The Strain Energy Release Rate of Composite Microcracking: A Variational Approach

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Abstract
A variational analysis approach has been used to determine the two- dimensional thermoelastic stress state in cross-ply laminates of type [0 m /90 n ] s and [90 m / 0 n ] s . The stress analysis was used to calculate the energy release rate due to formation of a new microcrack. The analysis accurately includes the effect of residual thermal stresses. When compared with experiments, the new energy release rate expressions are found to predict typical data using a single value for the critical energy release rate for microcrack ing. This critical energy release rate has a physical interpretation as a microcracking fracture toughness or as an intralaminar fracture toughness. We also used the variational solution to get an analytical expression for the longitudinal expansion coefficient of the microcracked cross-ply laminate as a function of microcrack density. Finally, variational theorems are used to show that this new microcracking fracture analysis is rigorously more accurate than previous attempts at the same problem.