Tuesday, November 17, 2009

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


Software Suite for Material Qualification and FEA Based Durability, Damage Tolerance, Reliability & Life Prediction

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
Figure 5 - Design Variables

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.

Table 1 - Improved design compared to initial one
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.

Figure 6 - Material damage volume as a result of applied loading obtained from PFA (before and after optimization)

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.

 

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Monday, July 13, 2009

Numerical Approach to Determine Crack Path and Delamination Growth in Composite Structures


Software Suite for Durability, Damage Tolerance, Reliability & Life Prediction
Enhances FEA Solvers MSC Nastran*, ABAQUS, ANSYS, RADIOSS & LS-DYNA

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This Week's Feature Composite Example

Numerical Approach to Determine Crack Path and Delamination Growth in Composite Structures


(a) Tension Test

(b) Three-Point Bending Test
 
Figure 1 - Predicted delamination process at the interface of flange and skin for a composite skin/stringer joint
Fracture mechanics based Discrete Cohesive Zone Modeling (DCZM) or Continuum Cohesive Zone Modeling (CCZM) approach is widely used in simulation of crack propagation and delamination growth (Figure 1) in composite structures; however, its effectiveness is limited as it requires prior identification of the crack path, which is usually obtained from test. This limitation makes DCZM/CCZM a test duplication tool for simulating fracture propagation rather than a test prediction one. Reliance on testing alone hinders the analysis process and reduces its potential benefits. The shortcoming of the DCZM/CCZM approach can fortunately be overcome with finite element/micro-mechanics based Progressive Failure Analysis (PFA) to determine analytically the crack path under increased stress.

Augmentation to Multi-scale Progressive Failure Analysis: 
A novel methodology is implemented in GENOA [1] to address the limitation of DCZM/CCZM with respect to crack path requirement for the analysis. GENOA is state of the art durability and damage tolerance (D&DT), and life and reliability prediction software. It is dedicated for the evaluation of composite structures made from tape, 2/3-D weave and braids, fiber metal laminates, and sandwich construction.

The methodology works in two consecutive steps:

1. PFA strength/strain based evaluation to determine the crack path;
2. Crack propagation analysis using DCZM/CCZM based on crack path predicted by PFA. 

The methodology combines the best of both capabilities: damage initiation and progression and failure initiation and crack path prediction via PFA and crack propagation/delamination via DCZM. PFA and DCZM are briefly described next. This is followed by examples to illustrate and validate the integrated PFA/DCZM approach.

The PFA approach [2] increments the load to failure while evaluating strength and strain composite failure criteria to identify loads that produce damage initiation and propagation, and fracture initiation. When it comes to modeling stress singularities such as those near crack fronts, PFA may have some limitations, which can be addressed by switching to linear elastic fracture mechanics method once fracture is initiated. In the fracture mechanics approach, nodes along the pre-defined crack path are initially tied together with DCZM elements and then released when mode I (crack opening), II (crack shearing or sliding) and III (crack tearing) components of strain energy release rate exceed the mixed-mode fracture criteria [3]. DCZM element is a spring type element and a triangle type cohesive law is applied as the spring internal force.

Application: A composite skin/stringer flange (lap type) joint [4] (Figure 2) subjected to tension and three-point bending load is used to validate the new methodology in GENOA. The skin lay-up consists of 14 plies ([0/45/90/-45/45/-45/0]s) and the flange consists of 10 plies ([45/90/-45/0/90]s). The flange and the skin are bonded together with CYTEC 1515 [5], a grade-5 film adhesive, with a final thickness of 0.102 mm [6]. Each ply in the flange and the skin is made of IM6/3501-6 graphite epoxy pre-preg tape with a nominal thickness of 0.188 mm. The material properties of both the unidirectional tape and adhesive are taken from references [5,6,7]. Figure 3 shows a side view of the ply lay-up setup. 
 
Figure 2 - Co-cured Skin/Stringer Joint [4]

 
Figure 3 - Ply lay-up setup in GENOA (side view)

As noted by Kruger et al [6], the kin/stringer flange joint specimens that were tested were subjected to tension and 3-point bending. These two tests are simulated numerically using the two steps approach described earlier: PFA followed by DCZM.

