Polar shear-lag analysis of a composite of concentric cylinders with longitudinal cracks: Application to internal checking in wood

Composites of concentric cylinders can fail by microcracks that span the thickness and length of one cylinder but arrest at the boundary to adjacent cylinders. This failure mode was analysed by developing a new polar shear-lag analysis for stresses in a cross-section of a concentric-cylinder composite. The analysis can accurately calculate stresses in each cylinder in the presence of microcracks. These stresses were used to calculate the energy release rate for formation of a new microcrack as a tool for predicting the microcracking process due to any source of applied or residual stresses. The target problem was to model internal checking in certain species of trees. In a tree, the alternating regions of early- and late-wood that form the growth rings are the concentric cylinders. Internal checking is microcracking in the early-wood layers. The shear-lag analysis was used to predict the propensity of growth rings to form internal checks.