| dc.description.abstract | Laminated composites are susceptible to damage when subjected to lateral impact loading due to their very poor transverse properties. The damage caused due to low?velocity impact, such as tool drop and runway debris hit, is considered potentially dangerous mainly because the damage occurs inside the laminate and might be left undetected. Hence, such damage is called Barely Visible Impact Damage (BVID). The presence of damage inside the laminate significantly reduces its compressive strength. Therefore, prediction of damage due to low?velocity impact is a very important practical problem in aerospace engineering. This thesis is an effort in that direction.
Experimental observations show that the low?velocity impact problem can be treated as an equivalent quasi?static problem, as the deformation and failure mechanisms in both cases are equivalent. Experiments also indicate that membrane stresses generated due to large deformations play an important role in predicting low?velocity impact damage. A comprehensive literature survey on low?velocity impact damage reveals a concentrated effort on laminated composite plates and meagre information on laminated composite shell panels. Moreover, the effect of curvature and stiffeners on damage needs to be investigated. In the present work, a quasi?static nonlinear finite element analysis is used for predicting damage in plain and stiffened laminated composite plates and shell panels subjected to low?velocity impact.
The low?velocity impact is simulated through an isotropic spherical ball impactor. The equivalent quasi?static load is calculated using an energy?balance model. The contact stiffness and the contact force developed between the impactor and the target are calculated using Hertz contact law. The equivalent quasi?static load is distributed elliptically over a circular area of contact. The validity of the Hertzian assumption for thin laminates under flexure is verified by comparing the present results with experimental data.
Three types of laminated composite finite elements are used in the present work. A four?noded, doubly curved quadrilateral thin shell element with 48 degrees of freedom (d.o.f.), bounded by two meridians and two parallel circles, is used for modelling plate and shell panels. Two types of curved shell stiffening elements, namely the Parallel Circle Stiffener Element (PCSE) and the Meridional Stiffener Element (MSE), are used to model the stiffeners. These stiffener elements are obtained as degenerate cases from the shell element using a line?member assumption, thus ensuring compatibility with plate and shell structures. Each stiffener element has two nodes with eight degrees of freedom per node.
The full Green’s strain tensor is used in the strain–displacement relationships. The principle of minimum potential energy is used in the formulation. The tangent stiffness matrix is derived using the total Lagrangian approach. An incremental–iterative technique based on the standard Newton–Raphson method is used to solve the resulting nonlinear algebraic equations. The formulation and the computer code developed are checked for correctness by solving various problems on isotropic, orthotropic, and laminated composite plates and shell panels, straight and curved beams, and symmetrically and eccentrically stiffened plates and shell panels, for which solutions are available in the literature.
Through the nonlinear finite element analysis, the in?plane ply stresses at all the Gauss points are obtained. The in?plane damage is predicted using the Tsai–Wu quadratic failure criterion. The modes of failure, such as matrix cracking and fibre breakage, are identified using maximum stress criteria. Progressive failure analysis is carried out by suitably degrading the material properties at points where failure has occurred. The predicted in?plane damage is compared with experimental and numerical results available in the literature. Subsequently, the effect of curvature and stiffeners on in?plane damage is studied for laminated composite plates and cylindrical and spherical shell panels subjected to low?velocity impact.
To obtain the through?the?thickness interlaminar stresses, integration of the three?dimensional equations of equilibrium is employed. The deformed geometry is considered in the equation of equilibrium in the thickness direction. The derivatives of mid?plane strains and curvatures are obtained using the finite difference method. The methodology developed is verified by comparing the interlaminar stresses obtained from linear analysis with analytical results. Delamination at the laminate interfaces is predicted using an impact?induced delamination quadratic failure criterion. The predicted delamination is compared with experimental and numerical results available in the literature. Subsequently, the effect of curvature on delamination is studied for laminated composite plates and cylindrical and spherical shell panels subjected to low?velocity impact.
From the problems solved, the following conclusions are drawn:
(a) The major mode of damage is matrix cracking, and it occurs along the fibre direction of the ply.
(b) The damage pattern follows the through?the?thickness in?plane strain distribution.
(c) The effect of curvature is to increase the extent of damage. For identical geometry, material properties, and impact energy, spherical shell panels suffer more damage than cylindrical shell panels, which in turn suffer more damage than flat laminates.
(d) Delamination at an interface occurs along the fibre direction of the ply below it.
(e) The software developed using the methodology described in this thesis can be used effectively in the aerospace industry for predicting the extent of damage caused by low?velocity impact. | |
