On a Possible Approximation of Changes in Elastic Properties of a Transversely Isotropic Material due to an Arbitrarily Oriented Crack

The present paper addresses an approximate analytical model for contribution of an arbitrarily oriented circular crack into effective elastic compliance of a transversely isotropic material. We numerically examine the bounds of applicability of the hypothesis that change in elastic potential due to an arbitrarily oriented circular crack in a transversely-isotropic material can be approximated by the change calculated for a certain isotropic environment. In particular, we obtained that the error of such an approximation is less than 20% if the extent of anisotropy is moderate – the ratio of Young’s moduli in transverse and in-plane directions is less than 1.87. The obtained result can be used for development of a simple model for microcracked transversely-isotropic materials with mild-to-moderate extent of anisotropy.     

Interaction of a penny-shaped crack with an elliptic crack under shear loading

The problem of interaction between equal coplanar elliptic cracks embedded in a homogeneous isotropic elastic medium and subjected to shear loading was solved analytically by Saha et al. (1999) International Journal of Solids and Structures 36, 619–637, using an integral equation method. In the present study the same integral equation method has been used to solve the title problem. Analytical expression for the two tangential crack opening displacement potentials have been obtained as series in terms of the crack separation parameter _i up to the order _i⁵,(i=1,2) for both the elliptic as well as penny-shaped crack. Expressions for modes II and III stress intensity factors have been given for both the cracks. The present solution may be treated as benchmark to solutions of similar problems obtained by various numerical methods developed recently. The analytical results may be used to obtain solutions for interaction between macro elliptic crack and micro penny-shaped crack or vice-versa when the cracks are subjected to shear loading and are not too close. Numerical results of the stress-intensity magnification factor has been illustrated graphically for different aspect ratios, crack sizes, crack separations, Poisson ratios and loading angles. Also the present results have been compared with the existing results of Kachanov and Laures (1989) International Journal of Fracture 41, 289–313, for equal penny-shaped cracks and illustrations have been given also for the special case of interaction between unequal penny-shaped cracks subjected to uniform shear loading.     

Quantitative evaluation of the fatigue limit of a metal with an arbitrary crack under a stress controlled condition – Stress Ratio R=−1

The static crack problem of a functionally graded coating-substrate structure with an internal or edge crack perpendicular to the interface is investigated under an in-plane load. The structure is made up of a functionally graded coating with an internal or edge crack and a homogeneous substrate of finite thickness. The material properties are assumed to vary continuously from the coating to the substrate. By use of Fourier transform method, the mixed boundary value problem is reduced to a singular integral equation which can be solved numerically. During the analysis, a higher-order term is obtained in the asymptotic analysis of the singular kernel to improve the convergence efficiency of numerical integrals. The influences of material constants and the geometry parameters on the stress intensity factors (SIFs) are studied. In Part II of this paper, the transient response of the structure subjected to an in-plane impact is investigated.