Let us talk Physics Based Simulation Technologies for Modeling and Analysis of Advanced Materials

Lets talk Physics Based Simulation Technologies for Modeling and Analysis of Advanced Materials

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

Issue #20 - April 13th, 2010

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

GENOA 4.4 Software Release News

GENOA's Material Qualification and Characterization (MCQ) Module

Figure 1 - MCQ Generated Ply Properties Features of MCQ: -          Laminate properties (mechanical-thermal/electrical) -          Load limits and damage/failure modes -          "As-built" and "as-is" material state -          Manufacturing defects and environmental effects   -          2D/3D composite architectures; Polymers  (Thermosets, Thermoplastic, and Chopped Fiber), Fiber-Metal-Laminate, Nano, and ceramics -          Allowables and carpet plots for test reduction -          Mesh-less unit cell simulation -          Accurate, robust, and user friendly -          Industry verified and endorsed

Alpha STAR released GENOA's MCQ forWindows 2000/XP/Vista/7 and Linux. It enables the ultra rapid modeling, design, and analysis of advanced polymer composites for aerospace, automotive, wind turbine, ship building, and infrastructure industries. MCQ uses a unit cell approach for assessing material behavior not requiring finite element modeling. It is applicable to all un-notched laminates where uniform state of stress persists. MCQ models all types of composite architectures including tape, 2-D /3-D woven and braided materials using simplistic multi-scale physics based micro-mechanics formulation. It accounts for "as built" and "as-is" state taking into consideration manufacturing defects and effect of uncertainties in material properties and specimen geometry.

MCQ is a one "stop shop" for:
(1) generating thermo-mechanical-electrical properties of laminated composites; (2) predicting laminate strength, damage and failure modes, and (3) generating material design envelope, carpet plots, and A- and B-Basis strength allowables. It relies on physics based multi-scale failure mechanisms to predict laminate behavior. Strength- and strain-based failure criteria accounting for matrix cracking, de-lamination, fiber failure and interaction between fiber and matrix are evaluated to determine conditions for damage initiation and growth and final failure.

Figure 2 - Design Failure Envelope Progression for a [0,90,45,-45] Symmetric Layup

Figure 3 - Virtual Generation of Allowables [1,2]: Cumulative Distribution Function Generated by Simulation Compared to Limited Test data for Polymer Composites at 180 F with 85% Relative Humidity (Aged Moisture)

MCQ is ideal for providing quick, simplistic, easy to use, and in-expensive guide to material selection. Accurate estimation of material properties plays a very important role in delivering a design that meets cost and production schedule requirements. MCQ comes with a dedicated data base of material properties for glass, carbon, ceramics and other systems. The code is designed for use by engineers and scientists who use micro-mechanics (fiber/matrix/interphase) type input and those who use macro-mechanics (ply level input). MCQ delivers accurate stiffness and strength properties as input to your Durability and Damage Tolerance (D&DT) evaluation.

 

Figure 4 - Material Performance Envelop Generated by the Software

MCQ Performs composite laminate analysis considering "as-built" and/or "as-is" material states: manufacturing anomalies (i.e., void size/shape, fiber waviness, interphase coating), design (i.e., ply orientation, thickness, 2D/3D architecture).

