Estimating fracture toughness of C–S–H using nanoindentation and the extended finite element method

  • Eslam M. Soliman
  • Sherif H. Aboubakr
  • Mahmoud M. Reda TahaEmail author


In this paper, an approach to integrating nanoindentation testing and finite element simulations is introduced to compute the fracture toughness of cementitious materials. Calcium silicate hydrate (C–S–H) was synthesized using the standard procedure of mixing calcium oxide (CaO) and silicate (SiO2) at a mixture ratio of 1.5. C–S–H powder was filtered, dried to a relative humidity of 11%, and then compacted at 400 MPa. Nanoindentation tests incorporating dwell time were performed on polished C–S–H specimens using a Berkovich indenter tip. The reduced elastic moduli of the C–S–H specimens were extracted from the nanoindentation measurements. Viscoelastic and viscoelastic-plastic finite element models with creep and cracking capabilities were developed to simulate the nanoindentation tests and to extract the fracture energy. The viscoelastic-plastic model utilized the extended finite element method (XFEM) to describe cracking and evaluate the cracking surface of C–S–H. The analysis showed that the proposed approach could fairly predict the fracture energy release rate and thus fracture toughness of C–S–H. The calculated fracture toughness was in agreement with the fracture toughness values reported in the literature.


C–S–H Nanoindentation Fracture toughness XFEM Creep Viscoelasticity 



The experimental work performed herein was supported by the National Science Foundation (NSF) Award #1131369. The authors acknowledge this financial support. Additional support to the authors by the University of New Mexico, USA and Assiut University, Egypt to conduct the computational work presented herein is greatly appreciated. Special thanks to Ms. Elisa Borowski for her detailed editorial review of the manuscript.


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Copyright information

© Indian Institute of Technology Madras 2017

Authors and Affiliations

  1. 1.Department of Civil EngineeringAssiut UniversityAssiutEgypt
  2. 2.Department of Civil EngineeringUniversity of New MexicoAlbuquerqueUSA

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