Cracks and re-entrant corners in functionally graded materials

Functionally graded materials (FGMs) are special composites in which the volume fractions of constituent materials vary gradually, giving continuously graded mechanical properties. The aim of this paper is the evaluation of the strength of structures composed by FGMs incorporating re-entrant corners – tending to the more common crack for vanishing corner angle. The end result is useful in engineering applications predicting the strength of the element corresponding to the unstable brittle crack propagation in such innovative materials. To show the general validity of the method, heterogeneous plates under tension and beam under bending containing re-entrant corners and by varying corner angle, depth and grading of the FGM are considered. Ad hoc performed numerical finite element simulations, by using the FRANC2D code, agree with the theoretical predictions.