A New Formulation for Multi-Scale Fatigue Crack Growth Analysis

Yongming Liu, Zizi Lu

Research output: Chapter in Book/Report/Conference proceedingChapter


A new formulation at the small time scale is proposed for multi-scale fatigue crack growth analysis in this study. The proposed model is fundamentally different from the traditionally used cycle-based approach and is based on the instantaneous crack growth kinetics at any arbitrary time point within a cycle. The key idea of the proposed small-scale model is to define the fatigue crack kinetics at any arbitrary time instant (dt) instead of the average crack growth during a complete cycle. The instantaneous crack growth rate is calculated using the geometric relationship between the crack tip opening displacement (CTOD) and the crack growth. Direct integration in the continuous time domain is used to calculate the crack length history under arbitrary random loadings. The stress ratio effect and near threshold crack growth are included in the proposed model. One advantage of the proposed model is that it can efficiently calculate the crack growth under variable amplitude loading without cycle counting. Another advantage is that the proposed model is it is suitable for multiple time scale simulation, while the classical fatigue analysis is limited to the time scale (e.g., the smallest time scale is one cycle). The reversed plastic zone concept and the crack closure concept are implemented into the proposed model for the fatigue crack growth prediction. Comparison of model predictions and experimental data indicates that the reversed plastic zone concept gives better results in terms of prediction accuracy. The proposed model is validated with extensive experimental data under constant and variable-amplitude loadings. Statistical error analysis indicates that the proposed small scale model gives a satisfactory result in the current investigation.

Original languageEnglish (US)
Title of host publicationFatigue of Materials
Subtitle of host publicationAdvances and Emergences in Understanding
Number of pages17
ISBN (Electronic)9781118013373
ISBN (Print)9780470943182
StatePublished - Nov 11 2010
Externally publishedYes


  • Crack closure
  • Fatigue crack growth
  • Multi-scale
  • Reverse plastic zone

ASJC Scopus subject areas

  • General Engineering
  • General Materials Science


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