Issue #15 - June 10th, 2008
Software Suite for Durability, Damage Tolerance, Reliability & Life Prediction
Enhances FEA Solvers MSC Nastran*, ABAQUS, ANSYS, RADIOSS & LS-DYNA
* Best Performance and Verified Solutions with MSC Nastran
This Week's Feature Composite Example
Predicting Post-Buckling Response and
Ultimate Failure of Composite 2-Stringer Panels
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Predicting the failure load of composite panels with post-buckled regions is a complicated undertaking as it involves buckling and damage evolution (Figure 1). The difficulty is complicated further by the fact that the ultimate failure (structural collapse) is driven by localized failures produced by damage in fiber and matrix in the post-buckled area of the structure. Reliable assessment of these load limits requires the application of advanced computational simulation that integrates composite mechanics at the micro-scale of fiber and matrix with finite elements, buckling, damage tracking and fracture analysis. The technical approach must rely on physics-based composite failure criteria capable of detecting all types of damages including non-visible ones. If localized buckling takes place before damage, the buckling mode shape is superimposed on the structure's geometry. Inception of damage prior to buckling requires repeated buckling analysis with degraded stiffness to account for detected damage. This analysis capability, integrated in the GENOA Software, was applied successfully to a two-stiffener composite panel under shear loading. The test results were closely reproduced with the analysis simulation. Including post-buckling effect was instrumental to replicate the test, since otherwise we risk over-predicting the failure load. As shown next, this analytical approach can be very effective in guiding the design and in reducing the number of tests of post-buckled composite panels.
Problem Description
The two-stringer J-stiffened composite panel evaluated for durability with post-buckling consideration is presented in Figure 2. It was made of AS-4/3501-6 carbon/epoxy unidirectional fabric. The fabric consisted of a wide sheet of unidirectional tows of fibers based together with polyester thread to keep it from unraveling. Twelve plies of the skin were laid up to form a 1.83 mm (0.072 in.) thick quasi-isotropic [0,90,45,0,-45,90]s laminate. The "J" shaped stiffeners were constructed with the same lay-up except for the flanges that were only half the thickness of the basic laminate. The skin panel and the stiffeners were stitched together with Kevlar and fiberglass threads [1,2]. The experimental results were adopted from the literature [1].
The two-stringer J-stiffened composite panel evaluated for durability with post-buckling consideration is presented in Figure 2. It was made of AS-4/3501-6 carbon/epoxy unidirectional fabric. The fabric consisted of a wide sheet of unidirectional tows of fibers based together with polyester thread to keep it from unraveling. Twelve plies of the skin were laid up to form a 1.83 mm (0.072 in.) thick quasi-isotropic [0,90,45,0,-45,90]s laminate. The "J" shaped stiffeners were constructed with the same lay-up except for the flanges that were only half the thickness of the basic laminate. The skin panel and the stiffeners were stitched together with Kevlar and fiberglass threads [1,2]. The experimental results were adopted from the literature [1].
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Figure 2 - Geometry of Two-stiffener composite panel [1]
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The panel was modeled with Mindlin-Reissner thick shell elements and loaded in tension in the diagonal direction at one corner of the panel while fixing the opposite corner [2]. Details of the technical approach are provided next followed by discussion of results.
Technical Approach
Using a representative finite element model with appropriate stiffness and strength limits of the various materials, the software assesses the performance of composite panels with post-buckling consideration by:
- Determining the buckling mode shape of the panel (in this case skin buckling mode). Typically selects the buckling mode shape with the lowest eigenvalue.
- Initiating durability analysis through the sequential application of incremented static loading till structural fracture takes place. During the load stepping process, the software checks and tracks damage resulting from: fiber failure in tension or compression, matrix cracking (transverse tension/compression and in-plane shear), and delamination (normal tension and transverse and longitudinal out-of-plane shear). The analysis strategy is described here:
- GENOA's progressive Failure Analysis (PFA) module starts with the full-scale finite element model and reduces the material properties down to the micro-scale of fiber and matrix. With every load step material properties are updated, reflecting any changes resulting from damage or cracks due to the applied loading.
