A ductile fracture model considering stress state and Zener–Hollomon parameter for hot deformation of metallic materials

Xiaoqing Shang, Zhenshan Cui, M. W. Fu

Research output: Journal article publicationJournal articleAcademic researchpeer-review

43 Citations (Scopus)


To articulate the ductile fracture behavior and predict its occurrence in hot deformation of metallic materials, the initiation condition of ductile fracture in hot working was identified by experiments, and an extended model for analysis of ductile fracture in hot forming of materials was established and validated. Firstly, experiments were conducted for 316LN stainless steel at elevated temperatures and the dynamic recrystallization (DRX) affected ductility was determined. Via using the Zener–Hollomon (Z) parameter to represent the temperature and strain rate dependent DRX behavior, the relationship between fracture strain and Z parameter in different DRX conditions was examined and identified. In the deformation of the material with DRX, the fracture strain decreases with the increase of Z parameter. However, in the deformation without DRX, the ductile fracture behavior is independent of Z parameter. An extended fracture model for hot working of metallic materials was thus established by incorporating the Z parameter and the influence of DRX into a stress based fracture model. For the DRX involved deformation, the fracture strain was designated as a function of stress state, Z parameter and the percentage of DRX. As for the deformation without DRX, the fracture strain was considered to be only affected by stress state, including stress triaxiality, Lode parameter and the changeable cut-off stress triaxiality. Considering the effect of hot working conditions on the cut-off value, a formulation representing the temperature and strain rate affected cut-off stress triaxiality was also proposed. The model was then incorporated into finite element (FE) code and corroborated via tailor-designed validation experiments. Furthermore, to validate the applicability of the developed model in industrial production, a case study of hot forging of a pressure vessel head was employed. The tendency of fracture initiation in the process was analyzed via using the model and the design of hot working process can thus be optimized with the help of the developed model.

Original languageEnglish
Pages (from-to)800-812
Number of pages13
JournalInternational Journal of Mechanical Sciences
Publication statusPublished - Aug 2018


  • Extended ductile fracture model
  • Hot deformation
  • Stress state
  • Zener–Hollomon parameter

ASJC Scopus subject areas

  • Civil and Structural Engineering
  • Materials Science(all)
  • Condensed Matter Physics
  • Mechanics of Materials
  • Mechanical Engineering


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