A three-dimensional crack tip element for energy release rate determination and delamination growth prediction

Date of Award


Degree Type


Degree Name

Doctor of Philosophy (PhD)


Mechanical and Aerospace Engineering


Barry D. Davidson


Crack tip, Delamination, Energy-release rate, Composites

Subject Categories

Mechanical Engineering


A plate theory-based three-dimensional crack-tip element approach is developed for energy release rate and delamination growth predictions in layered elastic structures containing an interfacial delamination. Firstly, the formulation of the three-dimensional crack tip element (3D CTE) is derived to obtain energy release rate and mode mix for a three-dimensional laminated structure. The approach is then applied to a wide variety of geometries, materials, lay-ups and loadings. When a classical singular field based mode decomposition procedure is used, the ERR components obtained by the CTE analysis are shown to have close correlation with the results of the classical three-dimensional finite element approach. However, compared with this latter approach, the CTE analysis is significantly simpler and requires orders of magnitude less development and execution time. Secondly, a variety of mode decomposition approaches, including singular field based and "non-singular field based," are adopted in the CTE analysis, and assessments of the delamination growth prediction capabilities of all these approaches are provided. It is demonstrated that an approach using the CTE and a non-classical mode decomposition procedure displays superior predictive capability to all other methods for a wide selection of continuous fiber reinforced polymeric composites, including both flat plates and complicated practical skin-stringer geometries. The poor delamination predictions obtained by the classical, singular field based approach are due to the relatively large near-tip damage zone in polymer matrix laminates, whereas the insensitivity to near-tip stress field of the non-singular field based approach enables it to have excellent predictive ability and close comparison with experimental results. Finally, the CTE and non-singular field based approach is adopted to predict delamination growth in a skin-stringer laminated structure under two different types of loadings, and excellent comparisons with experimental results are obtained. The computational efficiency and predictive accuracy of the CTE approach makes it a useful tool with wide potential applications in the design and analysis of laminated structures. The ease of incorporating different mode decomposition methods also makes it a very flexible methodology to meet the requirements for predicting delamination growth in future composite materials.


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