Free-Edge Effects in Composite Laminates

Abstract

There are many technical applications in the field of lightweight construction as, for example, in aerospace engineering, where stress concentration phenomena play an important role in the design of layered structural elements (so-called laminates) consisting of plies of fiber reinforced plastics or other materials. A well known stress concentration problem rich in research tradition is the so-called free-edge effect. Mainly explained by the mismatch of the elastic material properties between two adjacent dissimilar laminate layers, the free-edge effect is characterized by the concentrated occurrence of three-dimensional and singular stress fields at the free edges in the interfaces between two layers of composite laminates. In the present contribution, a survey on relevant literature from more than three decades of scientific research on free-edge effects is given. The cited references date back to 1967 and deal with approximate closed-form analyses, as well as numerical investigations by the finite element method, the finite difference method, and several other numerical techniques. The progress in research on the stress singularities which arise is also reviewed, and references on experimental investigations are cited. Related problems are also briefly addressed. The paper closes with concluding remarks and an outlook on future investigations. In all, 292 references are included.

Extended Kantorovich method for coupled piezoelasticity solution of piezolaminated plates showing edge effects

“…These localized stresses are of major concern because they may result in premature interlaminar failure, and reduction or complete loss of actuation/sensing authority of the piezoelectric layers. The need for accurate analytical/semianalytical solutions based on three-dimensional piezoelasticity/elasticity for such stress fields in laminated structures has been felt for a long time, but has remained largely unsolved so far [1], understandably so because of the inherent complexities involved in the problem. Here, three-dimensional piezoelasticity solutions refer to those wherein the governing equations of three-dimensional piezoelasticity are used to solve for the distributions of the field variables along the thickness direction, in contrast to the two-dimensional theories, which make a priori assumptions on the through-thickness distributions of the field variables, and the governing equations are obtained in terms of the inplane directions only.…”

A variational model for free-edge interlaminar stress analysis in general symmetric and thin-ply composite laminates

“…Kassapoglou and Lagace [10,19] were the first who applied the variational approach for analyzing stress concentrations near free edges. The reader is referred to the recent publications [1,2,16,17] for a detailed review of the developments in variational approach for the free-edge [1,2] and matrix cracking [16,17] stress transfer problems.…”

“…[7], it is not possible to develop a software based on the current variational formulations. It simply means that the results obtained from the available variational models regarding the free-edge stress transfer [1,2,10,19] are approximate and thus, do not reproduce very refined finite element results. In addition, due to implementation of the minimum complementary energy principle, all of the developed stressbased variational models either for analyzing cracked laminates or free-edge stress fields are formulated for traction loading conditions.…”

“…Although the free-edge problem is known from the 1970s, no analytical solutions exist that simultaneously satisfy the 3D elasticity governing equations along with all the traction free boundary conditions and the interface continuity conditions, due to the inherent complexities involved in the problem. Therefore, most approaches have been developed based on quasi-3D models or reduced 2D plate models [1] applied to a long rectangular composite laminate in which zero gradients along the axial coordinate are assumed. A comprehensive literature review on the methods proposed for determining the free-edge stress fields has been presented in Refs [1,2].…”

“…Therefore, most approaches have been developed based on quasi-3D models or reduced 2D plate models [1] applied to a long rectangular composite laminate in which zero gradients along the axial coordinate are assumed. A comprehensive literature review on the methods proposed for determining the free-edge stress fields has been presented in Refs [1,2].…”