Mode-3 spontaneous crack propagation in symmetric functionally graded materials

Mode-3 spontaneous crack propagation along functionally graded bimaterial interfaces

“…(14) o AE ¼ 1=ð2kL AE g Þ, and it is important to note that for the trivial homogeneous bimaterial system with L AE g ¼ 1, the convolution kernel derived by Breitenfeld and Geubelle (1998) is obtained. The convolution kernel derived here is a well behaved non-singular function, similar to the other spectral forms derived for various materials (Geubelle and Rice, 1995;Morrissey and Geubelle, 1997;Breitenfeld and Geubelle, 1998;Geubelle and Breitenfeld, 1997;Hwang and Geubelle, 2000;Kulkarni et al, 2007;Pal et al, 2007). The convolution kernel is even with respect to the inhomogeneity length scale L AE g and is depicted for three values of the same in Fig.…”

“…(16) to compute the displacements. In comparison with the formulation by Kulkarni et al (2007) and Pal et al (2007) the present spectral formulation is more generic as it can handle the inhomogeneities of two half-spaces independently. The present method, however, is computationally more intensive as two convolution integrals corresponding to the upper and lower half-spaces need to be evaluated separately.…”

“…The inhomogeneity length scale L g can be in the order of a few microns (as the case of thermal barrier coatings and layered solids) or in the order of several metres as in tectonic plates. Unlike in the previous FGM formulations by Kulkarni et al (2007) and Pal et al (2007), the inhomogeneity length scales are allowed to vary independently in either of the two halfspaces. The trivial case of a homogeneous material is obtained by assuming L AE g ¼ AE1.…”

Impact Energy of Functionally Graded Steels in Crack Arrester Configuration

“…Functionally graded materials (FGMs) are multi-phase systems in which composition varies gradually in some directions to obtain unique mechanical, thermal, and electrical properties that distinguish them from the conventional composites which in general are of discrete, piecewise nature with sharp interfaces (Ref [1][2][3][4]. To date very few fracture experiments involving FGMs, particularly on dynamic fracture, have been reported.…”

An equilibrium penny-shaped crack in an inhomogeneous elastic medium

“…19 The effect of a change in the properties of a material on the specific features of the development of a transverse shear crack as a function of the spatial variables was investigated numerically in Ref. 20. The eigenvalue scheme, which is used to investigate homogeneous materials, has been modified with the aim of taking account of the change in the properties of a material in a direction which is symmetrical about the plane of the crack.…”