Analysis of Cracks in Heterogeneous Solids

  • G. P. Sendeckyj
Part of the Fracture Mechanics of Ceramics book series (FMOC, volume 1)


It is well known that the strength of inherently brittle solids (such as, ceramics and some high performance composites) is governed by the propagation of a crack from a critical defect. Prediction of strength for such materials depends upon understanding the interaction between cracks and the heterogeneous structure of the material. For example, Cherepanov1 using dimensional analysis showed that the strength of a particulate composite with weak interfaces is governed by
$$ \sigma \surd d/{K_1} = G\left( {{\mu _2}/{\mu _1},D/{K_1},{\upsilon _1},{\upsilon _2},q} \right) $$
Where µ, υ, D, K1 q, d and σ are the shear modulus, Poisson’s ratio, adhesion modulus of the interface between the reinforcement and the matrix, adhesion modulus of the matrix, volume fraction of reinforcement, reinforcement dimension, and strength, respectively. Furthermore, the subscripts 1 and 2 refer to the matrix and reinforcement respectively. Equation (1) shows that the strength increases as the characteristic dimension d of the reinforcement decreases, other things being equal. Experimental data on rubber containing 42% NaCl crystals by weight indicates that Eq. (1) is correct.1


Crack Front Interface Crack Plane Deformation Radial Crack Rigid Inclusion 


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Copyright information

© Plenum Press, New York 1974

Authors and Affiliations

  • G. P. Sendeckyj
    • 1
  1. 1.Advanced Composites Branch, Structures Division Air Force Flight Dynamics LaboratoryWright-Patterson Air Force BaseUSA

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