Modelling and experimental study of parallel cracks propagation in an orthotropic elastic material

Abstract

The analysis of parallel cracks in an elastic orthotropic material, representing a fibre reinforced elastic composite is important from practical point of view. Such a case takes place in many engineering problems, particularly in operation of aircrafts, where local parallel cracks in structural parts of airplane can appear. The most important is to investigate if the cracks are stable or become suddenly unstable under certain level of loading.The paper presents analytical, numerical and experimental studies of the parallel cracks propagation and interaction. Two cases of cracks configuration were considered: two equal cracks and two un-equal cracks. The mathematical model was elaborated for two parallel cracks with different lengths in Mode I of fracture. Following Muskhelishvili formalism the stress and displacement fields were determined in the vicinity of the crack tips and using Griffith–Irwin theory the interaction between cracks was studied.The numerical calculations done within Finite Element Analysis (FEA) allows for estimations of the GI and GII for different directions of cracks propagation. The important for kinks initiation is the value of GII, but the growth of the cracks depends mainly on GI in considered two cases of cracks arrangement.The tests were performed for the orthotropic polymer matrix composite material used for production of helicopter parts. The two cases of cracks configuration were experimentally examined, i.e. the equal and un-equal cracks. In order to assess the displacement and strain fields in the tested materials, the 3-D digital image correlation system ARAMIS was used. The system allows for displacement and strain measurement in all three directions, on the whole measured area of a specimen, particularly near edges of cracks. Comparison to analytical analysis and numerical calculations confirms correctness of the proposed models.