Microplane damage model for fatigue of quasibrittle materials: Sub-critical crack growth, lifetime and residual strength

Kedar Kirane, Zdeněk P. Bažant*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

24 Scopus citations


In contrast to metals and fine grained ceramics, fatigue in concrete and other quasibrittle materials occurs in a large fracture process zone that is not negligible compared to the structure size. This causes the fatigue to be combined with triaxial softening damage whose localization is governed by a finite material characteristic length. A realistic model applicable to both has apparently not yet been developed and is the goal of this paper. Microplane model M7, shown previously to capture well the nonlinear triaxial behavior of concrete under a great variety of loadings paths, is extended by incorporating a new law for hysteresis and fatigue degradation, which is formulated as a function of the length of the path of the inelastic volumetric strain in the strain space. The crack band model, whose band width represents a material characteristic length preventing spurious localization, is used to simulate propagation of the fatigue fracture process zone. Thus the fatigue crack with its wide and long process zone is simulated as a damage band of a finite width. For constant amplitude cycles, the model is shown to reproduce well, up to several thousands of cycles, the Paris law behavior with a high exponent previously identified for concrete and ceramics, but with a crack growth rate depending on the structure size. Good agreement with the crack growth histories and lifetimes previously measured on three-point bend beams of normal and high strength concretes is demonstrated. The calculated compliance evolution of the specimens also matches the previous experiments. The model can be applied to load cycles of varying amplitude, to residual strength under sudden overload and damage under nonproportional strain tensor variation. Application to size effect in fatigue is relegated to a follow-up paper, while a cycle-jump algorithm for extrapolation high-cycle fatigue with millions of cycles remains to be researched.

Original languageEnglish (US)
Pages (from-to)93-105
Number of pages13
JournalInternational Journal of Fatigue
StatePublished - Jan 2015


  • Fatigue
  • Microplane model
  • Paris law
  • Quasibrittle
  • Size effect

ASJC Scopus subject areas

  • Modeling and Simulation
  • Materials Science(all)
  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering

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