in backward extrusion","volume":"207","author":"Wang","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_22","unstructured":"Kawahara, J., Matsumoto, R., Mori, S., and Osakada, K. (2011, January 11\u201314). Predicting fatigue life of carbide tool using elastic-plastic FEM. Proceedings of the The 44th Plenary Meeting of the International Cold Forging Group, Soenderborg, Denmark."},{"key":"ref_23","first-page":"625","article-title":"The exponential law of endurance tests","volume":"10","author":"Basquin","year":"1910","journal-title":"Proc.-Am. Soc. Test. Mater."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"163","DOI":"10.1111\/j.1460-2695.2008.01322.x","article-title":"Mean stress effects in stress-life fatigue and the Walker equation","volume":"32","author":"Dowling","year":"2009","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"854","DOI":"10.1111\/j.1460-2695.2011.01577.x","article-title":"A modification of Morrow and Smith-Watson-Topper mean stress correction models","volume":"34","author":"Ince","year":"2011","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_26","first-page":"50","article-title":"Mean stress correction effects on the fatigue life behavior of steel alloys by using stress life approach theories","volume":"10","author":"Bader","year":"2014","journal-title":"Int. J. Eng. Technol."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"1219","DOI":"10.1177\/1056789516651920","article-title":"Mean stress effect correction in strain energy-based fatigue life prediction of metals","volume":"26","author":"Zhu","year":"2017","journal-title":"Int. J. Damage Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1016\/j.ijfatigue.2013.02.019","article-title":"Mean stress effect correction using constant stress ratio S-N curves","volume":"52","year":"2013","journal-title":"Int. J. Fatigue"},{"key":"ref_29","doi-asserted-by":"crossref","unstructured":"B\u00f6hm, M., Kluger, K., Pochwa\u0142a, S., and Kupina, M. (2020). Application of the S-N curve mean stress correction model in terms of fatigue life estimation for random torsional loading for selected aliminum alloys. Materials, 13.","DOI":"10.3390\/ma13132985"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"149","DOI":"10.1111\/ffe.12341","article-title":"Effects of mean stress and stress concentration on fatigue behavior of short fiber reinforced polymer composites","volume":"39","author":"Mortazavian","year":"2016","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"939","DOI":"10.1111\/ffe.12553","article-title":"A mean stress correction model for tensile and compressive mean stress fatigue loadings","volume":"40","author":"Ince","year":"2017","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"106787","DOI":"10.1016\/j.engfracmech.2019.106787","article-title":"A unified mean stress correction model for fatigue thresholds prediction of metals","volume":"223","author":"Liu","year":"2020","journal-title":"Eng. Fract. Mech."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"346","DOI":"10.1115\/1.3225026","article-title":"Metal Fatigue in Engineering","volume":"103","author":"Fuchs","year":"1981","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_34","first-page":"145","article-title":"Behavior of metals under complex static and alternating stresses","volume":"1","author":"Sines","year":"1959","journal-title":"Met. Fatigue"},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"586","DOI":"10.1016\/j.mechmat.2007.11.006","article-title":"A new method for acquiring true stress\u2013strain curves over a large range of strains using a tensile test and finite element method","volume":"40","author":"Joun","year":"2008","journal-title":"Mech. Mater."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"311","DOI":"10.1016\/j.triboint.2008.06.012","article-title":"Effects of friction laws on metal forming processes","volume":"42","author":"Joun","year":"2009","journal-title":"Tribol. Int."},{"key":"ref_37","first-page":"115","article-title":"Numerical and experimental study on spring back in automatic multi-stage precision cold forging process of a steering yoke","volume":"28","author":"Kim","year":"2019","journal-title":"Trans. Mater. Processing"}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/7\/2351\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T22:40:57Z","timestamp":1760136057000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/15\/7\/2351"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,3,22]]},"references-count":37,"journal-issue":{"issue":"7","published-online":{"date-parts":[[2022,4]]}},"alternative-id":["ma15072351"],"URL":"https:\/\/doi.org\/10.3390\/ma15072351","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,3,22]]}}}