Improving MultiSite Damage (MSD) Fracture Mechanics

Improving MultiSite Damage (MSD) Fracture Mechanics Analysis using XFEM

Rivero Arévalo1, O. Valencia Rey2, N. Martín González3, B. de Nicolás Urrutia4, J. Gómez-Escalonilla Martín5

1,2,3,4,5Airbus Defence and Space, SpainEmail: [email protected]

(Airbus Defence and Space, Spain)

AbstractWidespread Fatigue Damage (WFD) is one of the most important challenges on the Fatigue and Damage Tolerance field for Aviation Industry and Airworthiness Authorities. Prevention and protection against WFD issues is crucial to ensure aircraft operational safety.

To properly assess the susceptibility of a structural component to WFD, extensive analysis supported by fatigue testing is required. However, it is not always easy to perform accurate fracture mechanics analysis of such problems using traditional approaches, especially when dealing with MultiSite Damage (MSD) scenarios where several damages or cracks are present at the same structural component and the interaction between them has to be properly quantified. Traditional approaches are mainly based on classical analytic solutions that can be too conservative when applied to complex MSD scenarios, penalizing the structural component in terms of weight and maintenance requirements. As structural optimization is essential in the aeronautical industry, more accurate while robust methodologies have to be developed and implemented.

Conventional Finite Element approaches can deal with complex configurations but are not practical for fracture mechanics analysis due to the high computational cost associated to the necessity of very fine meshing at crack tips, combined with continuous remeshing to adapt the model mesh to the crack propagation. However, advanced numerical methods such as the eXtended Finite Element Method (XFEM) can be applied to this kind of problems in order to provide accurate results with acceptable computational costs. Authors have developed an XFEM methodology based on Abaqus XFEM implementation able to deal with complex multi-crack scenarios under arbitrary loading conditions. This methodology has been implemented in a software tool, iCracx, validated for an extensive set of benchmark cases. Methodology fundamentals, software implementation and validation process will be presented in the paper. An application case study will also be presented and the results obtained will be correlated with alternative methodologies and fatigue testing results. Benefits in terms of improvements on maintenance requirements will also be explored.

1 Introduction

The aviation industry, in coordination with the Airworthiness Authorities (FAA, EASA, etc.), is highly interested about the damage tolerance of the aerostructures as a way to ensure aircraft operational safety. One of the most important and significant parts of this concern is the Widespread Fatigue Damage (WFD), its prevention and the protection against it.

WFD, in a structure, is considered in this context as the simultaneous presence of cracks at multiple points, that are of sufficient size and density such that, the structure will no longer meet its damage tolerance requirement and could fail.

WFD is a major concern in the structures as it is a phenomenon that is not easy to be predicted, neither with analysis nor with tests due to the high scatter related to the properties associated to the crack propagation.

In this scenario, it is even more complex to find an accurate prediction of the behavior of the structure when dealing with Multisite Damage (MSD) scenarios, where several damages or cracks are present at the same time in the component under investigation, with the additional difficulty of the interaction among these coexisting damages.

Traditionally, conservative classical methods [1], [2] or expensive tests have been used to analyze these complex MSD scenarios, what leads to a penalty in terms of weight of the structure, a critical design criteria in the aviation industry, and maintenance, and what is directly linked to the operational costs of the aircraft.

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Presence of cracks growing from fastener holes simultaneously at a skin panel

Figure 1 Example of Multisite Damage scenario

Therefore, from the previous paragraphs, it is deduced that optimizing the structures in order to reduce weight and operational cost (increasing the inspection intervals) is essential in the analyses. To get this target, more accurate predictive methods have to be developed and implemented in the industry.

At this point, it seems that a numerical methodology that is capable of simulate the propagation phenomenon is mandatory to accomplish with the previously stated target.

Conventional finite element methods are often not practical and efficient for fracture mechanics due to the needed flexibility to follow crack propagation without the use of fine meshed models. Also, re-meshing is necessary, what leads to an important processing time and cost.

Therefore, advanced numerical methods appear here as the most adequate procedure to solve these kind of problems. Many methods have been developed. Among them, it can be found the group of meshless methods [3] that combine the flexibility due to the non-dependency on the elements with the more or less ease to redistribute the control points to solve the algorithms.

