3D modeling of subsurface fatigue crack nucleation potency of primary inclusions in heat treated and shot peened martensitic gear steels

Rajesh Prasannavenkatesan, Jixi Zhang, David L. McDowell*, Gregory B. Olson, Herng Jeng Jou

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

85 Scopus citations


A computational strategy is developed to characterize the driving force for fatigue crack nucleation at subsurface primary inclusions in carburized and shot peened C61® martensitic gear steels. Experimental investigation revealed minimum fatigue strength to be controlled by subsurface fatigue crack nucleation at inclusion clusters under cyclic bending. An algorithm is presented to simulate residual stress distribution induced through the shot peening process following carburization and tempering. A methodology is developed to analyze potency of fatigue crack nucleation at subsurface inclusions. Rate-independent 3D finite element analyses are performed to evaluate plastic deformation during processing and service. The specimen is subjected to reversed bending stress cycles with R = 0.05, representative of loading on a gear tooth. The matrix is modeled as an elastic-plastic material with pure nonlinear kinematic hardening. The inclusions are modeled as isotropic, linear elastic. Idealized inclusion geometries (ellipsoidal) are considered to study the fatigue crack nucleation potency at various subsurface depths. Three distinct types of second-phase particles (perfectly bonded, partially debonded, and cracked) are analyzed. Parametric studies quantify the effects of inclusion size, orientation and clustering on subsurface crack nucleation in the high cycle fatigue (HCF) or very high cycle fatigue (VHCF) regimes. The nonlocal average values of maximum plastic shear strain amplitude and Fatemi-Socie (FS) parameter calculated in the proximity of the inclusions are considered as the primary driving force parameters for fatigue crack nucleation and microstructurally small crack growth. The simulations indicate a strong propensity for crack nucleation at subsurface depths in agreement with experiments in which fatigue cracks nucleated at inclusion clusters, still in the compressive residual stress field. It is observed that the gradient from the surface of residual stress distribution, bending stress, and carburized material properties play a pivotal role in fatigue crack nucleation and small crack growth at subsurface primary inclusions. The fatigue potency of inclusion clusters is greatly increased by prior interfacial damage during processing.

Original languageEnglish (US)
Pages (from-to)1176-1189
Number of pages14
JournalInternational Journal of Fatigue
Issue number7
StatePublished - Jul 2009


  • 3D finite element analysis
  • Fatigue crack nucleation
  • Inclusions
  • Residual stress
  • Shot peening
  • Subsurface cracking

ASJC Scopus subject areas

  • Modeling and Simulation
  • General Materials Science
  • Mechanics of Materials
  • Mechanical Engineering
  • Industrial and Manufacturing Engineering


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