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.

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 assumptions and a variational principle. The present article contains 136 references.

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In the second of a series of two papers, a refined closed-form analysis method for the calculation of interlaminar stress concentrations in the vicinity of rectangular wedges of thermally loaded composite laminates with arbitrary layup is presented. Based on adequate layerwise shape assumptions for the in-plane components of Cauchy’s stress tensor that automatically fulfill the conditions of traction free edges, the interlaminar stresses are derived from the three-dimensional equilibrium conditions in combination with the exact fulfillment of the given homogeneous boundary conditions of traction-free laminate facings and the requirement of continuity of the interlaminar stresses at the ply interfaces. The far field conditions of recovery of the stress results by classical laminate plate theory in the inner laminate regions with increasing distance from the laminate corner are accounted for. Free constants in the stress shape functions are determined by the minimization of the laminate’s complementary potential energy which can be accomplished in an iterative manner. The stress shape functions are assumed as simple exponential terms with respect to the in-plane coordinates, whereas polynomials are applied as thickness functions. The present analysis methodology is found to be in good agreement with finite-element computations and yields reasonably accurate results with little computational effort.

The Boundary Finite Element Method (BFEM), a novel semi-analytical boundary element procedure solely relying on standard finite element formulations, is employed for the investigation of the orders and modes of three-dimensional stress singularities which occur at notches and cracks in isotropic halfspaces as well as at free edges and free corners of layered plates. After a comprehensive literature review and a concise introduction to the standard three-dimensional BFEM formulation for the static analysis of general unbounded structures, we demonstrate the application of the BFEM for the computation of the orders and modes of two-dimensional and three-dimensional stress singularities for several classes of problems within the framework of linear elasticity. Special emphasis is placed upon the investigation of stress concentration phenomena as they occur at straight free edges and at free corners of arbitrary opening angles in composite laminates. In all cases, the BFEM computations agree excellently with available reference results. The required computational effort is found to be considerably lower compared to e.g. standard Finite Element Method (FEM) computations. In the case of free laminate corners, numerous new results on the occurring stress singularities are presented. It is found that free-corner problems generally seem to involve a more pronounced criticality than the corresponding free-edge situations.

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A refined and expanded closed-form analytic tool for the calculation of the stress field at free corners of thermally loaded cross-ply and angle-ply laminate structures is developed. Based on adequate approximations for the inplane stresses, the integrated equilibrium conditions yield a full-scale 3D stress field in the vicinity of a free corner. After adjusting the stress field to stress-free conditions at the free edges and facings and obeying conditions of continuity at the interfaces, the remaining free parameters in the stress representation are calculated by minimization of the complementary potential of the laminate. Comparison of the closed-form results with finite element computations shows a good agreement.Keywords Composite, Laminate, Free-edge effect, Free-corner effect, Stress localizations, Closed-form analysis IntroductionClassical laminate plate theory (CLPT) with its assumption of a layerwise plane state of stress in combination with Kirchhoff's kinematical assumptions is a widespread tool for the analysis of composite laminates. However, in real composite laminates, regions with 3D stress concentrations may be found where the stress predictions by CLPT need refinement. A well-known phenomenon of this class is the so-called free-edge effect, i.e. the occurrence of a fully 3D singular stress field in a relatively small boundary region at straight free edges of composite laminates under mechanical and/or thermal load. Depending on the stacking sequence of the laminate, the arising stresses may be either interlaminar normal stresses or interlaminar shear stresses or both, which decay with increasing distance from the free edge. In the inner regions of the laminate, the predictions of CLPT are then fully recovered. Interlaminar stresses in boundary regions may lead to premature failure of the laminate, e.g. by delamination. Basically, different elastic properties of the laminate plies give rise to these singular stress concentrations.Since the pioneering work of Pipes and Pagano, [1], the free-edge effect has been the topic of countless investigations. Numerical methods like FEM or finite difference (FD) analysis have been applied as well as several closed-form analytical approaches attempted, which of course can only provide an approximate insight, for an exact closed-form solution is unknown. Detailed surveys on the free-edge effect have been presented in e.g. [2][3][4][5].A related and advanced stress-concentration problem in the analysis of composite laminates can be found at free corners of layered structures. Here, the stress field is of a full 3D nature. As a first step it may be treated as a superposition of two free-edge effects, which combine to some kind of a ''free-corner effect''. Since numerical analyses of stress concentration problems in composite laminates are often tedious and involve much computational effort, the present work is devoted to an approximate closed-form analysis of the free-corner effect. We consider the case of a thermally loaded layered structure. Here, adequate app...

Like in the well-known free-edge effect situation, stress fields in the vicinity of free corners of layered plates exhibit a distinct three-dimensional and singular behavior and thus represent an important technical situation. Nevertheless, there are only few thorough investigations available concerning stress concentrations near free laminate corners. Since numerical analyses of stress concentration phenomena in composite laminates are computationally expensive, the present contribution is devoted to a simple closed-form higher-order theory approach for the calculation of displacements, strains, and stresses in the vicinity of a rectangular corner of a symmetric cross-ply laminate under thermal load. Appropriate representations for the displacement field in the manner of a single-layer theory with unknown inplane components and assumed trigonometric functions through the thickness yield closed-form expressions for the strains and stresses throughout the whole laminate. The inplane displacement functions are determined by equilibrium considerations in an integrated form with the solution of some resultant characteristic equations. Boundary conditions are fulfilled in an integral sense. The present approach can be applied easily, requires little computational effort and is in good conformity with comparative finite-element calculations and other closed-form analyses.