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.

Free-Edge Effects in Composite Laminates

Stress concentration phenomena in composite laminates are technically important situations. A well-known problem of this class is the free-edge effect in composite laminates or as a superordinated example the stress concentrations in the vicinity of free laminate corners (so-called free-corner effect). The present work is split into two parts. In the present contribution, after a short introduction to the given stress concentration problems in general we will survey relevant selected literature on the classical free-edge effect dating from 1967 until today. Beside accentuation on approximate closed-form analytic methods for the stress analysis in the free-edge effect situation, numerous references on numerical methods and investigations on the occurring stress singularities are also cited. In a subsequent paper we will present a simple closed-form method for the analysis of the stress fields in the vicinity of free laminate corners with arbitrary layup. The method is based on adequate stress shape assumpt...

Interlaminar Stress Concentrations in Layered Structures: Part I - A Selective Literature Survey on the Free-Edge Effect since 1967

Iterative free-edge stress analysis of composite laminates under extension, bending, twisting and thermal loadings

Free edge stresses in general composite laminates

Interlaminar hygrothermal stresses in laminated plates

An approximate method is presented to investigate the interlaminar stresses near the free edges of composite laminate plates that are subjected to a combined thermo-mechanical loading. The method is based upon admissible function representations of stresses which account for the effects of both the global mismatches and the local mismatches in two of the elastic properties, the Poisson's ratio and the coefficient of mutual influence. For this purpose, new thermo-mechanical mismatch terms are defined to reflect an effective deformation under the combined thermo-mechanical loading. Closed form solutions of all the stress components are sought by minimizing the complementary energy with respect to the unknown functions, in the stress representations, of the width coordinate. These unknown functions are determined by solving five ordinary differential equations along with a set of free edge boundary conditions, which allow complex as well as real roots for their exponential decaying rates. The resulting solutions satisfy the stress equilibrium and all of the boundary conditions exactly, but compatibility is met in a weak form. Numerical examples are given for several typical laminates, and are compared with previous results obtained by finite element and other approximate methods. It is found that the present approximate method yields interlaminar stress results in an efficient, fast and yet reliable way. It is also concluded that unlike some previous approximate methods, the current method is numerically robust and stable.

Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach

Direct interface engineering using dopant of hole transport layer for efficient inorganic perovskite solar cells

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Analysis of edge stresses in composite laminates under combined thermo-mechanical loading, using a complementary energy approach

Direct interface engineering using dopant of hole transport layer for efficient inorganic perovskite solar cells