Interlaminar Stresses in Symmetric Angle-Ply Laminates Subjected to Anticlastic Bending Deformation

By Johnathan Goodsell

Purdue University


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The aim of the present work is to develop a solution for the interlaminar stress field in a symmetric and balanced,  angle-ply laminate subjected to anticlastic bending deformation.  Further, this class of problems is considered in order to elucidate the behavior of angle-ply laminates consisting of large numbers of layers.  The solution is compared to finite-element solutions of the same boundary value problem, (as well as the cases of pure bending and cylindrical bending bending).  This study will extend the past work with extensional and thermal loading to include the effect of anticlastic bending.  This solution requires specific moment resultant inter-relations in order to satisfy the assumptions of the two earlier solutions for axial extension and thermal expansion, namely C45 = sy = sz = 0.  While these assumptions may appear restrictive, this requirement is far outweighed by the enhanced capability to study a major class of angle-ply laminates consisting of a large number of lamina in an accurate model (The effect of these assumptions on the solution will be investigated by finite element solutions of three problems where the assumptions are violated: the first where C45 ≠ 0 and the second and third where sy ≠ 0: pure bending and cylindrical bending).  As anticipated, the free-edge interlaminar stresses are significant in the angle-ply laminate subjected to bending curvature.  The boundary-layer nature of the interlaminar stresses can be demonstrated, as well as the singular nature of the interlaminar stress at material points where dissimilar ply interfaces intersect the free-edge.  The solution will be exercised to characterize the boundary layer dimensions of a symmetric and balanced angle ply laminate subjected to anticlastic bending deformation.  Finally, comparisons will be drawn between the anticlastic bending curvature solution and the solutions for uniform axial extension and uniform temperature change.


R. B. Pipes and N. J. Pagano, "Interlaminar Stresses in Composite Laminates - An Approximate Elasticity Solution," Journal of Applied Mechanics, vol. 41, pp. 668-672, 1974. R. B. Pipes, J. Goodsell, A. J. Ritchey, J. Dustin and J. Gosse, "Interlaminar Stresses in Composite Laminates: Thermoelastic Deformation," Composites Science and Technology, vol. 70, pp. 1605-1611, 2010.

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  • Johnathan Goodsell (2014), "Interlaminar Stresses in Symmetric Angle-Ply Laminates Subjected to Anticlastic Bending Deformation,"

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