An analytical expression for J2-integral of interfacial crack in orthotropic bimaterials

Laminated composite materials have found numerous engineering applications in marine, automotive, and aerospace industries. This can be attributed to their high specific strengths and stiffness. Layered dissimilar anisotropic materials have also been used in electronic devices such as, optical electronics, semiconductors, and micro-electro-mechanical systems. Unfortunately, researchers have found debonding and cracking to be the principal types of failure in these layered materials during manufacture and in service.

An interface crack in a bimaterial initiates opening and shearing features even for a single mode loading. Strain energy release rate per unit of the crack extension as well as stress intensity factors are fundamental parameters in forecasting brittle failure adopting linear elastic interfacial fracture mechanics. These parameters are dictated by crack geometrical properties and material characteristics.

Presently, the J1- integral, which is only applicable to straight cracks, has been adopted for industrial fracture analysis. This approach is less sensitive to the mesh dimensions of the crack tip as compared to the displacement method. However, it still requires stress analysis at internal points as well as refined contours around the crack front. In addition, in case of mixed mode problems, auxiliary equations are needed to decouple stress intensity factors. An alternative to this would be to evaluate the J2-integral for separating stress intensity factors.

Dr. Azam Tafreshi from the University of Manchester in England presented a new analytical expression that related J2-integral and the stress intensity factors in an in-plane traction-free crack between two orthotropic elastic solids implementing the complex function approach. By implementing the proposed analytical expression together with the values of J_{k ,} this allows for the computation of the corresponding stress intensity factors without an auxiliary relation. Her research work is published in the peer-reviewed journal, Fatigue & Fracture of Engineering Materials & Structures.

By implementing the complex function method, the author presented an analytical expression between J2-integral as well as the mixed mode stress intensity factors at the tip of an interface crack in debonded orthotropic elastic solids.

The computation of J1 has been found to be inadequate for computing stress intensity factors. Therefore, implementing the proposed analytical expression together with the values of J2 and J1 allowed for the corresponding stress intensity factors to be calculated without an auxiliary relation. In fact, given that the stress intensity factors already available, by implementing the proposed analytical expression, the author could obtain a precise value of J2.

These results can be helpful in forecasting the crack kink angle as well as the path of propagation of interface cracks in orthotropic bimaterials. The author also presented an example with known analytical solutions for stress intensity factors in order to identify the variation of J2-integral near the crack tip of a bimaterial orthotropic plate applying the available stress intensity factors. The author took into account various bimaterial combinations and demonstrated the effect of materials mismatch on J_k.