Tension: PFA evaluation is performed first to predict the crack path under tension load. Then the crack path is used as input to DCZM along with fracture toughness data from literature. This two steps approach indicated a delamination load of 22.2 kN. If we are to rely on PFA alone for this delamination growth simulation example, we would obtain a delamination load comparable to the one from DCZM. 

Three-point Bending: DCZM predicted a delamination load of 403.2 N using crack path obtained from PFA. If we are to run PFA for the whole simulation, we would obtain a delamination load of 417N independent of DCZM. The analysis shows that the flange is delaminated from the skin due to the failure of the adhesive (Mode I and II failure), just as the test results indicated. 
The use of PFA stand alone has a distinct advantage over DCZM stand alone as it is capable of assessing micro crack formation under increased loading. Unlike PFA, DCZM does not capture any damage in skin or flange before the onset of delamination. This phenomena is evident in Figures 4 and 5, which show the PFA and DCZM methodology predicted delamination at the interface of a skin/stringer flange specimen for the two loading cases. The red area in Figure 4b indicates the damage in the specimen as predicted by PFA. 
 
       (a) Tension                                                          (b) Three-Point Bending

Figure 4 - PFA predicted delamination at the interface of a skin/stringer specimen 
 
(a) Tension                                                             (b) Three-Point Bending

Figure 5 - DCZM predicted delamination at the interface of a skin/stringer specimen

Figure 6 gives a comparison of DCZM simulation results guided by PFA predicted crack path. The load displacement for the tension and three point bending specimen obtained from GENOA using PFA followed by DCZM are compared to experimental results. Results from PFA stand alone simulation are also plotted and compared to those from experiment [6]. The results from simulation match well with the test data. The predicted delamination loads are within the upper and lower bounds of the test data [4,6]. In addition, the predicted delamination pattern in each case is consistent with the experimental observations. The literature data focused mainly on delamination load. Therefore post-peak load behavior cannot be validated in these simulations for the PFA and DCZM approach.
 
         (a) Tension                                                           (b) Three-Point Bending

Figure 6 - Comparison of simulation using the PFA and new methodology with experimental results for a skin/stringer specimen under two loading cases
Conclusions: 
The delamination process of the flange from the skin due to adhesive failure for a skin/stringer flange specimen under tension or three-point bending is successfully simulated and predicted using a two step numerical approach: PFA followed by DCZM (CCZM). This development transforms the cohesive modeling capability from test duplication tool to a test prediction one. The PFA predicted fracture path needs to be qualified by the engineer before proceeding to step 2 (that is DCZM evaluation).  This technology provides an effective mean to determine the initiation and propagation of delamination in composite structures while minimizing the test efforts. 

References: 
1. GENOA Durability and Damage Tolerance Software, Alpha STAR Corp, Long Beach, CA 2009, www.ascgenoa.com

2. Garg, M., Abumeri, G. H., and Huang, D., 2008. "Predicting Failure Design Envelop for Composite Material System Using Finite Element and Progressive Failure Analysis Approach," SAMPE May 2008, Long Beach. Click here to email us for the technical publication.

3. Xie, D., Garg, M., Huang, D., and Abdi, F., 2008. "Cohesive zone model for surface cracks using finite element analysis," May 2008 AIAA, Illinois. Click here to email us for the technical publication.

4. Camanho, P. P., Davila, C. G., and Pinho, S. T., 2003. "Fracture analysis of composite co-cured structural joints using decohesion elements," Fatigue & Fracture of Engineering Materials & Structures, Vol.27, Issue 9, pp745-757. Click here to email us for the technical publication.

5. CYTEC 1515 product sheet.

6. Krueger, R., Cvitkovich, M. K., O?Brien, T. K., and Minguet, P. J., 2000. "Testing and analysis of composite skin/stringer flange debonding under multi-axial loading," Journal of Composite Material, Vol.34, No.15, pp1263-1300. Click here to email us for the technical publication.

