Beam Finite Element for Analyzing Free Edge Delaminations

Abstract

A method is proposed to obtain the strain energy release rate and the stresses ahead of the crack in a laminated composite plate due to free edge delamination under Mode I type loading situations. A shear deformable beam finite element with nodes offset to either the top or bottom side has been developed. The thermal effects originating from the curing process are included in the formulation of the problem. Two different methods are used to calculate the strain energy release rate. The first method uses the J-integral evaluated around a zero-area path surrounding the cracktip and the strain energy release rate is expressed in terms of the force and moment resultants in the elements surrounding the crack-tip. The second method is similar to the virtual crack closure method, and the strain energy release rate is expressed in terms of the forces transmitted by a rigid element placed at the crack-tip and the displacements of the nodes behind the crack-tip. The stresses ahead of the crack are obtained by using discrete spring elements in the uncracked portion of the beam. The results calculated are in good agreement with results obtained from other studies of the same problem. The advantage of the present method lies in its simplicity; in addition it requires less computational effort than the methods that use solid elements.

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