A combined analytical and experimental study is conducted to investigate the strength and failure behavior in the vicinity of holes on mechanically fastened joints of finite composite laminates which exhibit nonlinearly elastic behavior. The effects of fastener stiffness, frictional contact force between the fastener and the composite laminates, geometrical nonlinearities due to concentrated fastener load around the hole edge for the snug and clearance fit are also considered.
The major focus of the study is to predict failure strength and failure mode of joints subjected to in-plane loading utilizing an accurate contact stress analysis with the Coulomb friction based on a linear complementarity problem (LCP) formulation in an incremental form. The basis of the LCP formulation is the complementarities existing between pairs of variables, that is, contact pressure and gap, slackness in the friction equation and slippage, and constraint force and rigid body displacement.
The nonlinear analysis is composed of a combination of the updated Lagrangian formulation using the 2nd Piola-Kirchhoff stress and the Green-Lagrange strain of the frictional contact problem and the nonlinear failure criterion with the consideration of material nonlinearity in each ply. A new nonlinear parameter is introduced representing a nonlinear relation between shear stress and shear strain in a lamina. The failure strengths and failure modes are predicted based on the nonlinear failure criterion that is introduced as a combination of Yamada-Sun and Sandhu criterion along the characteristic curve for each lamina. A cost- effective nonlinear finite element code for failure analysis is developed including Lemke's complementary pivoting algorithm for solving the LCP.
Data from the existing literature and experimental results for carbon fibre reinforced plastics obtained from this study are used to validate the proposed analysis method. The detailed contact behavior and failure predictions are in good agreement with the published data and experimental results, and have shown significantly improved accuracy especially for the angle-ply and cross-ply laminates.
As an application of the proposed method, three examples are presented. The first is a clearance fit joint problem that is an example of nonlinearly expanding contact under monotonically increasing loads. The ratio of fastener to hole diameter is generally found to be a significant parameter in determining the failure strengths and failure modes. Both predictions and experimental results show that snug fit joints usually provide conditions for maximum failure strength and failure angle, and these are decreased slightly with increased clearance but the trends for the various laminates are quite different. In the case of an elliptic hole with a small eccentricity, which is frequently encountered in practice, the failure strength reduction is more serious when the long axis of the elliptic hole is perpendicular to the loading direction.
The second example is to study the effects of contact surface conditions between fastener and the hole. Three types of joint conditions are examined in terms of friction coefficients, that is, well-lubricated, normal dry friction and rough surface. The proposed method predicts the failure behavior very well for the well-lubricated and normal dry friction condition. However for the rough contact surfaces, there are some discrepancies. A new formulation which considers asperities may be necessary in this case.
The third example is to investigate the effects of stacking sequence and clamping force on the failure behavior for the quasi-isotropic laminated plates. Various laminates with three kinds of stacking sequences are tested and analyzed. It is found that the joint strengths depend on stacking sequence, and that the proposed method can predict joint strengths exactly by using the characteristic lengths which correspond to each specimen. This procedure can be considered as a first order approximation method of the three dimensional approach, which is left as a future topic.
