International Journal of Fracture

, Volume 181, Issue 2, pp 241–255 | Cite as

Spacing and failure mechanism of edge fracture in two-layered materials

  • Chunyan Bao
  • C. A. Tang
  • Ming Cai
  • Shibin Tang
Original Paper


The phenomenon of edge fractures is analyzed using a fracturing process approach. Such fractures often initiated from the free surface of layered materials, and often terminate at the interface that divides the fractured layer and the matrix layer, or continue to expand along the interface, or create a peel-crack. To understand better the pattern of fractures with different spacing and the fracture mechanism, a double-layer elastic model with the same material properties with a fractured overlying layer subjected to uniaxial tension is simulated firstly. The stress distribution between two adjacent fractures is periodically distributed as a function of the ratio of the fracture spacing to the thickness of the fractured layer (S/t ratio), and homogeneous and heterogeneous material properties are considered in the simulation. The simulation results show that both the stress distribution and the critical value of fracture spacing to layer thickness ratio are affected by material heterogeneity; the S/t ratio of heterogeneous material is much smaller and it is much easier to crack compared with the homogeneous materials. In particular, the fracture saturation mechanism is analyzed by stress state change. Then a numerical simulation is carried out to reveal the fracturing process from micro-fracture formation, propagation, coalescence, nucleation, fracture infilling, fracture saturation, termination, to interface delamination. A fitting curve of the relationship between strain and spacing to layer thickness radio is obtained. It is found that infilling fractures may grow near the bottom or the free surface of the fractured layer by coalescence of micro-fractures and flaws. We also find that fracture spacing in the case of interface delamination is greater than that without interface delamination. A study of stress transition between the two layers on fracture spacing in the fracture process is also carried out, with a focus on stress transfer mode.


Edge fracture Heterogeneity  Progressive fracture Numerical modeling  Layered materials 



This research in this paper was supported by the CNSF (National Natural Science Foundation of China) under contract numbers 50820125405 and 51121005, the 973 Program under contract number 2011CB013503, and the CNSF under contract number 51004020. We appreciate the valuable comments and suggestions provided by two external reviewers.


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Copyright information

© Springer Science+Business Media Dordrecht 2013

Authors and Affiliations

  • Chunyan Bao
    • 1
  • C. A. Tang
    • 1
  • Ming Cai
    • 2
  • Shibin Tang
    • 1
  1. 1.State Key Laboratory of Coastal and Offshore EngineeringDalian University of TechnologyDalianChina
  2. 2.Bharti School of EngineeringLaurentian UniversitySudburyCanada

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