{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,18]],"date-time":"2026-08-18T04:53:36Z","timestamp":1787028816963,"version":"build-2736575974"},"reference-count":40,"publisher":"MDPI AG","issue":"17","license":[{"start":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T00:00:00Z","timestamp":1630886400000},"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>Heat-assisted forming processes are becoming increasingly important in the manufacturing of sheet metal parts for body-in-white applications. However, the non-isothermal nature of these processes leads to challenges in evaluating the forming limits, since established methods such as Forming Limit Curves (FLCs) only allow the assessment of critical forming strains for steady temperatures. For this reason, a temperature-dependent extension of the well-established GISSMO (Generalized Incremental Stress State Dependent Damage Model) fracture indicator framework is developed by the authors to predict forming failures under non-isothermal conditions. In this paper, a general approach to combine several isothermal FLCs within the temperature-extended GISSMO model into a temperature-dependent forming limit surface is investigated. The general capabilities of the model are tested in a coupled thermo-mechanical FEA using the example of warm forming of an AA5182-O sheet metal cross-die cup. The obtained results are then compared with state of the art of evaluation methods. By taking the strain and temperature path into account, GISSMO predicts greater drawing depths by up to 20% than established methods. In this way the forming and so the lightweight potential of sheet metal parts can by fully exploited. Moreover, the risk and locus of failure can be evaluated directly on the part geometry by a contour plot. An additional advantage of the GISSMO model is the applicability for low triaxialities as well as the possibility to predict the materials behavior beyond necking up to ductile fracture.<\/jats:p>","DOI":"10.3390\/ma14175106","type":"journal-article","created":{"date-parts":[[2021,9,6]],"date-time":"2021-09-06T21:47:38Z","timestamp":1630964858000},"page":"5106","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Generalized Stress State and Temperature Dependent Damage Indicator Framework for Ductile Failure Prediction in Heat-Assisted Forming Operations"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6333-4305","authenticated-orcid":false,"given":"Alan A.","family":"Camberg","sequence":"first","affiliation":[{"name":"Chair of Automotive Lightweight Design, Faculty of Mechanical Engineering, Paderborn University, Mersinweg 7, 33100 Paderborn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Tobias","family":"Erhart","sequence":"additional","affiliation":[{"name":"DYNAmore GmbH, Industriestra\u00dfe 2, 70565 Stuttgart, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Thomas","family":"Tr\u00f6ster","sequence":"additional","affiliation":[{"name":"Chair of Automotive Lightweight Design, Faculty of Mechanical Engineering, Paderborn University, Mersinweg 7, 33100 Paderborn, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2021,9,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Serrenho, A.C., Norman, J.B., and Allwood, J.M. (2017). The impact of reducing car weight on global emissions: The future fleet in Great Britain. Philos. Trans. Ser. A Math. Phys. Eng. Sci., 375.","DOI":"10.1098\/rsta.2016.0364"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"2103","DOI":"10.1016\/j.jmatprotec.2010.07.019","article-title":"A review on hot stamping","volume":"210","author":"Karbasian","year":"2010","journal-title":"J. Mater. Process. Technol."},{"key":"ref_3","first-page":"55","article-title":"A review on forming techniques for manufacturing lightweight complex\u2014shaped aluminium panel components","volume":"1","author":"Zheng","year":"2018","journal-title":"Int. J. Lightweight Mater. Manuf."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1016\/j.cirp.2017.05.007","article-title":"Hot stamping of ultra-high strength steel parts","volume":"66","author":"Mori","year":"2017","journal-title":"CIRP Ann."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1016\/j.cirp.2019.05.007","article-title":"Models and modelling for process limits in metal forming","volume":"68","author":"Volk","year":"2019","journal-title":"CIRP Ann."},{"key":"ref_6","unstructured":"Nakazima, K., Kikuma, T., and Hasuka, K. (2021, August 29). Study on the Formability of Steel Sheets. Yawata Technical Report. Available online: https:\/\/www.researchgate.net\/publication\/284669125_Study_on_the_formability_of_steel_sheets."},{"key":"ref_7","unstructured":"International Organization for Standardization (2021). ISO 12004-2:2021 Metallic Materials\u2014Determination of Forming-Limit Curves for Sheet and Strip\u2014Part 2: Determination of Forming-Limit Curves in the Laboratory, International Organization for Standardization."