In this paper, authors have chosen eXtended Finite Element Method (XFEM [4], [5]) to analyze the MSD scenarios. The selection of this methodology is sustained in the fact that XFEM is using a preexisting FE mesh, what makes it a great candidate to be used in the industry because it is easy to move from FEMs (normally used by the engineers in the conventional analysis) to XFEM.

Figure 2 FEM (left) vs XFEM (right) for crack propagation analysis

At the same time, XFEM combined with Abaqus is offering the chance to implement the complex multicrack scenarios to be investigated. To manage these analyses, Airbus Defence and Space (Airbus DS), in collaboration

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with Safran Engineering Services, has also developed a tool, iCracx [7], which has been validated for an extensive set of benchmark cases. Some of them are shown in this paper.

Finally, this paper is introducing a typical application case in order to correlate it, and, therefore, validate it, with alternative methodologies and fatigue tests results. Consequently, the authors’ intention is to show that XFEM methodology implemented in iCracx is able to accurately predict the crack propagation, with significant time and cost savings and also to offer this as a potential tool to reduce weight and operational costs in the future aircraft fleets.

2 Theoretical Background

As explained in the previous chapter of this paper, the traditional methodology for analyzing MSD scenarios is compared with the numerical analysis based on XFEM within iCracx environment.

In this chapter, the basic concepts of the XFEM are introduced. Further and more extensive information about this Meshless Method (MM) can be found in [4] and [5].

As stated in the previous paragraph, XFEM is included in the group of numerical methods for solving Parcial Derivative Equations (PDEs) called Meshless Methods (MMs). These methods are developed in order to solve the PDEs avoiding the use of meshes, completely or partially.

Within this group of MMs, XFEM is based on the enrichment of solution-type functions by adding new degrees of freedom to the predefined traditional FEM mesh. These additional degrees of freedom are arbitrarily located depending on the problem to be solved. This is the main advantage of this numerical method for the cases studied in this paper for crack growth: the flexibility and adaptability to the geometry of the domain under investigation.

In [4] and [5], the main general formulation of the equations representing XFEM solutions are introduced. The equation representing the typical case studied within this paper (crack growth, considering the crack as a discontinuity) is shown next:

u x I J Kh * + = + + (1)

where:

Ii I

i i=∈∑ ( )φ x u (2)

Being ui the nodal parameters of the entire set of nodes (Set I) and f(x) the corresponding shape functions.

J Hj J

j j=∈∑ ( ) ( )φ x b x (3)

Being bj the nodal enriched degrees of freedom for the nodes of the elements that are fully cut by the discontinuity (Set J), and H(x) the jump-function.

K Fk K

kl

kll= ( ) ( )

∑ ∑

=∈φ x c x

3

6 (4)

Being ckl the nodal enriched degrees of freedom of the nodes of the element where the crack tip is located,

and Fl(x) adequate asymptotic functions for the displacement field near the discontinuity tip (Set K).The XFEM shown above is extensively used in this paper to solve some MSD scenarios in the following

chapters, in order to compare the results with the traditional methodologies successfully used within Airbus DS. In this paper, authors are showing the results obtained for the same MSD scenarios that where analyzed in [6], where several cracks are growing at the same time from the fastener holes in different panel configurations.

The scope of these checks is to validate the case studied with XFEM methodology and to show possible improvements in Stress Intensity Factor (SIF) calculation in order to optimize the structures involved in the analysis.

A more extensive description of the cases to be studied is found in the following chapters within this paper.

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3 Introduction to iCracx

In [7] a detailed evaluation and validation of Abaqus XFEM capabilities was performed. As a consequence of this evaluation, it was concluded that Abaqus offers a robust XFEM methodology to perform SIF and J-integral calculations; however some major limitations affect the crack propagation simulations. The most relevant limitations are the following:

− A reduced element enrichment formulation is used in the analysis; as a consequence, the crack tip cannot be located inside an element (the crack has to propagate across an entire element at each crack increment).

− Linear elastic material behavior as the analysis is based on Linear Elastic Fracture Mechanics (elastoplastic behavior cannot be simulated).