7. http://casl.ucsd.edu/data_analysis/carpet_plots.htm



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Monday, May 4, 2009

Certification-by-Analysis (CBA)


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

Certification-by-Analysis (CBA)


Objective and Benefit: Certification-by-Analysis (CBA) is a major cost and time saving approach as it minimizes physical testing of structural components. Using Alpha STAR Corporation's modular engineering software package, GENOA, a product's structural response can be rigorously tested and certified, virtually, to FAA standards, with minimal substantiation testing and reduced/accelerated certification time. The software simulates testing by integrating multi-scale physics based failure mechanisms with progressive failure analysis (PFA) to assess damage and fracture of composites. It implements the building block approach advocated by FAA, commencing at the coupon level through the detail, sub-component and component levels. Figure 1 shows the PFA test simulation of open-hole, three-point bending and facesheet delamination at coupon level followed by sub-component level oblique slot and filled hole fuselage panels as part of a comprehensive building block verification.
 
Structural Level
 
Sub-Component
Level
 
Coupon Level
 
Figure 1 - GENOA Building Block Supports Composite Certification from Coupon Level to Component Levels


The power of virtual testing by means of PFA lies in its ability to simulate the behavior of structural components where very few can be tested (example: fuselage panel/wing box). The simulation follows closely the FAA recommended building block approach for structural component certification shown in Figure 2. GENOA can virtually simulate the physical test of all type of coupons to accelerate the certification process for higher order parts and components. These building block elements may be notched/un-notched, stringer-stiffened, honeycomb sandwich or other construction. To achieve a valid CBA, accurate simulation of the fundamental constituent composite properties; e.g., fiber and matrix is needed. Thus, Genoa uses Material Characterization Analysis (MCA) to perform a calibration as a first step in CBA. Simple and inexpensive coupon tests provide the data needed for the MCA.  

GENOA uses the calibrated fiber/matrix properties in a layer-by-layer simulation, including through-the-thickness effects. This simulation is used in the finite element model development and analysis as well as the subsequent PFA. For each load case, the load level is incrementally changed, enabling the PFA process to pinpoint the damage initiation location and load level, the damage propagation process, fracture initiation, fracture propagation and final failure. This process tells the engineer where, when, how and why the structural design exhibits damage, fracture and failure.
  

Figure 2 - FAA building block approach for structural component
certification is implemented in GENOA (Courtesy of FAA)


Validation of GENOA-CBA: The software capability for CBA is validated by comparing predictions with actual test data at all levels of the building block process. The process started with generating calibrated material allowables from existing ATSM coupon test data; then validating those allowables against tailored, design-specific coupon test data; and comparing sealed envelop analytical results of full-scale "fuselage" panels to test results. Total of three honeycomb sandwich panels were simulated with PFA: baseline panels, circular hole panels, and slotted panels. The honeycomb sandwich panel configuration for these coupon tests represented the building block for curved fuselage panels which were also evaluated. The sandwich consisted of 3 ply (45/0/45) laminate facesheets bonded to a 3/4" Nomex honeycomb core. The base line and circular holes panels were evaluated using various load configurations: pressure only, longitudinal only and combined pressure and longitudinal loading. The slotted panels were evaluated for various loading as well: longitudinal slot, oblique slot, and circumferential slot combined loading. 

GENOA's PFA failure predictions matched the test results closely (force versus tensile strain plot in Figure 3a). The red zones represent lamina/laminate damaged areas (Figure 3b). The composite can still sustain loads but at a reduced level. When the composite material can no longer carry any load fracture initiates, elements are removed and stresses are re-distributed. GENOA Virtual Testing deviated less than 10% different from the actual test results. Predictions using the building block approach with accuracy such as these are revolutionary. With well established and well verified building block strategy structural components can now be simulated for a variety of flight loads reducing the number of physical tests for certification.

 
Figure 3a - Force vs. tensile strain for sandwich specimen with 1" diameter hole


Figure 3b - Damage pattern of sandwich specimen with 1" diameter hole 
Figures 3a - 3b   GENOA Virtual Testing of honeycomb sandwich tensile elements with through-the-sandwich hole.



References:
1. Scott Leemans, Peter J Rohl, Dade Huang, Frank Abdi, Jonas Surdenas, Raju Keshavanarayana, "Certification By Analysis: General Aviation Honeycomb Fuselage Panels". Sampe 2009 Conference Paper, Baltimore, MD, May 18-21, 2009.
Click here to email us for the technical publication.
  


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