Fundamental differences between plane strain bending and far-field plane strain tension in ductile plate failure

R. G. Andersen*, J. G. Londono, P.B. Woelke, K. L. Nielsen

*Corresponding author for this work

Research output: Contribution to journalJournal articleResearchpeer-review


The objective of this paper is to investigate the ductile fracture behavior of thin metal plates under nominally plane strain conditions, with an emphasis on the differences between far-field plane strain tension and plane strain bending. Recent experimental results show that the fracture strain obtained using far-field plane strain tension tests is significantly lower than that obtained under plane strain bending conditions. Investigating the source of these differences is of critical importance for multiple industries since it affects formability, crashworthiness and ductile failure of thin metal plates. The present work provides critical insights into this issue based on the results of a detailed numerical investigation of both tests to failure, using the micro-mechanics based Gurson material model. The numerical simulations reveal many similarities between plane strain bending and far-field plane strain tension until the onset of localization. In the far-field plane strain tension case, after Considère thinning, a through-thickness shear localization occurs, followed by a micro-crack formation in the center of the plate. This is accompanied by an increase of the stress triaxiality well above the nominal plane strain tension level (i.e.,  ∼ 0.57 for thin plates). In contrast, the absence of thinning in plane strain bending yields a stress triaxiality that equals nominal plane strain tension, which results in a significantly lower void growth rate (in reference to far-field plane strain tension). A surface instability (undulations) eventually forms on the tension side of the plate in plane strain bending, followed by multiple shear bands. The crack initiates inside the dominant shear band and propagates from the surface into the plate. These differences in the localization mechanisms and local stress states are responsible for the difference in the macroscopic fracture strain obtained under far-field plane strain tension and plane strain bending.
Original languageEnglish
Article number103960
JournalJournal of the Mechanics and Physics of Solids
Number of pages17
Publication statusPublished - 2020


  • Plane strain failure
  • Gurson model
  • Fracture strain

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