International Journal of Fracture

, Volume 216, Issue 2, pp 149–159 | Cite as

Shear–compression loaded interface crack between a rigid substrate and an FGM layer—frictional crack closure effects

  • A. DorogoyEmail author
Original Paper


A typical application of functionally graded materials (FGMs) is the coating of homogeneous or inhomogeneous substrates. This work investigates numerically an interfacial crack between an FGM coating and a rigid substrate that is subjected to shear–compression loading under the effect of friction. Two types of linearly graded coatings and one homogeneous coating exhibiting the same average Young’s modulus were examined. Two different numerical methods were applied for solving the singular receding contact problem: in-house finite difference software and a commercial finite element software. The effect of friction on the crack closure parameters such as tangential shifts and normal gaps of the crack face were studied with both methods and revealed an excellent agreement between the two. The effect of friction on the transition of the crack face from the slip to stick condition was studied as well. An extended J line formulation was used to extract the stress intensity factors (SIFs) for the crack tip for which the adjacent crack face experiences a large frictional contact. It was demonstrated that increasing the coefficient of friction causes a decrease in the tangential shifts and normal gaps until the whole crack face exhibits stick. The linear gradation in which the material is harder on the interface than on the top results in lower crack face displacement and SIFs.


FGM Crack closure Finite difference Finite elements Tangential shifts J line Stress intensity factor 



The assistance and support of Professor Daniel Rittel is greatly appreciated.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Mechanical EngineeringTechnion—Israel Institute of TechnologyHaifaIsrael

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