},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Banabic, D., Kami, A., Comsa, D.S., and Eyckens, P. (2019). Developments of the Marciniak-Kuczynski model for sheet metal formability: A review. J. Mater. Process. Technol., 116446.","DOI":"10.1016\/j.jmatprotec.2019.116446"},{"key":"ref_9","first-page":"577","article-title":"Stability of plastic shells under tension with kinematic boundary condition","volume":"17","author":"Marciniak","year":"1965","journal-title":"Arch. Mech. Stosow."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"452","DOI":"10.1016\/j.jmatprotec.2006.03.233","article-title":"Investigation of the thermo-mechanical properties of hot stamping steels","volume":"177","author":"Merklein","year":"2006","journal-title":"J. Mater. Process. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"841","DOI":"10.1016\/j.ijplas.2006.10.005","article-title":"Forming of AA5182-O and AA5754-O at elevated temperatures using coupled thermo-mechanical finite element models","volume":"23","author":"Abedrabbo","year":"2007","journal-title":"Int. J. Plast."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"265","DOI":"10.1016\/j.cirp.2008.03.049","article-title":"Testing formability in the hot stamping of HSS","volume":"57","author":"Bariani","year":"2008","journal-title":"CIRP Ann."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"251","DOI":"10.1016\/j.cirp.2013.03.050","article-title":"Hot stamping of AA5083 aluminium alloy sheets","volume":"62","author":"Bariani","year":"2013","journal-title":"CIRP Ann."},{"key":"ref_14","unstructured":"Hora, P. (2014, January 15\u201316). Failure Prediction in direct press hardening through virtual forming limit curves based on measurable material properties. Proceedings of the 7th Forming Technology Forum, Enschede, The Nederlands."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"4267","DOI":"10.1007\/s11665-015-1740-6","article-title":"Characterization of Tensile Properties, Limiting Strains, and Deep Drawing Behavior of AA5754-H22 Sheet at Elevated Temperature","volume":"24","author":"Panicker","year":"2015","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"5155","DOI":"10.1007\/s11665-017-2962-6","article-title":"Parameter Calibration of GTN Damage Model and Formability Analysis of 22MnB5 in Hot Forming Process","volume":"26","author":"Ying","year":"2017","journal-title":"J. Mater. Eng. Perform."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"361","DOI":"10.1007\/s12289-011-1057-4","article-title":"Enhanced material models for the process design of the temperature dependent forming behavior of metastable steels","volume":"5","author":"Krauer","year":"2012","journal-title":"Int. J. Mater. Form."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1016\/j.matdes.2015.04.009","article-title":"A method to evaluate the formability of high-strength steel in hot stamping","volume":"77","author":"Cui","year":"2015","journal-title":"Mater. Des."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"792","DOI":"10.1016\/j.ijmecsci.2017.07.043","article-title":"Forming limit prediction for hot stamping processes featuring non-isothermal and complex loading conditions","volume":"131\u2013132","author":"Gao","year":"2017","journal-title":"Int. J. Mech. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"012089","DOI":"10.1088\/1742-6596\/896\/1\/012089","article-title":"Forming limit prediction for AA7075 alloys under hot stamping conditions","volume":"896","author":"Gao","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1007\/s10704-016-0081-2","article-title":"An incremental stress state dependent damage model for ductile failure prediction","volume":"200","author":"Andrade","year":"2016","journal-title":"Int. J. Fract."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1115\/1.3225775","article-title":"A Continuous Damage Mechanics Model for Ductile Fracture","volume":"107","author":"Lemaitre","year":"1985","journal-title":"J. Eng. Mater. Technol."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"012081","DOI":"10.1088\/1742-6596\/896\/1\/012081","article-title":"Influence of Different Yield Loci on Failure Prediction with Damage Models","volume":"896","author":"Heibel","year":"2017","journal-title":"J. Phys. Conf. Ser."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"2066","DOI":"10.1016\/j.proeng.2017.10.1065","article-title":"Failure assessment in sheet metal forming using a phenomenological damage model and fracture criterion: Experiments, parameter identification and validation","volume":"207","author":"Heibel","year":"2017","journal-title":"Procedia Eng."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"15","DOI":"10.1007\/s12289-018-01461-4","article-title":"Damage and fracture during sheet-metal forming of alloy 718","volume":"13","author":"Schill","year":"2020","journal-title":"Int. J. Mater. Form."