Strain energy release rate formulae for skin-stiffener debond modeled with plate elements

doi:10.1016/0013-7944(95)00088-7

Engineering Fracture Mechanics

Volume 54, Issue 2, May 1996, Pages 211-228

https://doi.org/10.1016/0013-7944(95)00088-7 Get rights and content

Abstract

An efficient method for predicting the strength of debonded composite skin-stiffener configurations is presented. This method, which is based on fracture mechanics, models the skin and stiffener with two-dimensional (2D) plate elements instead of three-dimensional (3D) solid elements. The skin and stiffener flange nodes are tied together by two modeling techniques. In one technique, the corresponding flange and skin nodes are required to have identical translational and rotational degrees-of-freedom. In the other technique, the corresponding flange and skin nodes are only required to have identical translational degrees-of-freedom. Strain energy release rate formulae are proposed for both modeling techniques. These formulae are used for skin-stiffener debond cases with and without cylindrical bending deformations. The cylindrical bending results are compared with plane-strain finite element results. Excellent agreement between the two sets of results is obtained when the second technique is used. Thus, from these limited studies, a preferable modeling technique for skin-stiffener debond analysis using plate elements is established.

References (20)

J.H. Starnes et al.
Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression
AIAA J.
(1985)
N.F. Knight et al.
Postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression
M.W. Hyer et al.
Stiffener/skin interaction in pressure-loaded composite panels
AIAA J.
(1990)
J.T.S. Wang et al.
Skin/stiffener interface stresses in composite stiffened panels
NASA CR 172261
(1984)
M.W. Hyer et al.
Calculation of stresses and forces between the skin and stiffener in composite panels
D. Cohen et al.
Influence of geometric nonlinearities on skin-stiffener interface stresses
T.K. O'Brien
Characterization of delamination onset and growth in a composite laminate
Damage in Composite Materials, ASTM STP
(1982)
A.S.D. Wang et al.
Initiation and growth of transverse cracks and edge delamination in composite laminates, Part 1: an energy method
J. Composite Mater.
(1980)
J.D. Whitcomb
Instability-related delamination growth of embedded and edge delaminations
NASA Technical Memorandum 100655
(1988)
J.D. Whitcomb et al.
Strain-energy release rate analysis of a laminate with a postbuckled delamination
NASA TM 89091
(1987)

There are more references available in the full text version of this article.

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Other authors through experimental and finite element (FE) method investigate the correlation of skin-stiffener delamination and debonding defect in buckling [15] and post-buckling behavior [5,16,17]. The fracture mechanics was also used to numerically model the debonded region and evaluate the strain energy release rate [18,19]. The semi-analytical solution is possible for buckling problems in panels with some kind of discontinuity.
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A computational framework is presented for the delamination propagation analysis in laminated composite strips that combines an extended high-order layerwise model and a spectral finite element with high-order spatial approximation in the plane of the structure. The extended layerwise laminate mechanics approximate the through-thickness fields using Hermite cubic splines, while the discontinuities in displacement induced by a delamination crack are treated as generalized damage degrees of freedom (DOFs). The layerwise mechanics are integrated into a novel spectral strip finite element, which involves integration points collocated with the nodes, thus providing accurate nodal predictions of the interlaminar stresses on the interface and ahead of the delamination crack tip. Strain energy release rate is predicted by adapting the VCCT method to rely exclusively on the damage DOFs. Finally, an iterative solution method is developed that takes advantage of the damaged DOFs to quickly predict the crack propagation without remeshing. The proposed numerical scheme is applied to mode I, II and mixed-mode delamination fracture problems and is validated vs. reference literature solutions, experimental results and standard 2D plane-strain FE models. The numerical results ultimately illustrate the capacity of the present method to provide accurate predictions with moderately coarse meshes and high computational speed.
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For example, some studies [10,16,18] adopted shell elements to model the composite panel, which ignored the inter-laminar damage between layers caused by stress in the third direction. Moreover, some works [17,20,21] did not consider the intra-laminar damage mechanism of stiffened panels. The work in this paper investigated the effects of debonding defects on the postbuckling responses and failure behaviors of composite stiffened panels subjected to uniaxial compression, which comprehensively considered various failure modes aforementioned.
Effects of stiffener debonding defects on postbuckling responses and failure behaviors of composite stiffened panels which have extensive applications in aerospace structures attract significantly increasing attention recently. Aiming to this problem, a series of nonlinear analyses comprehensively accounting for multiple failure modes including intra- and inter-laminar damage in composite laminates, adhesive layer damage between stiffeners and skin, as well as buckling and postbuckling responses were carried out via a numerical model. This numerical model is combined with a progressive damage model and a cohesive zone model, and has been validated to be effective for predicting the postbuckling and failure responses of composite stiffened panels. Seventeen computational cases with different parameters including debonding sizes and positions which can affect buckling and postbuckling responses were conducted. It follows that debonding defects can change postbuckling deformation modes of stiffened panels and their development paths, which induce different degrees of inflection and distortion in structures, and change failure behaviors as well as the failure process of composite laminates, and further weaken the ultimate failure strength of the whole composite stiffened panels.
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VCCT offers an efficient numerical solution procedure and does not have convergence difficulties and mesh refinement requirements that are associated with the use of cohesive zones. Studies have shown that when using a transverse shear deformable shell element, mixed-mode energy release rates can be calculated accurately with VCCT [33,34,26,35–38]. Furthermore, it was shown that VCCT could be successfully combined with the FNM to model crack growth [39], though the combination with shell elements was not demonstrated.
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^†: Present address: Materials Division, NASA Langley Research Center, Hampton, VA, U.S.A.

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Engineering Fracture Mechanics

Abstract

References (20)

Postbuckling behavior of selected flat stiffened graphite-epoxy panels loaded in compression

AIAA J.

Postbuckling behavior of selected curved stiffened graphite-epoxy panels loaded in axial compression

Stiffener/skin interaction in pressure-loaded composite panels

AIAA J.

Skin/stiffener interface stresses in composite stiffened panels

NASA CR 172261

Calculation of stresses and forces between the skin and stiffener in composite panels

Influence of geometric nonlinearities on skin-stiffener interface stresses

Characterization of delamination onset and growth in a composite laminate

Damage in Composite Materials, ASTM STP

Initiation and growth of transverse cracks and edge delamination in composite laminates, Part 1: an energy method

J. Composite Mater.

Instability-related delamination growth of embedded and edge delaminations

NASA Technical Memorandum 100655

Strain-energy release rate analysis of a laminate with a postbuckled delamination

NASA TM 89091

Cited by (56)

A semi-analytical model for shear buckling analysis of stiffened composite panel with debonding defect

An extended layerwise spectral finite element framework for delamination growth simulation in laminated composite strips

Effects of debonding defects on the postbuckling and failure behaviors of composite stiffened panel under uniaxial compression

Tailoring of AP-PLY composite laminates for improved performance in the presence of delaminations

Use of an enriched shell finite element to simulate delamination-migration in a composite laminate

Inter-laminar delamination analyses of Spar Wingskin Joints made with flat FRP composite laminates