On propagation of shear crippling (kinkband) instability in a long imperfect laminated composite cylindrical shell under external pressure

Abstract

A fully nonlinear analysis for prediction of shear crippling (kinkband) type propagating instability in long thick laminated composite cylindrical shells is presented. The primary accomplishment of the present investigation is prediction of equilibrium paths, which are often unstable, in the presence of interlaminar shear deformation, and which usually deviate from the classical lamination theory (CLT)-based equilibrium paths, representing global or structural level stability. A nonlinear finite element methodology, based on a three-dimensional hypothesis, known as layerwise linear displacement distribution theory (LLDT) and the total Lagrangian formulation, is developed to predict the aforementioned instability behavior of long laminated thick cylindrical shell type structures and evaluate failure modes when radial/hydrostatic compressive loads are applied. The most important computational feature is the successful implementation of an incremental displacement control scheme beyond the limit point to compute the unstable postbuckling path. A long (plane strain) thick laminated composite [90/0/90] imperfect cylinder is investigated with the objective of analytically studying its premature compressive failure behavior. Thickness effect (i.e. interlaminar shear/normal deformation) is clearly responsible for causing the appearance of limit point on the postbuckling equilibrium path, thus lowering the load carrying capability of the long composite cylinder, and localizing the failure pattern, which is associated with spontaneous breaking of the periodicity of classical or modal buckling patterns. In analogy to the phase transition phenomena, Maxwell construction is employed to (a) correct the unphysical negative slope of the computed equilibrium paths encountered in the case of thicker cylinders modeled by the finite elements methods that fall to include micro-structural defects, such as fiber waviness or misalignments, and (b) to compute the propagating pressure responsible for interlaminar shear crippling or kinkband type propagating instability. This type of instability triggered by the combined effect of interlaminar shear/normal deformation and geometric imperfections, such as fiber misalignment, appears to be one of the dominant compressive failure modes for moderately thick and thick cylinders with radiusto-thickness ratio below the corresponding critical value. A three-dimensional theory, such as the LLDT, is essential for capturing the interlaminar shear crippling type propagating instability.