The “free-corner effect” in thermally loaded laminates

For a multilayered anisotropic laminate subjected to non-uniform temperature loads, the intense and localized interlaminar stresses in the vicinity of a free edge may be significantly affected by the temperature gradient in the thickness direction. An efficient and reliable analysis method is presented, based on polynomial expansions of the Lekhnitskii stresses functions in the various layers and the principle of complementary energy. The variational method yields closed-form solutions of the interlaminar stresses in terms of eigenfunctions. Two types of non-uniform temperature fields, one depending only on the thickness coordinate and the other varying linearly in the normal direction of the free edge, are considered. A suitable combination of the respective solutions yields the local approximations of the free-edge interlaminar stresses in laminates under general non-uniform temperature loads. A temperature gradient normal to the free edge has a relatively small effect upon the interlaminar stresses.

In this study, the interlaminar stresses for a thick AS4-PEEK laminate [0/±45/90]2s for three different strain rates are computed and investigated using the finite element procedure developed with the finite element program generator (FEPG) of Beijing Fegensoft Corporation Limited. The three-dimensional distribution plots at different interfaces are given. According to the interlaminar stress results for three different strain rates, the effects of the strain rates on the interlaminar stresses at different interfaces are elucidated. The interlaminar shear stresses τzx at the interfaces increase along with an increase in strain rates, but when the strain rate reaches a certain extent, the effects of the strain rates on the interlaminar shear stresses are gradually weakened. The effects of the strain rates on the interlaminar shear stresses τzy at the interfaces are similar. Except for the interlaminar normal stresses at the interface +45%-45, their strain rate dependence effects are slight. As far as the different interfaces are concerned, the effects of the strain rates on the interlaminar stresses at the interface 0%90 are the weakest, and the effects on the interlaminar stresses at the interface +45%-45 are the strongest. Furthermore, the variation circumstances of the interlaminar stresses along the free edges are studied and the interlaminar stresses for two strain rates at this location are analyzed.

Considering the influence of bridge fibers, a representative volume element (RVE) with damaged regions of vanishing thickness is developed to study for estimation of laminates with transverse matrix cracks. For the open and closed cracks, the tensile force, the compressive force and the shear force are mainly studied by the stress-based variational approach with the pending partition loads at the statically indeterminate boundary, with considering not only three cases of the ideal transverse cracks, the smooth plane-surface open crack, the smooth plane-surface closed crack and the perfect meshing open crack, but also two cases of the non-ideal transverse cracks, the open cracks and closed cracks with the resistance resisting the relative sliding of crack surfaces. The expressions of the stress components in the RVE are obtained by means of assumption of the function of inter-laminar shear stresses. The governing equations are derived from the variational analysis based on the principle of minimum complementary energy. Both the effective mechanical properties and the distributions stresses of the damaged laminates with the ideal transverse cracks and those of the laminates with the non-ideal transverse cracks are estimated on the basis of the analysis of deformation on surface of the RVE.

Chapter 8 - Basic Equations and Solution Procedure

With the displacement field taken as the only fundamental unknown field in a mixed-boundary-value problem for linear elastostatics, the principle of minimum potential energy asserts that a potential energy functional, which is defined as the difference between the free energy of the body and the work done by the prescribed surface tractions and the body forces --- assumes a smaller value for the actual solution of the mixed problem than for any other kinematically admissible displacement field which satisfies the displacement boundary condition. This principle provides a weak or variational method for solving mixed boundary-value-problems of elastostatics. In particular, instead of solving the governing Navier form of the partial differential equations of equilibrium, one can search for a displacement field such that the first variation of the potential energy functional vanishes. A similar principle of minimum complementary energy, which is phrased in terms of statically admissible stress fields which satisfy the equilibrium equation and the traction boundary condition, is also discussed. The principles of minimum potential energy and minimum complementary energy can also be applied to derive specialized principles which are particularly well-suited to solving structural problems; in this context the celebrated theorems of Castigliano are discussed.

Prediction of energy release rate due to the growth of an interface crack by variational analysis

Accurate determination of coupling effects on free edge interlaminar stresses in piezoelectric laminated plates

Free-edge stress reduction through fiber volume fraction variation

Interfacial stresses in plated beams with cracks

A multilayer hybrid-stress finite element analysis of a through-thickness edge crack in A ± 45° laminate

A note on the contributions of Cotterill, Castigliano, Crotti and Engesser to an energy principle of structures

Edge and interlaminar stresses of glass-cloth-reinforced epoxy laminates under uniform axial extension at cryogenic temperatures

Multiscale investigation of micro-scale stresses at composite laminate free edge

Axisymmetric stress distribution in the single filament pull-out test

Local FEM Analysis of Composite Beams and Plates: Free-Edge effect and Incompatible Kinematics Coupling