• Fiber, Matrix, and Lamina Calibration
  Reverse engineer effective linear fiber/matrix properties from lamina or laminate test data (strength and stiffness). The effective properties accounts for the thermal residual stresses and interface due to curing process. 
• Non-Linear Material Characterization Optimization (MCO)
  Reverse engineers effective fiber, matrix, ply non-linear properties (stress strain curves) from ply or from laminate test data.
• Ply Level Analysis
  Predicts equivalent ply properties (mechanical/thermal/electrical) using fiber matrix properties as input. Example of mechanical properties (Figure 1) is ply strength in 11, 22, 33, 12, 23, and 13 directions. Example of electrical properties is ply and laminate conductivity.
• Laminate Analysis
  Predict equivalent laminate properties using fiber/matrix or ply properties as input. The properties calculated include laminate strength and stiffness, and electrical and thermal properties as well.
• Design Failure Envelope
  Predicts design failure envelope for chosen failure criteria for laminates. Strength, strain, and interactive based failure mechanisms are available (Figure 2). Fiber failure under tension/compression including micro-buckling, matrix cracking under tension and compression and delamination (in-plane and out-of-plane) are determined for the ply and the laminate. Several Failure Criteria can be compared for better understanding and comparison against test data.
• Ply Characterization
  Graphically shows variation in strength as a function of ply orientation and fiber or void volume ratio
• A- & B- Basis Allowables
  Rapid and accurate prediction of A- and B-basis strength allowables for un-notched uniformly stressed coupons. This module provides the option of predicting allowables from a minimal number of test replicates. With a dedicated sensitivity analysis one can determine the influence of manufacturing parameters and material properties on the laminate strength. This helps reduce the scatter and improve the performance of the material (Figure 3 & 4).
• Parametric Carpet Plot
  Generate multiple carpet plots that show variation in thermo-mechanical properties, including strength, stiffness and thermal expansion, with variation in ply layup distributions (Figure 5). This capability is ideal for use at the beginning of a new program as it provides an accurate and a complete map of the material properties providing alternate design options rapidly and at low cost.

Figure 5 - Carpet Plot of Laminate Strength as Function of 0, 45, and 90 degrees Ply Angles (Red = Fiber Failure, Green = Matrix Failure, Blue = Matrix Shear Failure)

References: 
1. Galib Abumeri, Frank Abdi, and Mike Lee, "Verification of Virtual Generation of A- and B-Basis Allowables for Polymer Composites Subject to Various Environmental Conditions", SAMPE 2009 China Conference. Click here to email us for the technical publication.

2. DOT/FAA/AR-03/19, Final Report, "Material Qualification and Equivalency for Polymer Matrix Composite Material System: Updated Procedure" Office of Aviation Research, Washington, D.C. 20591, U.S. Department of Transportation Federal Aviation Administration, September, 2003.Click here to email us for the technical publication.

Visit us today and find out more about GENOA at www.ascgenoa.com.

Click here to read the full technical product data sheet of GENOA.

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

Issue #19 - November 17th, 2009

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.

 

Click here to read the full technical product data sheet of GENOA.

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

Issue #18 - July 9th, 2009

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

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

Click here to read the full technical product data sheet of GENOA.

This issue was brought to you by Alpha STAR Corporation.

Please visit us for more information at www.ascgenoa.com

Certification-by-Analysis (CBA)

Issue #17 - May 4th, 2009

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.

  

Click here to read the full technical product data sheet of GENOA.

Please visit us for more information at www.ascgenoa.com

Material Qualification and Certification Determine Allowables by Means of Virtual Simulation Combined With Limited Testing

Issue #16 - October 20th, 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

Material Qualification and Certification Determine Allowables by Means of Virtual Simulation Combined With Limited Testing

(a) Top View (laminate)  (b) Top View (individual plies) (c) Iso-View (laminate) (d) Iso-View (individual plies) Figure 1 - Virtual Testing of an Open-hole Coupon with Progressive Failure Analysis

A-basis and B-basis strength values are critical to reduce risk in structural design of composite aircraft structures. A previous newsletter presented a novel approach to determine A- and B-basis allowables for composite materials (click here for previous newsletter). This newsletter provides additional details of the A and B-basis allowable generation and describes a link between virtual testing and design carpet plots. 

