Nonlinear Failure Analysis Of Composite Laminated Beams With Delamination

Laminated composite beam is one of the most basic structures of composite materials.However,due to the manufacturing process,delamination may be produced which will reduce the stiffness and strength of the delaminated beams.Therefore,the damage analysis of the laminated composite beams with delamination has a very important practical significance.Based on nonlinear theory of plates and shells,mechanics of composite materials,fracture mechanics and variational principle,this thesis analyzes the delamination growth of fiber-reinforced composite rectangle beam with through-width delamination subjected to an in-plane distributed compressive load.The delaminated beam is simply supported on its two sides.The main contents of this thesis are as follows:In this thesis,the nonlinear large deflection theory of composite laminated beams with delamination is established.The delaminated composite beam with through-width delamination is divided into four sub beams,each having an independent coordinate system.The constitutive relationships of fiber reinforced,laminated composite beam are derived based on theory of composite materials.The nonlinear relationship between the contact force and the deflections of sub-regions above and below the delamination is established by analyzing the force-deformation mechanism at the interfaces of the delamination.Based on the von-Karmen nonlinear theory,the non-linear geometric equations are deduced.Post-buckling of laminated composite beam with delamination is investigated.By taking a free body diagram,differential equation of equilibrium of each sub-beam is established.Governing equation in terms of slope function is derived by introducing the anti-penetrating contact effect identified before.Boundary conditions at the two ends and continuous conditions at the delamination fronts are set up.The anti-penetrating contact effect is identified and is incorporated into the two stages.The governing equation as well as the boundary and continuous conditions are non-dimensionalized and expanded with respect to a small perturbation parameter.The first,second and third-order perturbation equations are established and are solved using Galerkin method.Analytical solutions of the buckling load,the deflection mode and the post buckling equilibrium path of in-plane load--deflection amplitude are obtained by performing perturbation analysis.The beam experiences two failure stages-post-buckling process and delamination propagation process.With available solutions from post-buckling analysis,the energy release rate for delamination propagation is derived according to variational principle and expressed as the summation of the products of the shear force and the slope at the delamination fronts on postbuckling equilibrium path.Threshold loads for onset of the delamination propagation are calculated from Griffith fracture criterion.Matlab programs are developed in order to carry out parametric studies.The effects of delamination length and depth on critical buckling load and threshold load for delamination propagation are studied.The theoretical solutions are compared with the results obtained from ABAQUS finite element analysis.The results show that the two solutions are in good agreement with each other.It is found that the contact performance is mainly affected by the location and size of the delamination.Furthermore,the shorter the delamination is,the higher the critical compressive load is required to propagate it.