This Week's Feature Composite Example

Durability & Reliability Enhancement of Assembled Composite Structures by use of Parametric Robust Design (PRD) Concept

Figure 1 - FEM of the panel-panel Joint Figure 2 - Test configuration

Parametric Robust Design (PRD) module is put to use to maximize durability and reliability of a complex assembled ceramic matrix composite (CMC) structure subjected to concentrated loads. PRD optimizes the geometry of the structure subject to prescribed constraints for the purpose of improving the durability. For the given structure, the ultimate load is increased by 6.5% after optimization. Additionally, the optimized structure exhibited higher reliability as the probability of failure is reduced from 0.08 (before optimization) to 0.02 (after optimization). Details of the technical approach and summary of results are discussed next.

Background: 

The durability and reliability of complex composite structures is affected by joint tolerances such as hole size and fitup, manufacturing discrepancies, environmental factors (temperature), fatigue (vibration), and loads due to assembly mismatch. Material properties as well as manufacturing scatter, such as voids, add to the complexity of evaluating assembled structures. The need exists to apply a comprehensive methodology to assess these effects on the structure's performance and assess its reliability without resorting to test every time. A computational approach integrating probabilistic methods with composite mechanics and finite element based Progressive Failure Analysis (PFA) is in order to assess durability and reliability of these complex structures. The approach applies parametric modeling and analysis to suggest competing designs to improve overall performance. This concept is demonstrated on a panel-to-panel joint structure made from ceramic matrix composites (CMC) [Ref 1-2].
The material candidate considered is carbon fiber reinforced silicon carbide (C/SiC) due to the stability of its properties through large temperature variations.

PRD is applied to X-37 joined components involving panel-to-panel configuration shown in Figure 1. The top row of bolts connects the two L-shaped plates made of 3D CMC laminate material with the two back-to-back vertical plates made of 2D CMC laminate material. The bottom row of bolts connects the back-to-back plates made of 2D laminate material. Fiber glass composite is used to support the specimen. Figure 2 shows the test configuration.

Progressive Failure Analysis of Existing Design:

PFA Results showed that damage initiates as interlaminar shear failure at the corner of the L-shaped angles (Figure 3). Then it propagates through the vertical and horizontal plates of the 2D laminates. Figure 4 shows damage initiation and propagation to failure.

 

Figure 3 - Damage initiation at lower L-shape corner

 

Figure 4 - Animation of Damage from initiation to fracture Simulation predicted failure load is 71,511 N compared to 79,178 N from test [Ref 1] (Failure modes are combined in-plane and interlamina shear)

Parametric Robust Design:

To improve the durability and damage tolerance of the assembled joint structure, the L-shape panels and corners were optimized by use of Parametric Robust Design capability in the GENOA software. This feature is founded on automatic update of geometric FEA model parameters. It also includes optional material properties and ply-manufacturing details parameters. A large number of designs can be generated in a very short time once the high and low bounds for each design variable are identified. This tool reduces the number of real designs by use of virtual simulation. It simply provides alternate designs that can enhance the part's performance. 

For the present case, four design variables were chosen from initial deterministic results (Figure 5):

• 2D Flange radius: flange_radius
   

• 2D Flange thickness: flange_t
   

• 3D Flange radius: top_flange_radius
   

• 3D Flange thickness: top_flange_t

In addition, other variables representing material and fabrication uncertainties were integrated for more realistic performance:

• 2D & 3D Flange Fiber content: FVR
   

• 2D & 3D Flange Void content: VVR
   

• 2D & 3D Flange Fiber orientation: Angle
   

• 2D & 3D Flange Matrix shear strength: SmS
   

• 2D & 3D Flange Fiber shear modulus: Gf12 and Gf23

Technically, many more variables could be considered. Attention has to be paid to optimization constraints and dimensions of the part, volume, weight and eventually computer resources. The results of the parametric robust design analysis are shown in Table 1.

With marginal increase in weight and volume, the ultimate load is improved by 6.5%. Figure 6 shows a bar chart of the load applied load versus the material damage volume percent for the initial and optimized models. With optimization, the structure became more damage tolerant as it sustained more damage before fracture.
 

Reliability evaluation of the optimized joint was undertaken to determine the effect of the new design on the probability of failure. Random variables pertaining to geometry, fabrication parameters, and material properties were considered. Sensitivity analysis results are presented in Figure 7 showing the relative effect of random variables on the joint failure load. It ranks the random variables by order of importance. As noted in the same figure, the void content (VVR) in the 2D panels is the most influential parameter. Information from the sensitivity analysis can be used as a guide to reduce testing for design certification by eliminating variables from the test matrix that show no effect on desired response.

 

Figure 7 - Probabilistic Sensitivities of geometric, material and fabrication random variables

With prescribed uncertainties and distributions of the random variable, probabilistic analysis was performed before and after optimization. The cumulative probability is plotted before and after optimization in Figure 8. It is evident that a structure with enhanced durability subjected to the same uncertainties is bound to exhibit increased reliability. For example, if the design load is 60,000 N, the reliability before optimization is 0.92 (probability of failure of 0.08). After optimization, for the same design load, the reliability is 0.98. More information on the study can be found in reference 3.

Figure 8 - Cumulative probability for joint failure load

References: 

1. F. Abdi, X. Sue, J. Housner, "Durability Evaluation of NASA's X-37 2D/3D C/SiC CMC Assembled Sub-Elements". SAMPE Conference Paper, May 2008. Click here to email us for the technical publication.

2. F. Abdi, T. Castillo, D. Huang, V. Chen, A. Del Mundo "Virtual Testing of the X-37 Space Vehicle". SAMPE Conference Paper, 2002. Click here to email us for the technical publication.
 

3. F. Rognin, F, Abdi, J. Housner, and K. Nikbin, "Robust Design of Assembled Composite Joining Concepts, a Combined Durability-Reliability Evaluation", SAMPE Conference Paper, 2009. Click here to email us for the technical publication.