The calculation of allowables for polymer matrix composite for aerospace applications is governed by FAA and Military Handbook 17-E standards and rules. The process is costly and time consuming as large numbers of coupon tests are inevitable (example: the generation of allowables for the IM7 fiber and 5250 resin for the F22 program cost close to 100 million dollars). To accelerate the prediction of allowables and reduce the number of coupon tests, GENOA combines multi-scale composite modeling with progressive failure analysis (PFA), probabilistic analysis and minimum test data to determine A- and B-basis values. Figure 1 shows the multi-scale PFA. The PFA is used to produce virtual scatter data using probabilistic analysis. Figure 2 shows the process flowchart. The scatter in material strength is determined by iterating on coefficient of variations (COV) of random variables from single or multiple sources of uncertainties (i.e. fundamental material properties and fabrication variables). The iterative process replicates scatter in the strength value obtained from the test of one coupon of each material batch. If the scatter is unknown, then maximum of 10% coefficient of variation can be chosen as per the FAA regulations for composite materials. However, when test data variation is known, then a COV can be estimated, as shown in Figures 3 and 4. In Figure 3, a COV of 0.06 provides a good estimate of the test data and in Figure 4, a COV of 0.01 is used. The methodology is applicable to notched (Figure 5) and un-notched coupons and structures and has the potential of reducing the coupon count for testing by over 60%. 

It is important to have design envelopes before and after the A- and B-Basis values are generated. The design envelop is a graphical representation of the variation in material properties (stiffness, Poisson's ratio, and strength) with variation in ply angle [e.g., 0/+45/-45/90] distribution in the laminate. The graphical representation is referred to as a 'Carpet Plot' in industrial practice. A typical Carpet Plot is shown in Figure 5. The carpet plot is a powerful tool which can be used as a design reference. In GENOA, a carpet plot is generated automatically after virtually simulating ASTM standard or other chosen testing methods (Figure 1). First, the layup in the laminate is automatically varied and ASTM or user defined tests are virtually simulated for each laminate layup. This is an automated process, requiring minimal user interface. Next, the virtual test database is filtered for the carpet plot information desired and plotted graphically.  The carpet plots generated need not be limited to A and B-basis allowables. Other carpet plot options include laminate stiffnesses, first ply failure and final failure. If test data is available, then test results can be plotted on top of the virtually generated carpet plots for verification.

More focus on virtual testing and carpet plot utilization to reduce physical test matrix reduction will be shown in upcoming future newsletters.

 

Figure 2 - Flowchart for generating A-basis and B-Basis Allowables in GENOA using testing standards for ASTM and MIL-HDBK 17-E and FAA

Figure 3 - Cumulative Density Functions (CDFs) with assumed coefficients of Variation of 0.06, 0.075, 0.10 for compressive composites un-notched composite coupon  [1]

 

Figure 4 - Scatter from test and simulation for the strength of the open-hole coupon along with GENOA predicted A- and B-Basis values [2]

 

Figure 5 - Carpet plot for various percent of 45 deg plies is useful to reduce coupon testing

References:

1. G. Abumeri, M. Garg, and M. R. Talagani, A Computational Approach for Predicting A- and B-Basis Allowables for Polymer Composites, SAMPE Fall Conference, TN, 2008.
Click here to email us for the technical publication.

2. M. R. Talagani, Z. Gurdal, and F. Abdi, S. Verhoef ?Obtaining A-basis and B-basis Allowable Values for Open-Hole Specimens Using Virtual testing? AIAAC-2007-127, 4. Ankara International Aerospace Conference, 10-12 September, 2007 ? METU, Ankara.
Click here to email us for the technical publication.

Click here to read the full technical product data sheet of GENOA.

This issue was brought to you by Alpha STAR Corporation.

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Predicting Post-Buckling Response and Ultimate Failure of Composite 2-Stringer Panels

Issue #15 - June 10th, 2008

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This Week's Feature Composite Example

Predicting Post-Buckling Response and
Ultimate Failure of Composite 2-Stringer Panels

Figure 1 - Damage & Durability Analysis of a Composite 2-Stringer Panel Subjected to Post-Buckling Analysis

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].

 

Figure 2 - Geometry of Two-stiffener composite panel [1]

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:

1. Determining the buckling mode shape of the panel (in this case skin buckling mode). Typically selects the buckling mode shape with the lowest eigenvalue.
2. 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: 

1. 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. 
2. 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. 
3. 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. 
4. 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. 

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

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.

 

(a) Delamination Initiation                                         (b) Delamination Propagation

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.

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.

 

Figure 5 - Comparison of experimental and analytical load deflection curves for composite two-stringer panel [2]

 

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.

Click here to read the full technical product data sheet of GENOA.

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