Applying the new experimental midpoint concept on strain energy density for fracture assessment of composite materials

Zahra Khaji, Mahdi Fakoor*, Hannaneh Manafi Farid, René Alderliesten

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

4 Citations (Scopus)
3 Downloads (Pure)


A mixed-mode I/II fracture criterion for predicting the fracture response of composite materials is proposed. This criterion is derived based on a comprehensive study and the consideration of the physics of fracture onset. The fracture phenomenon that causes the various damage mechanisms at the vicinity of the crack tip is examined. It is elucidated that the stress distribution at the crack tip ought to be defined using the reinforcement isotropic solid (RIS) stress state. This new criterion, which is called Improved Strain Energy Density with Mid-point (ISEDM), includes the effect of the fracture process zone (FPZ) and T-stress, which remarkably affect the mixed-mode fracture process, particularly, when mode II is dominant. Substituting the strain energy density in a pure mode I with the strain energy density in the midpoint of mixed-mode I/II is the creative idea employed in proposing this criterion. Because in pure mode I the effects of FPZ are minimal, change of fitting point on fracture limit curve (FLC) from KIc to midpoint critical stress intensity factors (CSIF's) makes it possible to consider the effects of FPZ more accurately. In the ISEDM criterion, fracture behavior depends on mechanical properties and CSIF's of the midpoint. Crack initiation angle is considered along minimum strain energy density and this angle is derived in the midpoint of mixed-mode I/II. RIS theory is used as an applicable theory for modeling orthotropic materials in this paper and causes valid and reliable fracture behavior to be extracted. In addition, changing fracture point from pure mode I to the mid-point of experimental data causes the effects of FPZ to be considered without estimating the toughening mechanisms in this zone, and the fracture behavior is extracted with higher accuracy. FLC's in comparison with available experimental data prove that the ISEDM criterion anticipates the fracture behavior of orthotropic materials well. Finding KIIc based on the analytical method is a valuable achievement. In this article, KIIc can be predicted with appropriate accuracy, only by CSIF's of mid-point and using ISEDM criterion.

Original languageEnglish
Article number103522
Number of pages13
JournalTheoretical and Applied Fracture Mechanics
Publication statusPublished - 2022

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project
Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Crack initiation angle
  • Midpoint of experimental data
  • Minimum strain energy density
  • Orthotropic materials


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