− Abaqus only allows a linear modelization of the da/dN curve (Paris’ law) − Abaqus Direct-Cyclic approach is not able to deal with problems in which changes in the status of the

contacts between the different components are produced. This limitation also affects the contact between the crack surfaces (it can be very important if compression load states are applied)

− The efficiency of the Direct-Cyclic approach is highly reduced if complex loading spectra are applied as damage growth extrapolation through load cycles is not possible.

These limitations usually have an impact over the efficiency of Abaqus to perform Crack Propagation simulations for actual industrial cases. To overcome these limitations, Airbus DS, with the collaboration of Safran Engineering Services, launched the development of a Python software tool, named iCracx (Improved Crack Abaqus Computation with Xfem), capable to perform crack propagation simulations without a pre-defined crack path (solution-based propagation) calculating simultaneously Stress Intensity Factor and J-integral calculations without the limitations in terms of contacts, material model, loading spectra complexity, etc., inherent to the approach implemented in Abaqus.

Next figure shows the basic scheme of iCracx.

Figure 3 iCracx basic workflow

In addition, in [7] a set of validation cases was included to ensure iCracx robustness and accuracy.

4 Implementation of Multicrack Capabilities in iCracx

The initial version of iCracx (iCracx v1), used in [7], was able to perform a full crack propagation simulation considering only a single crack. As a consequence, it was not suitable to perform simulations at MultiSite Damage scenarios as intended in this paper.

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Due to the necessity of providing iCracx with multicrack capabilitites, a new version (iCracx v2) has been developed by Airbus DS. This new version is able to perform a full crack propagation simulation allowing an arbitrary number of cracks growing simultaneously and interacting each other. The same philosophy and capabilities of initial iCracx version are maintained. iCracx has been developed to run Abaqus 6.14-2.

Figure 4 Sample case of MSD scenario analyzed with iCracx v2

5 Validation of iCracx Multicrack Capabilities for an MSD Scenario Supported by Test Evidence

To validate iCracx capabilities to accurately perform Fracture Mechanics analysis for MultiSite Damage scenarios, the case study proposed in [6] to validate an analytic approach for MSD is selected. For this validation case, both analytic results and test results, from [8] and [9] are available and will be used for comparison with iCracx results.

The proposed scenario consists in a 2024T3 alloy sheet specimen with a collinear row of open holes with several initial artificial cracks. These cracks are allowed to grow under a monotonic tensile stress spectrum. Several initial crack configurations were analysed and tested at different specimens. For iCracx validation purposes, three different specimens with different crack configurations are selected.

Figure 5 MSD scenario used for iCracx multicrack validation

Table 1 Initial cracks for specimens selected for the validation

Specimen Conf.

Left hole from the central hole (mm)

Central hole (mm)Right hole from the central

hole (mm)

Tip ACrack 1A

Tip CCrack 1C

Tip ACrack 2A

Tip CCrack 2C

Tip ACrack 3A

Tip CCrack 3C

H1 1 - 2.23 1.20 1.32 2.29 -

H3 2 2.12 - 0.93 1.38 - 2.12

H5 3 1.15 1.25 1.17 1.24 1.29 1.15

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An Abaqus model for each specimen has been generated for each specimen with the initial cracks defined according to the previous table. An iCracx analysis has been launched for each model to perform the Crack Propagation simulation.

As a sample, tnext figure shows the stress plot obtained with Abaqus for the specimen H5 at an intermediate crack propagation state.

Figure 6 Abaqus model – Specimen H5

The Stress Intensity Factor (SIF) results obtained from iCracx analysis for the 3 specimens at each crack tip, identified in previous table, are shown in the next figures. These results are compared with the analytic and test results from [6], [8] and [9]. SIF values for test specimens have been obtained from crack growth data measured during the tests, deriving the corresponding SIF from measured crack growth rate using the da/dN curve for the specimen material, 2024T3.

