Journal of Materials Science

, Volume 31, Issue 3, pp 749–755 | Cite as

Fracture toughness and crack morphology in indentation fracture of brittle materials

  • M. Tanaka


The relationship between the indentation fracture toughness, Kc, and the fractal dimension of the crack, D, has been examined on the indentation-fractured specimens of SiC and AIN ceramics, a soda-lime glass and a WC-8%Co hard metal. A theoretical analysis of the crack morphology based on a fractal geometry model was then made to correlate the fractal dimension of the crack, D, with the fracture toughness, KIC, in brittle materials. The fractal dimension of the indentation crack, D, was found to be in the range 1.024–1.145 in brittle materials in this study. The indentation fracture toughness, Kc, increased with increasing fractal dimension, D, of the crack in these materials. According to the present analysis, the fracture toughness, KIC, can be expressed as the following function of the fractal dimension of the crack, D, such that
$$In K_{IC} = {1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}\{ In[2\Gamma E/(1 - \nu ^2 )] - (D - 1)In r_L \}$$

Where Γ is the work done in creating a unit crack surface, E is Young's modulus, v is Poisson's ratio, and rL is rmin/rmax, the ratio of the lower limit, rmin, to the upper limit, rmax, of the scale length, r, between which the crack exhibits a fractal nature (rminrrmax). The experimental data (except for WC-8%Co hard metal) obtained in this study and by other investigators have been fitted to the above equation. The factors which affect the prediction of the value of KIC from the above equation have been discussed.


Fracture Toughness Fractal Dimension Crack Surface Brittle Material Fractal Geometry 
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Copyright information

© Chapman & Hall 1996

Authors and Affiliations

  • M. Tanaka
    • 1
  1. 1.Department of Mechanical Engineering, Mining CollegeAkita UniversityAkitaJapan

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