Localization and shear-crippling (kinkband) instability in a thick imperfect laminated composite ring under hydrostatic pressure

Abstract

A fully nonlinear finite elements analysis for prediction of localization representing shear-crippling (kinkband) instability in a thick laminated composite (plane strain) ring (infinitely long cylindrical shell) under applied hydrostatic pressure is presented. The primary accomplishment of the present investigation is prediction of meso(lamina)-structure-related equilibrium paths, which are often unstable in the presence of local imperfections and/or material nonlinearity, and which are considered to “bifurcate” from the primary equilibrium paths, representing periodic buckling patterns pertaining to global or structural level stability of the thick cross-ply ring with modal or harmonic imperfection. The present nonlinear finite elements solution methodology, based on the total Lagrangian formulation, employs a quasi-three-dimensional hypothesis, known as layerwise linear displacement distribution theory (LLDT) to capture the three-dimensional interlaminar (especially, shear) deformation behavior, associated with the localized interlaminar shear-crippling failure. A thick laminated composite [90/0/90] imperfect (plane strain) ring is investigated with the objective of analytically studying its premature compressive failure behavior. Numerical results suggest that interlaminar shear/normal deformation (especially, the former) is primarily responsible for the appearance of a limit (maximum pressure) point on the post-buckling equilibrium path associated with a periodic (modal or harmonic) buckling pattern, for which a modal imperfection serves as a perturbation. Localization of the buckling pattern results from “bifurcation” at or near this limit point, and can be viewed as a symmetry breaking phenomenon. In order to investigate a localization of the buckling pattern, a local or dimple shaped imperfection superimposed on a fixed modal one is selected. With the increase of local imperfection amplitude, the limit load (hydrostatic pressure) decreases, and also the limit point appears at an increased normalized deflection. Additionally, the load–deflection curves tend to flatten (near-zero slope) to an undetermined lowest pressure level, signaling the onset of “phase transition” in the localized region, and coexistence of two “phases”, i.e., a highly localized band of shear crippled (kinked) phase and its unshear-crippled (unkinked) counterpart along the circumference of the ring. Interlaminar shear-crippling triggered by the combined effect of imperfection, material nonlinearity and interlaminar shear/normal deformation appears to be the dominant compressive failure mode. A three-dimensional or quasi-three-dimensional theory, such as the afore-mentioned LLDT is essential in order to capture the meso-structure-related instability failure such as localization of the interlaminar shear crippling, triggered by the combined presence of local imperfection and material nonlinearity.