- If the applied load reaches the skin buckling load, the buckled shape is superimposed onto the panel. In this way the panel is placed into its bifurcated and stable lower energy state. In a physical test it would naturally move to this state.
- If material damage is detected prior to local buckling, the code updates the stiffness and repeats the buckling analysis with reduced stiffness to extract a new buckling load.
- When material and structural equilibrium states are reached, the load is incremented to the next level. With every additional load step, buckling analysis is repeated to update the mode shape. As the load increases, damage in the panel will initiate, grow and accumulate leading to ultimate panel failure, as shown next in the simulation results.
For the considered two-stiffener composite panel, experimental data indicated that local buckling of the skin occurred prior to reaching the ultimate load. Figure 3 shows the analytical results illustrating damage in the panel at initiation stage in the post-buckled region and damage progression when the ultimate load is reached. The software was used first to perform a linear bifurcation buckling analysis. The Buckling analysis showed that the initial buckling load is 8.275 kips (36.81 kN), which is very close to the experimental results [2]. As the load was incremented during the progressive failure analysis, the software superimposed the buckling mode shape on the structure's geometry when the applied load reached the buckling load of 8.275 kips. From that forward, the buckling analysis was repeated every time the load was increased followed by update in the structure's geometry to include the mode shape effect. Structural damage was detected at a load higher than the buckling load. The PFA process allows for localized failures to occur in the panel that ultimately results in panel collapse. Delamination due to relative rotation of the plies is shown in Figure 4.
(a) Damage Initiation (b) Damage Progression
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Figure 3 - Net damage due to progressive failure for composite two-stringer panel under diagonal tension. (Red indicates areas where failures have occurred) a) at initiation of post-buckled region and b) near ultimate load.
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(a) Delamination Initiation (b) Delamination Propagation
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Figure 4 - Delamination location with respect to individual plies due to progressive failure analysis for composite two-stringer panel under diagonal tension. (Red indicates delamination locations) a) at initiation of post-buckled region and b) near ultimate load.
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Load deflection results obtained from the simulation are compared to test and shown in Figure 5. The technical approach employed here yielded excellent agreement between the simulation and experimental results when progressive failure technique is used in a post-buckling analysis; i.e., when the panel is allowed to go into its lower energy buckled state prior to performing the progressive failure analysis. Figure5 also shows the diagonal deflection versus applied load obtained via simulating the progressive failure analysis without any buckling and post-buckling effects. The simulation results for the unbuckled panel clearly indicates that the ultimate load is over-predicted by about 35% and the stiffness by about 7.6% [2]. The results presented here demonstrate the effectiveness of the methodology integrated in GENOA. It can be reliably used to perform iterative designs prior to committing to a large test program. Testing can be done once satisfactory performance is derived from the software.
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Figure 5 - Comparison of experimental and analytical load deflection curves for composite two-stringer panel [2]
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References:
1. Yeh, H-Y and Chen, V., 1996. Experimental Study and Simple Failure Analysis of Stitched J-Stiffened Composite Shear Panels. Journal of Reinforced Plastics and Composites, Vol. 15, pp. 1070-1087. Click here to email us for the technical publication.
2. Minnetyan, L. and Huang, D., 2001. Progressive Fracture of Stitched Stiffened Composite Shear Panels in the Postbuckling Range. Journal of Reinforced Plastics and Composites, Vol. 20, pp. 1617-1632. Click here to email us for the technical publication.
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GENOA's Probabilistic Progressive Failure Analysis capability enables the prediction of structural reliability in presence of uncertainties in fabrication parameters, cure, material, geometry, and loading. First, perform low fidelity probabilistic analysis to identify influential random design variables. Second, reduce the list of variables to include critical ones and perform high fidelity simulation (e.g. Monte Carlo) to obtain a measure of reliability. As additional benefits, you will obtain a database of competing designs to improve the product performance and reduce the number of unnecessary tests. For more information on this feature and trying out GENOA through our demos, please contact 
