Application of Reddy's third-order theory to delaminated orthotropic composite plates

Abstract

In this work the third-order shear deformation theory by Reddy is applied and modified to analyze delaminated orthotropic composite plates . The delaminated plate portion is captured by Reddy's traditional theory, while a novel double-plate system is developed for the undelaminated part. It is shown that in the uncracked part four conditions are required to satisfy in symmetrically delaminated plates. The conditions involve the imposition of traction-free boundaries and the interface constraints. These four conditions enable the reduction of the parameters from nine to five in the displacement field. The governing equations show significant coupling among the stress resultants of the uncracked portion, that has to be considered in the continuity conditions between the delaminated and undelaminated parts. To demonstrate the application of the present model a simply-supported delaminated plate subjected to a concentrated force is analyzed. The distribution of the mode-II and mode-III energy release rates and their ratio are calculated using the 3-dimensional J -integral. The finite element model of the plate is also created using brick-type elements. The comparison of the analytical and finite element results shows very good agreement. It is shown that the deformations around the delamination front can be captured by the third-order plate theory with high accuracy. • We derive the governing equations of modified Reddy's theory. • The displacement field is based on the interface constraints. • The delamination causes sudden changes in the strains and stresses. • Third-order plate theory is required to capture the crack tip deformations.