An analysis of interlaminar stresses in unsymmetrically laminated plates

Abstract

The results of a numerical study of interlaminar stresses within unsymmetrically laminated plates is presented. The focus of the study is upon the linear thermoelastic response of thin square laminated composite plates subjected to extensional, compressive, or thermal loading. Symmetric and unsymmetric 0/90, +45/-45, and 0/+45 laminate stacking sequences are examined to determine the effects of mismatch between adjacent layers in Poisson’s ratio, coefficient of mutual influence, and coefficients of thermal expansion. Since the out-of-plane (transverse) deflections of unsymmetric laminates are typically large, a geometrically nonlinear kinematic description is used to account for the large displacements and rotations. The geometrically nonlinear three-dimensional boundary value problems are formulated from nonlinear elasticity theory and approximate solutions are determined using the finite element method. A total Lagrangian, displacement-based, incremental finite element formulation is implemented using Newton’s method. Geometrically nonlinear global/local finite element analysis is used to obtain improved free edge stress predictions.

For laminates subjected to external loading, the mismatch in material properties between adjacent layers causes interlaminar stresses to arise near the free edges. For unsymmetric laminates under external loading, the mismatch in material properties about the geometric midplane causes out-of-plane deflections. For the laminates and loading conditions considered, the results of this study show that the out-of- plane deflections of unsymmetric laminates reduce interlaminar shear stresses. In addition, the out-of-plane deflections reduce interlaminar normal stresses for some laminates and increase these stresses for others. For the two-layer unsymmetric laminates considered, the effect of out-of-plane deflections upon interlaminar normal stress was shown to be dependent upon the type of in-plane strain mismatch (i.e., normal and/or shear) caused by the dissimilar material properties. The results also show that as the out-of-plane deflections become large, the effects of geometric nonlinearity upon this stress-deformational response become important. These conclusions apply to extensional, compressive (prior to a change in mode shape), and thermal loading. The numerical results include interlaminar stresses for laminated plates which have buckled as a wide column under compressive loading.