Lode parameter dependence and quasi-unilateral effects in continuum damage mechanics: Models and applications in metal forming

Celal Soyarslan, Helmut Richter, Swantje Bargmann

Research output: Chapter in Book/Report/Conference proceedingConference contributionAcademicpeer-review


This work concerns with two successive modifications of the Lemaitre's damage model to meet the requirements of formability prediction for today's modern steels. The first one is the quasiunilateral damage evolution which modifies the damage driving force by scaling the elastic energy release rate due to compressive principal stress components. The second one is the shear modification by which the damage rate is multiplied by a normalized maximum shear stress dependent factor. With the assumption of non-rotating principal axes of deformation, proportional strain paths and rigid plasticity, closed form expressions for the isochronous fracture surfaces are derived for each model variant and resulting surface plots at various spaces are compared. The findings show that the former modification not only remedies the pathological reflective symmetry of the fracture surface across the Π plane with vanishing stress triaxiality ratio, but also allows hindering fracture under uniaxial compression. The latter modification by adding a direct Lode parameter dependence to the damage evolution function allows prediction of premature fracture at generalized shear stress states, a condition observed for certain advanced high strength metallic sheets. Parameter calibration is realized for each model variant using the experimental data from the literature. It is shown that the fracture model with both the shear modification and the quasi-unilateral enhancement shows the best fitting quality. Finally, the models are implemented as user subroutines for ABAQUS/EXPLICIT and used in prediction of initiation and propagation of cracks for a series of deep-drawing punch tests. A good agreement with the outputs reported in the literature is observed in terms of the shear damage occurrence zones as well as corresponding punch force-displacement diagrams.

Original languageEnglish
Title of host publicationKey Engineering Materials
EditorsAldo Ofenheimer, Cecilia Poletti, Daniela Schalk-Kitting, Christof Sommitsch
PublisherTrans Tech Publications Ltd
Number of pages6
ISBN (Print)9783038354710
Publication statusPublished - 2015
Externally publishedYes
Event18th International ESAFORM Conference on Material Forming, ESAFORM 2015 - Graz, Austria
Duration: 15 Apr 201517 Apr 2015
Conference number: 18

Publication series

NameKey Engineering Materials
ISSN (Print)1013-9826
ISSN (Electronic)1662-9795


Conference18th International ESAFORM Conference on Material Forming, ESAFORM 2015
Abbreviated titleESAFORM 2015


  • Continuum damage mechanics
  • Ductile fracture
  • Lode parameter dependence
  • Metal forming
  • Quasi unilateral damage
  • n/a OA procedure


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