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"012057","DOI":"10.1088\/1757-899X\/651\/1\/012057","article-title":"Predicting plasticity and fracture of severe pre-strained EN AW-5182 by Yld2000 yield locus and Hosford-Coulomb fracture model in sheet forming applications","volume":"651","author":"Camberg","year":"2019","journal-title":"IOP Conf. Ser. Mater. Sci. Eng."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1177\/1056789513507731","article-title":"The development of continuum damage mechanics-based theories for predicting forming limit diagrams for hot stamping applications","volume":"23","author":"Lin","year":"2014","journal-title":"Int. J. Damage Mech."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"3437","DOI":"10.1007\/s00170-016-8853-4","article-title":"Application of a continuum damage mechanics (CDM)-based model for predicting formability of warm formed aluminium alloy","volume":"88","author":"Bai","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1016\/0013-7944(85)90052-9","article-title":"Fracture characteristics of three metals subjected to various strains, strain rates, temperatures and pressures","volume":"21","author":"Johnson","year":"1985","journal-title":"Eng. Fract. Mech."},{"key":"ref_30","unstructured":"Buyuk, M. (2013). Development of A Tabulated Thermo-Viscoplastic Material Model with Regularized Failure for Dynamic Ductile Failure Prediction of Structures under Impact Loading. [Ph.D. Thesis, The George Washington University]."},{"key":"ref_31","unstructured":"Haight, S.H. (2016). An Anisotropic and Asymmetric Material Model for Simulation of Metals Under Dynamic Loading. [Ph.D. Thesis, George Mason University]."},{"key":"ref_32","unstructured":"Sengoz, K. (2017). Development of A Generalized Isotropic Yield Surface for Pressure Insensitive Metal Plasticity Considering Yield Strength Differential Effect in Tension, Compression and Shear Stress States. [Ph.D. Thesis, The George Washington University]."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1016\/j.ijplas.2014.01.003","article-title":"Effect of strain rate on ductile fracture initiation in advanced high strength steel sheets: Experiments and modeling","volume":"56","author":"Roth","year":"2014","journal-title":"Int. J. Plast."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.mechmat.2017.07.020","article-title":"Stress-state and strain-rate dependent ductile fracture of dual and complex phase steel","volume":"116","author":"Erice","year":"2018","journal-title":"Mech. Mater."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"256","DOI":"10.1016\/j.ijimpeng.2019.05.008","article-title":"Dynamic perforation of ultra-hard high-strength armor steel: Impact experiments and modeling","volume":"131","author":"Fras","year":"2019","journal-title":"Int. J. Impact Eng."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"314","DOI":"10.1016\/j.ijplas.2005.03.005","article-title":"Forming of aluminum alloys at elevated temperatures\u2014Part 1: Material characterization","volume":"22","author":"Abedrabbo","year":"2006","journal-title":"Int. J. Plast."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"51","DOI":"10.1016\/0749-6419(89)90019-3","article-title":"Plastic behavior and stretchability of sheet metals. Part I: A yield function for orthotropic sheets under plane stress conditions","volume":"5","author":"Barlat","year":"1989","journal-title":"Int. J. Plast."},{"key":"ref_38","unstructured":"Lee, Y.W. (2005). Fracture Prediction in Metal Sheets. [Ph.D. Thesis, Massachusetts Institute of Technology]."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"01033","DOI":"10.1051\/epjconf\/20159401033","article-title":"Effect of strain rate on shear properties and fracture characteristics of DP600 and AA5182-O sheet metal alloys","volume":"94","author":"Rahmaan","year":"2015","journal-title":"EPJ Web Conf."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"117066","DOI":"10.1016\/j.jmatprotec.2021.117066","article-title":"Friction characterization and application to warm forming of a high strength 7000-series aluminum sheet","volume":"293","author":"Noder","year":"2021","journal-title":"J. Mater. Process. Technol."}],"container-title":["Materials"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/17\/5106\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T06:57:17Z","timestamp":1760165837000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1996-1944\/14\/17\/5106"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2021,9,6]]},"references-count":40,"journal-issue":{"issue":"17","published-online":{"date-parts":[[2021,9]]}},"alternative-id":["ma14175106"],"URL":"https:\/\/doi.org\/10.3390\/ma14175106","relation":{},"ISSN":["1996-1944"],"issn-type":[{"value":"1996-1944","type":"electronic"}],"subject":[],"published":{"date-parts":[[2021,9,6]]}}}