Figure 7 Stress Intensity Factors for Specimen H1

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Table 2 shows the average ratio between the results obtained with iCracx and the analytic approach for each Specimen:

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Table 2 Average SIF ratio between iCracx and Analytic results

iCracx / Analytic average SIF ratio

Crack Specimen H1 Specimen H3 Specimen H51A NA 1.06 1.04

1C 1.09 NA 1.03

2A 1.01 1.02 1.06

2C 1.04 1.04 1.05

3A 1.09 NA 1.02

3C NA 1.07 1.05

The main deviations between test values and both analytic and XFEM results appears for small crack sizes. These deviations can be explained taking into account two facts:

− For small crack sizes, crack length measurements performed during tests have a higher associated relative error due to the measurement instrument precision. The deviations in the length measurements produced an inherent error in the SIF values obtained from the test.

− For small crack sizes, da/dN data used for SIF derivation from crack length measurements performed during test has a non-linear behavior with a higher level of dispersion in comparison with the quasi-linear behavior inherent to medium crack sizes.

.Figure 10 Sample of typical da/dN curve

Taking into account the previous considerations it can be concluded that a good correlation between iCracx results and both analytic and test values have been obtained. Therefore Fracture Mechanics calculations for MultiSite Damage scenarios can be performed using iCracx with a level of reliability equivalent to analytic approaches.

6 Taking Benefit from iCracx Application to MSD Analysis

As discussed in section 1, the use of XFEM approaches to perform Crack Propagation analysis allows the reduction of the conservatisms required when performing a conventional analysis using analytic approaches. An example of these conservatisms is the calculation of the interaction effect between cracks for analytic approaches.

6.1 Calculation of interaction effect between cracks using analytic solutions

In case of MSD scenarios, in the conventional Fracture Mechanics approach followed by Airbus Defence and Space, the interaction effect between cracks over the Stress Intensity Factor (SIF) is quantified using the

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solutions provided in [1] for multiple cracks at flat plates. These solutions provide the factor to be applied to the SIF of the isolated crack to take into account the interaction effect of another crack and they were obtained for through-thickness cracks. The use of interaction factors obtained for through-thickness cracks can be too conservative when applied to scenarios with corner cracks growing from holes (typical scenario in aeronautical structures) as the interaction effect of a corner crack over another crack is much lower than the effect of a through crack. The reason of using this conservative approach is the unavailability of consolidated analytic solutions for corner crack interaction valid for aircraft certification analysis. This conservatism has a direct penalty impact on the maintenance requirements for the aeronautical structures.

6.2 Calculation of interaction effect using iCracx

By using iCracx, the interaction effect between two arbitrary cracks under an arbitrary loading condition can be easily obtained. As a case study, it will be obtained the interaction effect between a small corner crack and another through-thickness crack. Interaction factor results will be compared with the equivalent interaction factors calculated with the conventional analytic approach. This scenario is typical in aeronautical structures, where larger cracks (rogue flaws or primary cracks) grow simultaneously to smaller corner cracks (quality flaws).

Figure 11 iCracx model to obtain interaction effect between cracks

The interaction effect of the primary crack over the quality crack has been obtained under tensile stress state.

Figure 12 Interaction effect over the quality crack

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The results included in the previous figure will be discussed:

− For small primary cracks (up to 15% of cracked net section for this case study), the analytic approach provides conservative results. It is due to the fact that the analytic solution is considering the primary crack as a through-thickness eccentric crack to compute the interaction effect over the quality crack while the XFEM model considers the actual crack geometry (crack growing from hole) which has a much lower interaction effect. This reduction of the interaction effect can be significant in terms of improvement of Crack Growth Life for MSD scenarios.

− For medium size primary cracks (from 15% to 50% of cracked net section) both methodologies provide the same results, as analytic approach assumptions are coincident with the scenario analyzed in the XFEM model (the effect of a large through-thickness crack at a hole is equivalent to an eccentric crack). Analytic results validate XFEM results.

− For large cracks (more than 50% of cracked net section) the analytic approach results are conservative. For this kind of very large cracks secondary effects are responsible of the discrepancy between analytic and XFEM results.

6.3 Potential impact over structural maintenance inspections

Inspection thresholds and intervals for aircraft structural inspections are quite often determined by Crack Propagation analysis. Inspection frequencies are directly related to the Crack Growth Lives in terms of flights. As a consequence refinements in these calculations produce a direct benefit in terms of reduction of structural maintenance costs.

