A STUDY OF QUASI-STATIC DELAMINATION IN SANDWICH STRUCTURES
Srinivasan Sridharan and Yupeng Li
Washington University in St. Louis, St. Louis, Missouri, 63130, USA
E-mail: ssrid@seas. wustl. edu
Delamination of sandwich columns is studied using a relatively simple cohesive layer model. The model is described in some detail and is incorporated as a user supplied element (UEL) in a finite element package. The model is shown to predict accurately the test results of delamination of a facing sheet of a sandwich member. The accuracy of the model is seen to be superior to a model previously proposed by the authors, which predicts an earlier termination of crack growth. The UEL model is applied to a sandwich column investigated by earlier investigators – a column that is relatively stout (ratio of length (L) to depth (d) ~ 7.3) and has stiff facing sheets (ratio of depth d to the thickness (h) of facings ~ 15). The model is able to capture the onset of delamination buckling, sudden delamination growth at nearly constant compression, stable delamination growth and reaching of a limit point of the load carrying capacity. A slender sandwich column with relatively thin facings (L/d ~ 15, d/h ~ 40) is next considered. It indicates that overall bending tends to inhibit delamination growth under quasistatic loading as it tends to keep the delaminated surfaces in contact.
An often encountered failure mode of sandwich structural components is the core facing debonding. Once such debonding occurs the integrity of the structure is compromised and a significant reduction in the stiffness and the load carrying capacity occurs. A sandwich member under compression is delamination-sensitive as the delaminated skin tends to buckle thus accentuating the risk of delamination growth.
Under quasi-static loading the extent of the growth of delamination depends upon the overall bending stiffness of sandwich beam as a whole as well as the bending stiffness of the delaminating facing sheet. As the structure bends in an overall sense, delamination tends to close notwithstanding the sense of bending and inhibit the growth of crack. The delamination growth may come to a standstill despite a continuing increase in the load carried. By the same token the delamination growth is inhibited in a sandwich column undergoing wrinkling – a mode of deformation composed of short waves. (The last point, however, is of academic interest only, as with the onset of wrinkling the total exhaustion of the load carrying capacity is not far.)
Previous experience (Sridharan, S., 2001 and El-Sayed, S. et al, 2002) has indicated that the delamination failure in sandwich members is principally in mode I (opening mode) with shear playing a negligibly small role. Thus the most significant parameter required for tracing the delamination growth is the critical value of strain energy release rate (SERR), viz. GIc. In order to trace the delamination growth without interference by the user, a cohesive layer model interposed between the facing and the core is employed. Authors have developed two types of the model (Li, Y. et al, 2005) which are used in conjunction with a widely used nonlinear finite element program (Abaqus, 2001):
(i) UMAT model: The cohesive layer is of finite thickness and represented by a layer of elements of a type available in a standard finite element package, but with user supplied material properties, hence called the UMAT model. The material property that is significant here is the relationship between incremental stress and incremental strain in the transverse direction.
(ii) UEL model: The cohesive layer has zero thickness initially and is represented by a set of user supplied elements. The user has to define the nodal forces and the current stiffness of the elements based on the relative displacement suffered by the element between its two separating surfaces.
M. Pandey et al. (eds), Advances in Engineering Structures, Mechanics & Construction, 615-626. © 2006 Springer. Printed in the Netherlands.
An effort is made to maintain utmost simplicity in the formulation of the model in either form. The paper also discusses briefly selection of the maximum cohesive stress of the material – which is crucial for capturing the crack initiation point precisely. It is seen, as in the case of laminated composites (Li, Y. et al, 2005) that the UMAT model ceases to be reliable as the crack advances and predicts a premature shutting down of crack growth.