SYMPOSIA PAPER Published: 01 January 2001

A Method for Calculating Strain Energy Release Rates in Preliminary Design of Composite Skin/Stringer Debonding Under Multiaxial Loading


Three simple procedures were developed to determine strain energy release rates, G, in composite skin/stringer specimens for various combinations of uniaxial and biaxial (in-plane/out-of-plane) loading conditions. These procedures may be used for parametric design studies in such a way that only a few finite-element computations will be necessary for a study of many load combinations. The results were compared with mixed-mode strain energy release rates calculated directly from nonlinear two-dimensional plane-strain finite-element analyses using the virtual crack closure technique. The first procedure involved solving three unknown parameters needed to determine the energy release rates. Good agreement was obtained when the external loads were used in the expression derived. This superposition technique, however, is applicable only if the structure exhibits a linear load/deflection behavior. Consequently, a second modified technique was derived which was applicable in the case of nonlinear load/deformation behavior. The technique, however, involved calculating six unknown parameters from a set of six simultaneous linear equations with data from six nonlinear analyses to determine the energy release rates. This procedure was not time efficient, and hence, less appealing.

Finally, a third procedure was developed to calculate mixed-mode energy release rates as a function of delamination lengths. This procedure required only one nonlinear finite-element analysis of the specimen with a single delamination length to obtain a reference solution for the energy release rates and the scale factors. The delamination was subsequently extended in three separate linear models of the local area in the vicinity of the delamination subjected to unit loads to obtain the distribution of G with delamination lengths. This set of subproblems was solved using linear finite-element analyses, which resulted in a considerable reduction in CPU time compared to a series of nonlinear analyses. Although additional modeling effort is required to create the local submodel, this superposition technique is very efficient for large parametric studies, which may occur during preliminary design where multiple load combinations must be considered.

Author Information

Krueger, R
NASA Langley Research Center, Hampton, VA
Minguet, PJ
Structures Technology Research & Development Group, Philadelphia, PA
O'Brien, TK
NASA Langley Research Center, Hampton, VA
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Developed by Committee: D30
Pages: 105–128
DOI: 10.1520/STP14506S
ISBN-EB: 978-0-8031-5449-0
ISBN-13: 978-0-8031-2862-0