SIF statistics in micro cracked solid: Effect of crack density, orientation and clustering

The paper addresses the problem of stress intensity factors (SIFs) statistics in a randomly cracked solid. For this aim, the representative unit cell approach has been used. The geometry of a microcracked solid is modeled by a periodic structure with a unit cell containing a number of cracks sufficient to account for the micro structure statistics. The method developed recently by Kushch et al. [V.I. Kushch, I. Sevostianov, L. Mishnaevsky Jr., Stress concentration and effective stiffness of aligned fiber reinforced composite with anisotropic constituents. International Journal of Solids and Structures 45 (2008) 5103–5117] is applied to obtain the exact series solution for the local stress field and SIFs for each separate crack. The method combines the superposition principle, the technique of complex potentials and new results in the theory of special functions. An appropriate choice of potentials provides reduction of the boundary-value problem to a set of linear algebraic equations and thus high numerical efficiency of the method. A wide series of computational experiments has been performed and the statistically meaningful results have been obtained discovering the way and extent to which the SIF statistics is affected by the micro structure parameters, namely, the crack density, their angular scattering and cluster formation. It is found that SIF distribution follows the Gnedenko–Gumbel asymptotic rule. An analytical expression is suggested for the SIF statistics in a microcracked material and a simple meso mechanical model of the cluster of cracks is proposed.