Session: 05-06-01: Lightweight Sandwich Composites and Layered Structures

Paper Number: 120197

120197 - The Effect of Large Deflections on the Energy Release Rate and Mode Partitioning of Face/core Debonds in Sandwich Composites 

The effects of large deflections  on the energy release rate and mode partitioning of face/core debonds are investigated.  The study is done for the Single Cantilever Beam Sandwich Composite testing configuration, in which a shear force and/or bending moment are applied at the debonded face.  Up to now, studies in this topic have been done by employing geometrically linear theories (either Euler-Bernoulli or Timoshenko beam theory). This assumes that the deflection at the tip of the loaded debonded part is small, which is not always the case.  To address this effect, we employ the elastica theory, which is a nonlinear theory, for the debonded part.  An elastic foundation analysis and the linear Euler Bernoulli theory is employed for the   “joined” section  where a series of springs exists between the face and the substrate (core and bottom face).  Notice that the displacements in the latter part are still small and, therefore, the Euler-Bernoulli theory is used.  The continuity conditions at the common section are used to formulate the problem. This includes the slope continuity at the beginning of the elastic foundation, the moment and shear force equality at the beginning of the elastic foundation and the conditions of zero moment and shear at the unloaded right edge of the beam.  The special case of only applied moment is treated separately, as the elastica equations are different in this case resulting in a fully closed form solution.  Subsequently, a closed form expression for the energy release rate is derived by use of the J-integral. Another closed form expression for the energy release rate is derived from the energy released by the differential spring as the debond propagates. Furthermore, a mode partitioning angle is defined based on the displacement field solution from the elastic foundation approach.  The formulation results in two non-linear algebraic equations in terms of the rotations of the debonded face at the loaded end and at the tip of the debond (where the elastic foundation begins).  The results from this semi-closed form analysis are compared with the corresponding ones from a finite element analysis for a wide range of loadings and face and core materials as well as debond lengths.  The J-integral and FEA results for the energy release rate are mostly within two percent of each other, i.e., very close. Moreover, the results from the J-integral are practically coincident with the ones based on the energy released by the “breaking” of a differential spring at the elastic foundation.   For the mode partitioning, the results are within three degrees of the mode mixity results from finite elements. Thus, the results from this semi-closed form formulation are in very good agreement  with the corresponding ones from the finite element analysis. The results show that large deflection effects reduce the energy release rate but do not have a noteworthy effect on the mode partitioning. A small deflection assumption can significantly overestimate the energy release rate for relatively large applied loads and/or relatively long debonds.

Acknowledgments. The financial support of the Office of Naval Research, Grant N00014-20-1-2605, and the interest and encouragement  of the Grant Monitors, Dr. Jessica Dibelka, Dr. Paul Hess and Dr. Y.D.S. Rajapakse,  are both gratefully acknowledged.

Presenting Author: George Kardomateas Georgia Tech

Presenting Author Biography: Professor of Aerospace Engineering

Authors:

George Kardomateas Georgia Tech
Daniel Okegbu Georgia Institute of Technology