Figure 13 Typical simplified process for definition of structural maintenance requirements due to Damage Tolerance assessment

For the case study considered in this paper, for small primary crack sizes the XFEM analysis allows a slight reduction of the interaction factor. This reduction in the factor applied to the Stress Intensity Factor of the crack leads to a significant reduction of the crack propagation rate, as SIF is related to crack propagation rate following a potential equation.

The next figure shows the comparison in terms of Crack Propagation curve from initial crack size (quality flaw of 0.127x0.127mm). The use of the interaction factors obtained with XFEM results in an increment of 18% in terms of Crack Growth Life from initial crack size to critical crack in comparison with analytic results.

Transition to through crack

Figure 14 Crack propagation comparison

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By improving the accuracy of the crack propagation rate calculation, higher Crack Growth Lives in terms of flights can be obtained and therefore less penalizing structural inspections can be defined while maintaining an equivalent level of flight safety. So it is clear that the use of XFEM solutions for Fracture Mechanics analysis can lead to an optimization of the structural requirements, especially for MultiSite Damage analysis due to the complexity of dealing with these scenarios in an accurate and non-highly-conservative way using conventional analytic approaches.

Conclusion

A numerical approach based on XFEM solutions has been developed and successfully applied to perform Fracture Mechanics analysis at MultiSite Damage (MSD) scenarios. Results comparison with test evidence shows a level of accuracy and reliability equivalent to conventional analytic approaches. This numerical methodology, implemented in the software iCracx and based on Abaqus XFEM formulation, is able to perform Crack Propagation simulations for complex 3D geometries under arbitrary loading conditions without a pre-defined crack path (solution-based crack propagation).

The potential benefit derived from the use of this methodology for MSD analysis in terms of optimization of structural maintenance requirements for aeronautical structures have also been discussed through a case study.

Developments currently in progress associated to iCracx are focused on optimization of the software flow, smooth integration with Airbus DS standard tools and validation for a wider set of practical cases.

Acknowledgment

The authors want to recognize the continuous support provided by their colleagues from Airbus Defence and Space, especially from Mª del Mar Andrés, Javier Segurado, Emilio Murcia, Efraín Mirón, Jose Ignacio Armijo, Fernando Sánchez, Eduardo Oslé and Darío Fernández. Without their contribution it would not have been possible to reach the goal of this work.

References

[1] Rooke, D.P.; Cartwright, D.J. (1974). Compendium of Stress intensity factors. Her Majesty’s Stationery Office, ISBN 0117713368, 1976.

[2] JSC-22267B (2002). Fracture Analysis Software NASGRO 3.0.18.[3] Fries, T.; Matthies, H. Classification and Overview of Meshfree Methods. Institute of Scientific

Computing, Technical University Braunschweig, Brunswick, Germany. July, 2004.[4] Belytschko, T.; Black, T. (1999). Elastic crack growth in finite elements with minimal remeshing: Int. J.

Numer. Methods Eng., 45(5), 601– 620.[5] Moës, N.; Dolbow, J.; Belytschko, T. (1999). A finite element method for crack growth without remeshing:

Int. J. Numer. Methods Eng., 46, 131–150.[6] Segurado, J.; Caffyn. P; et al. Probabilistic approach to the inspection interval determination in a Multi-

Site Damage susceptible structure. 28th ICAF Symposium, Helsinki, 3rd – 5th June 2015. [7] Rivero, I.; Gómez-Escalonilla, J. XFEM-based fracture mechanics analysis of aeronautical structures

affected by residual stresses: 30th Congress of the International Council of the Aeronautical Sciences, DCC, Daejeon, Korea, September 25th – 30th 2016.

[8] Pártl, O. and Schijve, J. Multiple-site-damage in 2024-t3 alloy sheet. Report, LR-660. Faculty of Aerospace Engineering. Delft University of Technology. January 1992.

[9] Pártl, O. Compilation of results associated to the problems of multiple-site-damage in open-hole sheet. Document B2-91-04.Faculty of Aerospace Engineering. Delft University of Technology. August 1991

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Improving MultiSite Damage (MSD) Fracture Mechanics