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Fracture: Toughness

  1. Qingda Yang,
  2. James W. Giancaspro

Published Online: 20 JUL 2012

DOI: 10.1002/9781118097298.weoc097

Wiley Encyclopedia of Composites

Wiley Encyclopedia of Composites

How to Cite

Yang, Q. and Giancaspro, J. W. 2012. Fracture: Toughness. Wiley Encyclopedia of Composites. 1–12.

Author Information

  1. University of Miami, Coral Gables, FL

Publication History

  1. Published Online: 20 JUL 2012


This article begins by reviewing the analytical solutions that have been used to interpret fracture toughness from composite fracture testing using beam-like geometries. It has been demonstrated that the crack length corrections needed for estimation of mode I and mode II energy release rates (ERRs) cannot be used as simple additions to physical crack lengths for analytical specimen compliance calculations (which have been used in the literature). Improved analytical expressions for ERR, specimen compliance, and load versus load-point displacement relationships have been rederived for generally orthotropic double cantilever beam (DCB) (mode I), end-loaded split (ELS) and end-notched flexure (ENF) (mode II), and MMB (mixed-mode bending) specimens based on the framework of Andrews and Massabo 1. These new solutions account for the effects of transverse shear and crack-tip rotations and are accurate for both short and long beams within 2% as long as the length-to-thickness ratio of each subbeam is > 2λ1/4. The crack-tip rotation effects on an indeterminate single cantilever beam (SCB) specimen with varying mixed-mode ratio have also been investigated. This investigation was facilitated by establishing a solving procedure with explicit consideration of crack-tip rotations. It has been found that the crack-tip rotation not only changes the specimen compliance but also affects the distribution of end reaction forces and moments at the specimen boundaries. Consequently, these influence the crack-tip ERR and phase angle. Through direct comparisons with the benchmark results obtained using rigorous two-dimensional finite-element analysis, it has been shown that the analytical solutions can accurately capture the convoluted crack-tip rotation effects and can offer excellent predictions on the end reaction forces and moments, fracture loads, and crack-tip phase angles (as functions of crack length). However, if crack-tip rotations are not considered, the beam theory results can have significant error, especially for short beams with high degree of material orthotropy.


  • fracture;
  • fracture toughness;
  • composites;
  • root rotation;
  • fracture testing